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Production Control Mechanisms Comparison using Multi-Objective Simulation Optimization FACTS Analyser

Master Degree Project in Automation Engineering 22.5 ECTS Spring Term 2009 Muhammad Irfan Zia Supervisor: Amos H.C.Ng Examiner: Mats Jägstam

Abstract The choice of an efficient and effective production control mechanism (PCM)

along with the appropriate buffer allocation pattern is very important for any

production engineer/decision maker when designing a production line in order to

attain the required system performance. This project work aims to give an insight

with different PCMs, different buffer allocation patterns and arrangement of

workers of different capability to help the production engineers/decision makers

to select the right mechanism and pattern. This study has been performed with

multi-objective simulation optimisation (MOSO) tool. The result from many

experiments have shown that the ascending buffer allocation pattern stands out

as the prominent choice when the goal was to attain maximum throughput (TP)

and simultaneously keeping minimum cycle time (CT) and work in process (WIP).

The PCMs and workers imbalance patterns performance is different in different

regions of the Pareto-optimal CT-TP data plots obtained from MOSO so their

selection is depending on the interest of the desired level of throughput together

with the limit of cycle time.

Certificate Submitted by Muhammad Irfan Zia as a dissertation of a Master’s Degree in

Automation Engineering at the University of Skövde.

I certify that all the material in this final thesis that is not my own work, has been

identified and that no material is included for which a degree has previously

conferred.

Skövde, Sweden, 28 May 2009

_________________

Muhammad Irfan Zia

Acknowledgments I am pleased to thank and give my great gratitude to my supervisor Amos H.C.Ng

his support, patience, and persistence during this project and studies. Without his

encouragement and constant guidance, I could not have finished this project. I

would like to express profound gratitude to my Program Coordinator Mr. Matias

Urenda Moris, for his invaluable support and useful suggestions throughout my

studies at University of Skövde.

I am as ever, especially indebted to my parents for their love and support

throughout my life, without their knowledge, wisdom, and guidance, I would not

have the goals I have to strive and be the best to reach my dreams.

________________

Muhammad Irfan Zia

Table of contents 1. Introduction ...................................................................................................... 1

1.1 Motivation ................................................................................................... 1 1.2 Aim and Objectives ..................................................................................... 2 1.3 Thesis Organisation .................................................................................... 3

2. Literature Review ............................................................................................. 5 2.1 Multi-Objective Optimisation ....................................................................... 5

2.1.1 What is an Optimisation problem? ....................................................... 5 2.1.2 Multi-Objective Optimisation ................................................................ 5 2.1.3 Multi-Objective Optimisation using Evolutionary Algorithms ................ 7

2.2 Discrete Event Simulation ........................................................................... 8 2.3 Simulation Optimisation .............................................................................. 9 2.4 Production Control Mechanisms ............................................................... 11

2.4.1 PUSH Production Control Mechanism ............................................... 12 2.4.2 KANBAN Production Control Mechanism .......................................... 13 2.4.3 CONWIP Production Control Mechanism .......................................... 14 2.4.4 DBR Production Control Mechanism .................................................. 14

3. Multi-Objective Simulation Optimisation for PCM Comparison ....................... 16 3.1 Methodology to determine unbalanced flow line with sharp bottleneck .... 17

3.1.1 Steady State Analysis ........................................................................ 17 3.1.2 Replication analysis ........................................................................... 18

3.2 Methodology to determine unbalanced flow line with variability imbalance ....................................................................................................................... 20

3.2.1 Elitist Non-Dominated Sorting Genetic Algorithm (NSGA-II) .............. 20 3.2.2 Crowding Distance ............................................................................. 21 3.2.3 Pareto front ........................................................................................ 22 3.2.4 Significant Dominance ....................................................................... 23 3.2.5 Attainment surface ............................................................................. 24

3.3 FACTS Analyser ....................................................................................... 25 4. Case Studies ................................................................................................. 28

4.1 Case 1: Unbalanced flow line with sharp bottleneck ................................. 28 4.1.1 Case1: simulation settings ................................................................. 31

4.2 Case 2 Unbalanced flow line with variability imbalance ............................ 33 4.2.1 Case2: simulation settings ................................................................. 34

5. Experiments, Results and Analysis ............................................................... 39 5.1 Experiment No: 1 Simple unpaced flow line ............................................. 39 5.2 Experiment No: 2 The effect of a non-balanced line ................................. 41 5.3 Experiment No: 3A The effect of coefficient variation on simulation analysis at CV1............................................................................................................. 43 5.4 Experiment No: 3B The effect of coefficient of variation on simulation analysis at CV 1.5 ........................................................................................... 44 5.5 Experiment No: 4A The effect of upper and lower bound in the processing time distribution at CV 1.................................................................................. 47

5.6 Experiment No: 4B The effect of upper and lower bound in the processing time distribution at CV 1.5 ............................................................................... 48 5.7 Experiment No: 5A The effect of buffer allocation on the performance of the line at CV 1 ..................................................................................................... 51 5.8 Experiment No: 5B The effect of buffer allocation on the performance of the line at CV 1 UB and LB are zero ..................................................................... 53 5.9 Experiment No: 5C The effect of buffer allocation on the performance of the line at CV 1.5 ............................................................................................ 55 5.10 Experiment No: 5D The effect of buffer allocation on the performance of the line at CV 1.5 UB and LB are zero ............................................................ 57 5.11 Experiment Number: 6A The effect of buffer allocation on the performance of the line at CV 1 and total buffer capacity 150 ........................ 60 5.12 Experiment Number: 6B The effect of buffer allocation on the performance of the line at CV 1, UB and LB are Zero, total buffer capacity 150 ....................................................................................................................... 61 5.13 Experiment Number: 6C The effect of buffer allocation on the performance of the line at CV 1.5 and total buffer capacity 150 ..................... 63 5.14 Experiment Number: 6D The effect of buffer allocation on the performance of the line at CV 1.5, UB and LB are Zero, total buffer capacity 150 ................................................................................................................. 65 5.15 Experiment Number: 7 Variability Imbalance .......................................... 68 5.16 Experiment No: 7A Ascending Workers Arrangement ............................ 69 5.17 Experiment No: 7B Descending Workers Arrangement .......................... 72 5.18 Experiment No: 7C Bowl Workers Arrangement ..................................... 74 5.19 Experiment No: 7D Inverted-Bowl Workers Arrangement ....................... 76 5.20 Experiment No: 8 Comparison of Production Control Mechanisms based on MOO .......................................................................................................... 78

6. Conclusions and Further Work ....................................................................... 86 References ......................................................................................................... 88

Tables and Figures Table no: 1 Different allocation patterns of 70 Buffers capacity Table no: 2 Different allocation patterns of 150 Buffers capacity Table no: 3 Different arrangements of workers in production line Table no: 4 Inputs and Outputs for the optimization Table no: 5 Objective functions for the optimization Table no: 6 Optimization algorithm and corresponding parameters Figure no: 1 Interaction of optimization package and simulation Figure no: 2 Push Production Control System Figure no: 3 Kanban Pull system Figure no: 4 CONWIP Pull System Figure no: 5 DBR Production System Figure no: 6 Steady state analysis Figure no: 7 Replication Analysis Figure no: 8 NSGA-II Figure no: 9 Crowding distance calculation Figure no: 10 Pareto Front of objective f1 and f2 Figure no: 11 Attainment Surface Figure no: 12 The system architecture of FACTS Analyser Figure no: 13 Model of production line with 15 workstation and 14 buffers Figure no: 14 PUSH Production Control Modeled in FACTS Figure No: 18A CONWIP Production control mechanism Figure No: 18B KANBAN Production control mechanism Figure No: 18C DBR Production control mechanism Figure No: 19A steady state analysis of experiment no: 1 Figure No: 19B Replication analysis of experiment no: 1 Figure No: 20A steady state analysis of experiment no: 2 Figure No: 20B Replication analysis of experiment no: 2 Figure No: 21A steady state analysis of experiment no: 3A Figure No: 21B Replication analysis of experiment no: 3A Figure No: 22A steady state analysis of experiment no: 3B Figure No: 22B Replication analysis of experiment no: 3B Figure No: 23A Replication analysis of experiment no: 4A Figure No: 23B Replication analysis of experiment no: 4A Figure No: 24A Steady state analysis of experiment no: 4B Figure No: 24B Replication analysis of experiment no: 4B Figure No: 25A The graph of throughput versus cycle-time Figure No: 25B The graph of throughput versus work in process Figure No: 25C The graph of cycle-time versus work in process Figure No: 26A The graph of throughput versus cycle-time Figure No: 26B The graph of throughput versus work in process Figure No: 26C The graph of cycle-time versus work in process Figure No: 27A The graph of throughput versus cycle-time Figure No: 27B The graph of throughput versus work in process

Figure No: 27C The graph of cycle-time versus work in process Figure No: 28A The graph of throughput versus cycle-time Figure No: 28B The graph of throughput versus work in process Figure No: 28C The graph of cycle-time versus work in process Figure No: 29A The graph of throughput versus cycle-time Figure No: 29B The graph of throughput versus work in process Figure No: 29C The graph of cycle-time versus work in process Figure No: 30A The graph of throughput versus cycle-time Figure No: 30B The graph of throughput versus work in process Figure No: 30C The graph of cycle-time versus work in process Figure No: 31A The graph of throughput versus cycle-time Figure No: 31B The graph of throughput versus work in process Figure No: 31C The graph of cycle-time versus work in process Figure No: 32A The graph of throughput versus cycle-time Figure No: 32B The graph of throughput versus work in process Figure No: 32C The graph of cycle-time versus work in process Figure No: 33A steady state analysis of experiment no: 7 Figure No: 33B Replication analysis of experiment no: 7 Figure No: 34A The graph of throughput versus cycle-time Figure No: 34B The graph of throughput versus work in process Figure No: 34C The graph of cycle-time versus work in process Figure No: 35A The graph of throughput versus cycle-time Figure No: 35B The graph of throughput versus work in process Figure No: 35C The graph of cycle-time versus work in process Figure No: 36A The graph of throughput versus cycle-time Figure No: 36B The graph of throughput versus work in process Figure No: 36C The graph of cycle-time versus work in process Figure No: 37A The graph of throughput versus cycle-time Figure No: 37B The graph of throughput versus work in process Figure No: 38C The graph of cycle-time versus work in process Figure No: 39A KANBAN PCM with different workers arrangement patterns Figure No: 39B CONWIP PCM with different workers arrangement patterns Figure No: 39C PUSH PCM with different workers arrangement patterns Figure No: 39D DBR PCM with different workers arrangement patterns Figure No: 40A Ascending arrangement of workers with different PCMs Figure No: 40B Descending arrangement of workers with different PCMs Figure No: 40C Bowl arrangement of workers with different PCMs Figure No: 40D Inverted-Bowl arrangement of workers with different PCMs

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1. Introduction

1.1 Motivation Industries are forced to improve their production technologies in order to meet

the competitive market of the world. With the intention of improvement in

production system it is persuade to analyze and evaluate the current system.

However, production systems are not always easy to model with analytical

techniques due to their complexity. The tools like discrete event simulation are

helpful to analyze the complex systems [6]. The model building though is more

like an art in simulation tools, the details of complex models can be easily

modeled to evaluate the performance but the evaluation results are not optimal

one. The process to find an excellent solution can be too time consuming and in

some cases nearly impossible due to wide search space. In order to find the

optimal design settings the tools like simulation based optimisation are needed.

Comparatively it’s a new technique applied to find the optimal settings for

complex systems. It is based on one or many performance measures generated

from a simulation by using various searching methodologies [1].

It is widely accepted that simulation based optimisation is a hot research topic.

While extensive search has been done so far in this field, some simulation

optimisation commercial software has also been launched but virtually all of

today’s commercial packages suffer with a few limitations that require sufficient

research efforts. Particularly, they do not address multi-objective problems

despite the fact that nearly all production systems require simultaneously

optimisation of more than one objective function. Mostly the objectives are in

conflict with each other, for example, the objective of a production system is to

maximize the throughput at the same time by minimizing the cycle-time and work

in process. In practice it’s a complex problem, there exist several solutions with

respect to all objectives as improving the performance of one objective would

deteriorate performance of one or more than one objectives. An easy way to

handle such problems is to form a composite objective function as the weighted

sum of conflicting objectives. Because the weight for an objective is proportional

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to the preference factor assigned to that specific objective, this method is also

called preference-based strategy. [1]

In a general way sometimes it is even possible to make small changes in the

existing system may give productive results with the intention of improving the

objective functions. As an example, the buffer capacity and their arrangement in

line is a great deal to improve the system performance. In the same way, having

the workers of different capability in a production line is a normal phenomenon,

which is known as variability imbalance. In this case, the arrangement of workers

in different patterns will also be one factor to improve the performance. Another

factor that has considerable effect in production lines is their control

mechanisms. Having a suitable production control mechanism helps the

companies to achieve their goals. For example, the Toyota Production Systems

(TPS) has paid emphasis on how to implement effective production control

mechanism to achieve the system performance with the minimum required

resources. On the other hand, many researchers have so far worked to find the

optimal settings of a production line like the buffer patterns with their optimal

capacity.

1.2 Aim and Objectives The project is concern with two major cases. First extensively a comparison of

different variability’s in simulation settings with a sharp bottleneck production line

(The term sharp bottleneck mean here the position of bottleneck is already

known in production line) at different buffer capacities and their allocation

patterns. As discrete event simulation (DES) tools are evaluative ones so to

evaluate this case a DES tool will be utilized to generate the results. The effect of

coefficient variation, the change in upper bound and lower bound limits of

processing time with different buffer capacities and different allocation patterns

will explore the effect on different performance measures. Second part is concern

with the workers variability imbalance (having workers of different working

capability in production line) together with different buffer allocation patterns to

find the bottleneck position in unbalanced flow line and one part of this case is

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compare different workers imbalance patterns with different production control

mechanisms based on multi-objective simulation optimisation.

The aim of first case is to explore different buffer allocation patterns performance

in order to help the decision makers to select the pattern accordingly their

preference of different measure. The second case gives a very clear insight of

different PCMs performance with different patterns of variability imbalance aiming

the same as of first case. The objective of the project is to illustrate how

simulation-based optimisation and multi-objective simulation optimisation can be

used for the comparison and study of the effect of various production control

mechanisms and buffer allocations on the performance of production systems

design.

1.3 Thesis Organisation In this first chapter, an introduction to the project’s motivation and aim is found.

The steps taken to obtain the objective are also further described with the

background of thesis topic. Chapter 2 gives the details of each sub-topic of this

thesis work and the concepts are explained clearly. The theories related to

different research issues can also be found in this chapter. Chapter 3 discusses

the methodologies to the approach used in this project with some details of the

experimental tools. The algorithm used for MOSO is discussed with some

important related topics in the same chapter. Chapter 4 introduces the two

different case studies as shown in the Flow Chart 1. The different set of

experiments and simulation settings can also be found in this chapter. Two

different cases with extensive experiments and results analysis are in Chapter 5.

The conclusions and suggested further works are found in Chapter 6.

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Flow Chart: 1 Thesis organization

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2. Literature Review

2.1 Multi-Objective Optimisation

2.1.1 What is an Optimisation problem? Optimisation problems are often made up of three basic elements; the objective

of the function, variables that affect the objective and set of constraints that allow

taking best value of the objective function. [2]

1) An objective function which needs to minimize or maximize. For example, in a

manufacturing process, the objective function is more often to maximize the

profit or minimize the cost. In designing an automobile chassis, the objective

might be to maximize the strength.

2) A set of variables which influence the value of the objective function. In the

manufacturing problem, the variables might include the sum of different

resources used or the time spent on each activity. In the chassis design

problem, the variables used define the shape and dimensions of the chassis.

3) A set of constraints which allow the unknowns to take on definite values but

exclude others. For the manufacturing problem, it does not make logic to

spend a negative amount of time on any activity, thus the constraint here is all

the time variables to be non-negative. In the chassis design problem probably

the aim is to limit the weight of the product and to constrain its shape.

The optimisation problem is subsequently to find values of the variables that

minimize or maximize the objective function while satisfying the constraints. [2]

2.1.2 Multi-Objective Optimisation

Nearly all realistic optimisation problems require simultaneously optimisation of

more than one objective function. Typically, the different objectives are not well-

matched; the variable settings that optimize one objective may be far from

optimal for the others. Here are some examples of multi-objective optimisation in

real life to make it understand that what multi-objective optimisation is.

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• In bridge construction, an excellent design is characterized by low total

mass and high rigidity (Two objectives are stated here).

• Aircraft design requires simultaneous optimisation of fuel efficiency,

payload, and weight that they can carry maximum. (Three objectives are

stated here).

• A good sunroof design in a car could aim to minimize the noise the driver

hears and maximize the ventilation.

• The traditional portfolio optimisation problem attempts to simultaneously

minimize the risk and maximize the fiscal return.

In above examples and in most other cases, it is implausible that the different

objectives would be optimized by the same substitute parameter choices. Hence,

some trade-off between the criteria is needed to ensure a reasonable design [2].

The same way most of the production systems design problems also require the

simultaneous optimisation of more than one conflicting objective. For instance,

an ideal configuration of a production system is the one that maximizes system

throughput whereas simultaneously minimizing manufacturing lead times and

work-in-process. Unluckily, this is not at all an easy task because in the largest

part of the real-world complex systems, these objectives are in conflict with each

other. In a common multi-objective optimisation problem, there exists no single

best solution with respect to all objectives as improving performance on one

objective would go down performance of one or more other objectives. An easy

way to deal with a multi-objective optimisation problem is to reformulate as

single-objective problem like in a composite objective function either forming a

weighted combination of the different objectives or else replacing some of the

objectives by constraints. Because a weight for an objective is proportional to the

preference factor assigned to that specific objective, this method is also called

preference-based strategy. [1]

It seems that preference-based multi-objective optimisation is simple to apply

because by scalarizing an objective vector into a single multiple objective

functions, a multi-objective optimisation problem can be changed into a single-

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objective optimisation problem and as a result a single trade-off optimal solution

can be hunted effectively. Though, the major disadvantage is that the trade-off

solution obtained by using this practice is very sensitive to the relative preference

vector. Therefore, the option of the preference weights and the obtained trade-off

solution is greatly subjective to the particular decision maker. On the other hand,

without the comprehensive knowledge about the system under study, it is also

very tricky job to select the suitable preference vector. As a result for a decision

maker who is responsible for production systems design, particularly during the

conceptual phase, it would be very helpful if the posterior Pareto front (define in

section 3.2.3) can be generated quickly by using a multi-objective optimisation

simulation based optimisation algorithm so that he/she can choose a

configuration that is the “best” trade-off among these conflicting performance

measures [1].

2.1.3 Multi-Objective Optimisation using Evolutionary Algorithms Genetic algorithms have been successfully used as search and optimisation tools

in various problems including science, commerce and engineering. The primary

reasons for their success are their broad applicability, ease of use and global

perspective [14].

In last ten years there have been many multi objective evolutionary algorithms

proposed by different researchers like Vector-Evaluated Genetic Algorithm

(VEGA), Niched-Pareto Genetic Algorithm (NPGA), Multi-objective Genetic

Algorithm (MOGA), Eltist Non-Dominated Sorting Genetic Algorithm (NSGA),

Fast Eltist Non-Dominated Sorting Genetic Algorithm (NSGA-II). [1]

The working principle of GAs is very different from most of classical optimisation

techniques. The evolutionary algorithms work with a population of solutions,

instead of one solution in each iteration. Genetic algorithms (GA) behave like a

random search process, it starts with a random set of solution, and evolutionary

algorithms (EA) modify the current population to a different population in each

iteration. Working with a number of solutions provides an EA with the ability to

capture multiple optimal solutions in one single simulation run. They have two

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diverse operations, that is to say selection and search. In selection operation,

better solutions in the current population are highlighted by duplicating them in

the mating pool. In search operation, new solutions are created by exchanging

partial information among solutions of the mating pool and by tormenting them in

their neighborhood. They do not use any gradient information during selection

and search operation, their illustration are flexible. These properties make EAs

flexible to be used in extensive variety of problem domains. The GAs search

procedure behaves like a random search process. The reliable application of

GAs will be to make sure that it starts looking for solution in right direction. [3]

2.2 Discrete Event Simulation The mathematical or analytical modeling practices are not adequate enough if a

comprehensive analysis is required of complex manufacturing systems. As an

alternative of using experts to build an extensive mathematical model by using

the analytical approach, computer-based simulation is used. Computer-based

simulation is seen as a vital business tool giving flexibility and expediency in

designing, planning and analyzing complex manufacturing processes and

systems. This is because the computer-based modeling and simulation method

has the capacity of representing the complex static structure as well as the

dynamic behavior of manufacturing systems. Modeling and simulation for

manufacturing systems is the technique of building a conceptual logical model

that characterizes a real system, and describes the internal actions of its

components and their interactions together with stochastic variability. The model

represented by computer program gives information about the system, can be

used to ape the operation of a real system, such as the day-to-day operations of

an assembly flow line in a factory, and to predict the behavior of complex

manufacturing systems by calculating the movement and interaction of system

components. [4]

“A discrete event simulation concern the modeling of a system as it is evolves

over time by a representation in which the state variables change

instantaneously at separate points in time” [6]. Discrete event simulation has

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foremost many advantages in use over mathematical or analytical methodologies

like:

When analyzing a complex system, stochastic elements cannot be exactly

described by a mathematical model and cannot be evaluated critically as modern

manufacturing systems. This subject has been solved in discrete event

simulation software’s. Dynamic systems keep randomness that changes with

time. The modeling of complex dynamic systems theoretically require too many

simplifications, quite often it is far difficult to model it mathematically. The

dynamics are much easier to model it in discrete event simulation software’s. [4]

2.3 Simulation Optimisation Simulation based optimisation (SO) is a reasonably new practice applied to ask

for the “optimal” setting for a complex system based on one or multiple

performance measures generated. Though wide research focus has been made

to simulation optimisation since mid 1990s, when the first commercial SO

package was launched, until now, almost all of today’s commercial SO packages

undergo two major restrictions that necessitate significant research efforts: first

they work in a deterministic mode, without taking into account the stochastic

outputs from DES and second they do not explicitly address multi-objective

problem. [1]

The optimisation of simulation models agreed with the situation in which possibly

many sets of model specifications direct to optimal performance. In design of

experiments, the input parameters linked with a simulation model are called

factors. The output performance actions are called responses. In the area of

optimisation, the factors (inputs) become decision variables and the responses

(outputs) are used to model an objective function and constraints. Whereas the

goal of experimental design is to expose which factors have the greatest effect

on a response, optimisation search for the combination of factor levels that

minimizes or maximizes a response subject to constraints imposed on factors

and responses. [5]

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Taking an example of a manufacturing industry, whereas the task can be to

formulate an optimisation model that seeks to minimize cycle time by

manipulating the number of workers and machines, while limiting capital

investment and operational costs as well as sustaining a minimum utilization

level of all resources. A model for this optimisation problem would consists of

decision variables related with labor and machines as well as a performance

measure based on a cycle time obtained from running the simulation of the

manufacturing facility. The constraints are formulated both with decision

variables and responses. In the environment of simulation optimisation, a

simulation model can be although as a “mechanism that turns input parameters

into output performance measures” [6]. Further the simulation model is a function

that evaluates the value of a set of specifications, normally represented as set of

values. [5]

Figure no: 1 Interaction of optimisation package and simulation model

The interface among the optimisation package and the simulation model is

shown in figure 1. The concept of the figure has been taken from Averill M. Law

fourth edition of simulation modeling and analysis. The optimisation package

initially instructs the simulation model to make one or more replications of an

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early system arrangement. The results from these replications are fed back into

the optimisation package, which then uses its built-in search algorithm to decide

on a further configuration to simulate. This process is continued until the

optimisation package stopping rule has been fulfilled. It is essential to keep in

mind that the results are not definite to be absolutely optimal. [6]

2.4 Production Control Mechanisms Production Control Mechanisms are critical tools for meeting increasingly high

customer demands in the present highly competitive manufacturing industry.

The spotlight of such functions include reducing Work in Progress (WIP),

minimizing cycle time, lower stockholding costs, improving throughput, and

improving Delivery Date (DD) adherence. These all factors consequently improve

the profit of the business that helps the company to compete the market in a

better way. To attain the goal these important objectives has to be counted, so

the choice of right production control mechanism is hence a crucial strategic

decision. [7]

“Efficient production control systems are those that produce the right parts, at the

right time, at a competitive cost.” [8] The successful production control in any

manufacturing system is the management of the total stream of goods through

the system, from the acquirement of raw parts to the delivery of finished products

to the customers, is the key to competitiveness of the system. Production control

is an optimisation problem that typically addresses the question of when and how

much to produce in order to achieve a satisfactory customer service level while

keeping low in-process inventories. The practical approach to deal with the

production control problem is to confine the search for a production control

strategy to a class of simple, sub-optimal strategies that are easy to implement

and try to determine the optimal strategies within this class. Much of the research

effort in this area has focused on developing and evaluating simple production

control strategies that depend on a small number of parameters and have often

emerged from actual industrial practice. [9]

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Production control mechanisms are usually divided into two types: the push and

the pull systems. The push systems, such as MRP, schedule releases based on

the forecast value of lead time, while the pull systems, such as kanban, generic

kanban and CONWIP authorize releases based on the rate at which the products

have been consumed. The pull systems control the WIP (Work-In-Process)

directly, and hence minimize it to facilitate quick responses to changes in

demand and production fluctuations. The advantages of pull over push are

observable, efficiency, variability, and robustness. [10]

Diverse studies have been conducted to propose new forms of production control

mechanisms and compare their performance with existing ones to determine

which one performs best under different situations. The research work in this

practice is focused on four different production control mechanisms.

1. PUSH Production Control Mechanism

2. KANBAN Production Control Mechanism

3. CONWIP Production Control Mechanism

4. DBR Production Control Mechanism

2.4.1 PUSH Production Control Mechanism In a push production control, the flow of material is regulated at the first operation

in the process. Once material is released to this operation, it continues through

the system as fast as production resources allow. [11] As soon as there is place

available in front of source it place the entities in the system and entities stacks

up in front of slow proceeding process, this can result high level of work in

progress so in push control mechanism the WIP level increase that cause to

increase the lead time. In the section of different production control mechanism it

will be compared that how the other parameters are affected by increase of work

in process. The flow of process in a push control system is shown in figure 2.

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Figure no: 2 Push Production Control System

2.4.2 KANBAN Production Control Mechanism Kanban is the more generally known and renowned type of pull system, Kanban

meaning card or marker in Japanese. Sometimes Kanban referred to as the

Toyota Production System. Kanban pull system uses card sets to closely control

work in progress between each two workstations. The entire system WIP is

restricted to the summation of the number of cards in each card set. Production

begins at a workstation only if raw material is available and the material has a

card sanction. Material is pulled through the system only when it receives card

authorization to move. [12]

Figure no: 3 Kanban Pull System

The Figure 3 is redrawn from Richard P. Maerk’s paper. It exemplifies a serial

Kanban system. Each Kanban card set among workstations authorizes material

to be pulled into the upstream workstation for processing and delivery to the

downstream workstation. As an example, card set 2 between Workstations 1 and

2, authorizes an order in the queue before Workstation 1 and raw material to be

released for processing at Workstation 1 and delivery to Workstation 2 so here

the individual WIP is controlled by cards and in the same way the WIP is

controlled on each stage.

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2.4.3 CONWIP Production Control Mechanism A CONWIP pull system uses a single general set of cards to control total WIP

everywhere in the system. Material enters a CONWIP system simply when

demand occurs, and the raw material receives a card authorizing entrance; the

same card allows the material to move from beginning to end the system and

complete production. Whilst the final product leaves the system, the card is free,

allow new material to enter the system. Here the WIP is not controlled at each

individual workstation. The total WIP in the system is constant, that is limited by

the amount of cards in the system. [12]

Figure no: 4 CONWIP Pull System

The Figure 4 is redrawn from Richard P. Maerk’s paper. It illustrate a CONWIP

system. In CONWIP system the material is controlled only at the front of the line

to get enter in the system and then it is free to float in the line like in push system

therefore CONWIP is also known as hybrid push-pull system . The new material

enters in the system when there is new order or demand is said by customer.

CONWIP systems are easy to handle, for there is only one set of global cards

that requires evaluation and modification.[12]

2.4.4 DBR Production Control Mechanism A recently developed alternative to traditional planning and control systems is the

drum–buffer–rope (DBR), which is the key element of the theory of constraints

(TOC) in manufacturing organizations. The DBR methodology was developed by

Goldratt and is now being implemented by a growing number of manufacturing

organizations. Schragenheim and Ronen call attention to that this approach to

shop floor control can reduce work in process and improve the general

productivity of job shop operations.

Irfan Zia Page 15

B3B2B1

A3 A4 A5A2A1

B4 B5 B6

DrumRope

Buffer

Finished Goods

Raw Material

Figure no: 5 DBR Production System

The DBR consists of three foremost components. The drum is the bottleneck

resource, which is the constraint of the system; the constraint defines the overall

pace of the system. In many cases, the drum has to comprise a detailed

schedule of the constraint to make sure the exploitation of the constraint. Since

the constraint (in this case drum) decides the output of the entire process and to

keep it engaged all the time this buffer is required, thus buffer is protection time.

Buffers are employed to keep the bottleneck from disruptions in the processing

steps preceding the constraint. The rope is just kept to prevent flooding of the

constraint with surplus WIP especially on the upstream process This is a

mechanism to force all the parts of the system to work up to the pace dictated by

the drum. The concept of figure 5 has been taken from John H. Blackstone. It

shows the main components of a DBR system. It is a combination of push/pull

logistical procedure whereas materials are pulled into the shop via the rope

based upon the rate of use of these materials at the bottleneck. [8]

Irfan Zia Page 16

3. Multi-Objective Simulation Optimisation for PCM Comparison Numerous studies have been conducted in the last decade to propose new forms

of production control mechanisms and compare their performance with existing

ones to determine which one performs best under different situations. However,

most of these comparisons suffer from the problems of lacking a unified

framework for comparison so that some mechanisms are not augmented with the

optimal parameter setting when applied to the system under testing. On the other

hand, it is also important to take into account the optimal tradeoff between more

than one objectives when comparing different production control mechanisms

(PCM). The research at the University of Skövde has proposed the concept that

PCM comparisons can be done effectively within the context of multi-objective

simulation optimisation (MOSO). Specifically, a technique called confidence-

based significant dominance to handle uncertainty from stochastic simulation

outputs has been developed. Promising results from applying MOSO and

significant dominance to some simple unbalanced and asynchronous flow lines

for comparing four different PCMs, including Push, CONWIP, DBR and CWIP,

have been obtained. In this project two different cases are going to be discussed

in detail.

(1) Unbalanced flow line with sharp bottleneck

(2) Unbalanced flow line with variability imbalance

For the case number one several different buffer allocation patterns, different

buffer capacities, different values of coefficient variation and some other

parameters of lognormal distribution has been studied precisely that how they

effect on system performance in terms of cycle time, work-in-process and

throughput. In this case the Push production control mechanism is only studied.

In the second case first with variability imbalance of workers arrangement

patterns in Push production control mechanism with different buffer allocation

patterns bottleneck has been detected in the flow line and aside here the cycle

time, work-in-process and throughput is also been examined, that how the

Irfan Zia Page 17

workers variability imbalance effect in unbalanced flow line on said measures.

The second half of this part is to conduct the multi-objective optimisation for the

different workers arrangement patterns combined with different production

control mechanisms. Each case with its methodology is described below in detail.

3.1 Methodology to determine unbalanced flow line with sharp bottleneck The find out the effect of coefficient variation, effect of upper bound and lower

bound limits on processing time, different buffer allocation patterns and different

number of buffers how they effect on system performance simulation model is

modeled in Tecnomatix Plant Simulation 8.2.0 (by Siemens). To run the

experiments for simulation model need to perform the steady state analysis and

replication analysis. The results from the experiments of buffer allocation pattern

are ported in excel and from there graph been plotted to compare and contrast

the measures.

3.1.1 Steady State Analysis A non-terminating simulation has no natural event to specify the length of run.

Designer or planners are interested in the behavior of the system in long run

when it is operating normally. The state when system start behaving normally is

said to be steady state. A Steady-state analysis is used to determine the warm-

up period of the simulation system (i.e. the time it takes for the system to

stabilize). The technique applied here to calculate the warmup time is taken from

Welch method. It determine the warmup period when transient curve flattens out

[6].

In this case it is done by plotting the data collected in the initial simulation run

consisting of 10 replications each of 200 hours. Using MS Excel to plot the graph

gives a graphical view of at which time the transient state (warm-up) passes over

to a steady state independent of starting conditions such as empty buffers. The

figure no: 6 shows that how the WIP increased in line and then after some time it

is quite stable close to 14 units.

Irfan Zia Page 18

According to Welch to produce a clearer graph, adjacent data values are

grouped together and divided into an average. This method is called moving

average and makes the graph appear “smoother”, effectively diminishing

fluctuations and making the overall trend of the graph clearer. Steady state

appears to have been reached at x-value 27. Therefore, no data collected

between the times 0-27h is used in further simulation. This steady state time is

used in one experiment and for all different experiments steady state time has

been calculated in the same way.

Moving Avg

0.00

2.00

4.00

6.00

8.00

10.00

12.00

1 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196

Moving Avg

Figure no: 6 Steady state analysis

3.1.2 Replication analysis Replication analysis involves the purpose of the number of simulation runs that

are required to analyze statically the difference between simulation models [15].

To check the systems behave with different parameters and also to improve the

system it is necessary to run several simulations. Input variability effects output

measure performance because of this reason it is not correct to make

Irfan Zia Page 19

conclusions from a unique replication. To get a reliable performance of the

system it is necessary to calculate the number of simulation that is needed to get

reliable result. The purpose of a replication analysis is to calculate how many

simulations are needed in order to reach a specific absolute precision within a

desired confidence interval. In the followed experiments the initial amount of

replications is set to ten, which is enough to gather reasonably trustworthy

statistical data [15]. By using a dedicated MS Excel sheet and the standard

deviation and mean value collected from the data of the ten replications, together

with a confidence interval of 95 % and a set absolute precision of 0,1 for average

throughput per hour, 5 for average cycle time, 1 for average work in process and

1 for WIP calculated by little-law (according to little’s law WIP is the product of

throughput and cycle time). It is possible to calculate how many replications that

are needed to reach the desired confidence interval. The result of one replication

analysis is shown in figure no: 7. after four runs it is clear that no less than 10

replications must be made. The said replication analysis has been made by

following the method said by Christopher A.Chung in simulation modeling

handbook.

Repl. Average MEAN

Average STDEV

Std. error 95%

Absolute precision

Est. # of simulations

needed Conf. Int. Run 1

10 9,6 0,13100 0,09 THP 0,1 8,78189 10 300,2 5,9459 4,25 CT 5 7,2367 10 48,08 1,0233 0,73 WIP 1 5,3586 10 48,04 1,0104 0,72 Little_WIP 1 5,2243 Run 2

9 9,6 0,13660 0,11 THP 0,1 9,9225 9 298,7 4,09 3,14 CT 5 3,5547 9 47,79 0,491 0,44 WIP 1 1,2804 9 47,77 0,5778 0,72 Little_WIP 1 1,7753

Run 3 10 9,6 0,1310 0,09 THP 0,1 8,78189 10 300,2 5,946 4,25 CT 5 7,2367 10 48,08 1,023 0,72 WIP 1 5,3586 10 48,04 1,104 1,14 Little_WIP 1 5,2243 Run 4

9 9,6 0,1366 0,11 THP 0,1 9,9225 9 298,7 4,09 3,14 CT 5 3,5574

Irfan Zia Page 20

9 47,79 0,491 0,38 WIP 1 1,2804 9 47,77 0,5778 0,44 Little_WIP 1 1,7753

Figure no: 7 Replication Analysis

3.2 Methodology to determine unbalanced flow line with variability imbalance In this case a multi-stage production line is studied. The production line is

comprises on different work-stations and in between the workstations there are

buffers. Each work-station is handled by one worker; there are workers of three

different skills, junior they work for the same object with the coefficient variation

of 1.5, medium their coefficient variation is one and senior their coefficient

variation value is 0.5, the mean value for all types of workers is 240 second. Here

the workers variability imbalance with buffer allocation pattern under different

production control mechanisms has been compared to find out which PCM

results better than others and which pattern of workers arrangement will be great

deal for increase in throughput besides taking in to consideration minimum cycle

time. Hence this case study is a multi-objective optimisation (MOO) problem. To

find out the best trade-off solutions a number of different configurations need to

run in simulation software and from these numbers of simulation run results can

be compared by Artificial Intelligence techniques. In this case to run number of

simulations, simulation based optimisation (SBO) tool has been used, this SBO

tool has been developed at University of Skövde and the results of simulation

optimisation are contrived by the application of evolutionary algorithm. In the

direction to draw the results from the simulation-optimisation the best choice is to

draw the posterior Pareto front that can be quickly generated by using Fast Elitist

Non-Dominated Sorting Genetic Algorithm (NSGA-II).

3.2.1 Elitist Non-Dominated Sorting Genetic Algorithm (NSGA-II) This algorithm has been suggested by Kalyanmoy Deb, It uses an explicitly

diversity-preserving mechanism to develop a more efficient selection mechanism

in order to preserve population diversity in scaling problems. The word elitism

can be introduce in a simple way when two offspring are created using the

Irfan Zia Page 21

crossover and mutation operators, they are compared with both of their parents.

Then, among the four parent-offspring solutions, the best two are selected,

thereby allowing elite parents to compete with their offspring for a slot in the next

generation. In NSGA-II, the offspring population Qt is first created by using the

parent population Pt, instead of finding the non-dominated front of Qt only, first

two population are combined together to form Rt of size 2N. Then the entire

population Rt is classify by using non-dominated sorting. The new population is

filled by solutions of different non-dominated fronts. The filling starts with the best

non-dominated front and continues with solutions of the second non-dominated

front, followed by the third non-dominated front and so on. Since the overall

population size of Rt is 2N. Then perform the crowding distance sorting

procedure and include the most widely spread solution to Pt+1. This process is

exemplified in figure 8 that is redrawn from Kalyanomy Deb [3].

Pt

Qt

Rt

F1F2

F3

Pt+1

Rejected

Crowding distance sorting

Non-dominated sorting

Figure no: 8 NSGA-II

3.2.2 Crowding Distance “To get an estimate of the density of the solutions surrounding a particular

solution i in the population, take the average distance of two solutions on either

side of solution i along each of the objectives. Shown in figure 9 The crowding

distance of i-th solution in its front is the average side length of the cuboid”[3].

The figure 9 is redrawn from Kalyanomy Deb book on Multi-objective optimization

using evolutionary algorithms.

Irfan Zia Page 22

1

f2

ii-1

i+1

cuboid

f1

Figure no: 9 Crowding distance calculation

3.2.3 Pareto front The set of trade-off optimal solutions generated in the optimisation is called the

Pareto front. To derive the Pareto front many MOO algorithms use the concept of

dominance. A solution X1 is said to dominate the other solution X2, if both of the

following two conditions are true:

1. The solution X1 is no worse than X2 in all M objectives: i.e.

)( 1xf j )( 2xf j ∀ Mj ,......2,1=

2. The solution X1 is strictly better than X2 in at least one objective, i.e.

)()( 21 xfxf jj < for at least one },......2,1{ Mj∈

)(/)( 21 xfxf jj ∀ Mj ,......2,1=

Where < denotes “is better than”

If any of these two conditions is false, the solution X1 does not dominate the

solution X2. If X2 is dominated by X1, X1 is said to be non-dominated by X2. If the

solution X1 is strictly better than X2 in all objectives, X1 is said to strongly

dominate X2. Among a set of solutions X, the solutions which are not dominated

by any other member of X is called the non-dominated set. When the set X

corresponds to the entire search space, the resulting non-dominated set equals

Irfan Zia Page 23

the Pareto front. In figure 10 the pareto front of two objectives in a search space

is shown. [1]

Minf2

Min f1

Figure no: 10 Pareto Front of objective f1 and f2

3.2.4 Significant Dominance The concept of significant dominance is applied to draw the Pareto front. A

solution X1 is said to significantly dominate the other solution X2, if both of the

following two conditions are true:

1. The solution X1 is not significantly worse than X2 in any of the M objectives: i.e.

)( 1xf j )( 2xf j ∀ Mj ,......2,1=

If >)( 1xf j )( 2xf j for a },......2,1{ Mj∈

But Welch CI [ ]2121 ,))()(( ccxfxf jj =−

Such that [ ]21 ,0 cc∈

Then we can conclude that )( 1xf j )( 2xf j

2. The solution X1 is significantly better than X2 in at least one objective, i.e.

)( 1xf j )( 2xf j for at least one },......2,1{ Mj∈

Where denotes “is significant better than”

If )()( 21 xfxf kk < for a },......2,1{ Mk∈

And Welch CI ))()(( 21 xfxf kk − does not cover 0

Irfan Zia Page 24

Then we can conclude that )( 1xf k )( 2xf k

The Welch CI can be calculated by:

2

222

1

121

21,ˆ

21

)()()()(

nns

nns

txfxfMa

fkk +±−

−

Where

)( 1xf k =mean of objective function value of obj x for solution 1

)( 2xf k = mean of objective function value of obj x for solution 2

)( 11 ns =standard deviation of objective function value of obj x for solution 1

)( 22 ns =standard deviation of objective function value of obj x for solution 2

1n = number of replications generating solution 1

2n = number of replications generating solution 2

Mft

21,ˆ

α−

= student –t distribution with degree of freedom f̂ and probability M2

1α

−

The degree of freedom can be obtained by the Welch estimation:

1

)(

1

)(

)()(

2

2

2

222

1

2

1

121

2

2

222

1

121

−

+−

+

=

n

nns

n

nns

nns

nns

f)

Instead of a 1-α confidence region, the confidence level has to be constructed by

replacing the error rate α with α/M if there are M objectives, due to the Bonferroni

Inequality. So, for a MOO problem of two objective functions, to obtain a 95%

confidence (i.e. 100 × (1−0.05) %) for the non-dominated sorting, each objective

has to be compared with 97.5% (i.e. 100×(1−0.025)%) confidence level. [1]

3.2.5 Attainment surface The obtained non-dominated solutions are usually joined with a curve; curve

provides a better illustration of a front however there is no promise that any in-

between solutions are Pareto-Optimal. Instead of joining the obtained non-

Irfan Zia Page 25

dominated solutions by a curve, an envelope can be formed marking all those

solutions in the search space which are sure to be dominated by the set of non-

dominated solutions. The generated envelope is called attainment surface. [3]

The graph in figure no: 11 is representing the attainment surface obtained from

solution of a SBO, where the objective function on X-axis is to minimize and on

Y-axis is to maximize.

Figure no: 11 Attainment Surface

3.3 FACTS Analyser As the simulation by itself is not a real optimisation tool. A step that joins

simulation and optimisation is hardly in need to solve multi-objective simulation

optimisation problems. This approach is called Simulation-Based Optimisation

(SBO). At the University of Skövde, an Internet-based SBO system called

FACTS (Factory Analysis in Conceptual phases using Simulation) Analyser,

which is specifically analysis and optimisation, has been developed. The

followed experiments are being performed in FACTS analyser.

FACTS analyser is a Web Services based client/server system architecture, it

provides the features required for making DES easier to use as well as speed up

Irfan Zia Page 26

the time-consuming model building and optimisation process. FACTS Analyser is

designed with the principle of illusion of simplicity and system neutrality. It is

designed to be a “thick” client application that accesses the server components

through the Web Services interface as shown in figure 12 (figure has been

printed by the permission of author, Amos H.C. Ng). The server components

include the model generator, DES, optimisation algorithms, data analysis

functions and the underlying integrated database management system. In terms

of optimisation, these services are virtually provided by connecting the FACTS

server components to the OPTIMISE server components [13].

At the heart of the OPTIMISE architecture there are many different optimisation

engines, enclosed by a set of OPTIMISE Server Components which spread

across three tiers:

(1) Web Server

(2) Optimisation

(3) Simulation subsystem

In a SBO application propped up by the OPTIMISE structure, the optimisation

engine (OptEngine) in the optimisation tier is the most important component

because they provide the core functionality for major algorithmic processing and

act as the hubs for coordinating other functions, including data logging and

metamodelling. Server components can be accessed by client applications

through consuming the OPTIMISE Web services, hosted by the Web server. The

Web server listens to the XML requests and acts accordingly. Most often the

functionalities that client applications request are controlling a SBO process and

retrieving data from an Optimisation Database. The Optimisation Manager is

mainly a Windows service that listens to the request from the Web Server to

launch different optimisation algorithms [1].

Irfan Zia Page 27

Figure no: 12 The system architecture of FACTS Analyser

Irfan Zia Page 28

4. Case Studies This project is aimed to study unbalance flow line with sharp bottleneck and with

the workers variability imbalance. To find out the optimal production control

mechanism, different buffer allocation patterns comparison, different numbers of

buffers in the same production line and the effect of different coefficient variation

with the constrain of processing time lower bound and upper bound on

production line many different experiments have been done. This project is

consisting on these two cases.

4.1 Case 1: Unbalanced flow line with sharp bottleneck In this case a multistage production line is studied precisely to find out the warm

up time and number of replications that how these two considerations effected by

the change in size of buffer, coefficient variation, limitations of lower bound and

upper bound.

The first experiment is performed on simple unpaced flow line to find out the

warm up time and number of replications and then in the same line by making

one station as a bottleneck it has been studied that how does it effect on steady

state time and replication run. Keeping the same setting and by making change

only in coefficient variation first to ‘1’ and then ‘1.5’ again steady state time and

number of replication been calculated. In next set of experiment; the limitation of

processing time has been changed to notice how it effects on performance.

The major set of experiments in this case is testing the effect of buffer allocation

patterns on the performance of the line first with total buffer capacity of 70 and

then increase up to 150. The buffer allocation patterns are also tested by the

change in coefficient variation and processing time limitations (upper bound and

lower bound). This case study in a way helps the decision makers to find out the

best buffer allocation pattern and how many will be good enough to attain the

maximum level of through put (TH) by keeping minimum cycle time (CT) and

work in progress (WIP). On the whole sets of experiments in this case are

followed.

Irfan Zia Page 29

1. Find the steady state time and number of replications in a simple unpaced

flow line of 15 workstations and 70 buffers.

2. Find the steady state time and number of replications in a simple unpaced

flow line having sharp bottleneck at one workstation, the line is consisting

of 15 workstations and 70 buffers.

3. The effect of coefficient variation on steady state time and number of

replications in a simple unpaced flow line having sharp bottleneck at one

workstation.

4. The effect of upper bound and lower bound in processing time on steady

state time and number of replications in a simple unpaced flow line having

sharp bottleneck at one workstation.

5. Testing the effect of buffer allocation patterns on the line performance TH,

CT and WIP when coefficient variation is ‘1’ and total buffer capacity is 70.


CT and WIP when coefficient variation is ‘1’ keeping the processing time

lower bound 0 and upper bound infinity and total buffer capacity is 70.


CT and WIP when coefficient variation is ‘1.5’ and total buffer capacity is

70.


CT and WIP when coefficient variation is ‘1.5’ keeping the processing time



CT and WIP when coefficient variation is ‘1’ and total buffer capacity is

150.


CT and WIP when coefficient variation is ‘1’ keeping the processing time



CT and WIP when coefficient variation is ‘1.5’ and total buffer capacity is

150.

Irfan Zia Page 30


CT and WIP when coefficient variation is ‘1.5’ keeping the processing time


The buffer allocation patterns for the capacity of 70 buffers are shown in table

no:1 and the total buffer capacity of 150 is shown in table no: 2.

Patterns 1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 Most buffers to the end 1 1 1 1 1 1 1 1 1 1 1 1 1 56

2 Ascending 1 1 2 2 3 3 4 4 5 5 8 8 12 12

3 Big Bowl 12 8 5 4 3 2 1 1 2 3 4 5 8 12

4 Small Bowl 6 5 5 5 5 5 4 4 5 5 5 5 5 6

5 Balanced 5 5 5 5 5 5 5 5 5 5 5 5 5 5

6 Small Inverted Bowl 4 5 5 5 5 5 6 6 5 5 5 5 5 4

7 All around the bottleneck 1 1 1 1 1 1 28 28 1 1 1 1 1 1

8 Big Inverted Bowl 1 2 3 4 5 8 12 12 8 5 4 3 2 1

9 Descending 12 12 8 8 5 5 4 4 3 3 2 2 1 1

10 Most of the buffers to the front 56 1 1 1 1 1 1 1 1 1 1 1 1 1

Table no: 1 Different allocation patterns of 70 Buffers capacity

Patterns 1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 Most buffers to the end 1 1 1 1 1 1 1 1 1 1 1 1 1 137

2 Ascending 1 1 2 2 3 3 8 8 12 12 15 15 34 34

3 Small Bowl 17 15 10 10 10 8 5 5 8 10 10 10 15 17

4 Big Bowl 34 15 12 8 3 2 1 1 2 3 8 12 15 34

5 Balanced 1 10 10 11 11 11 11 11 11 11 11 11 11 10 10

6 All around the bottleneck 1 1 1 1 1 1 69 69 1 1 1 1 1 1

7 Balanced 2 11 11 11 11 11 10 10 10 10 11 11 11 11 11

8 Small Inverted Bowl 5 8 10 10 10 15 17 17 15 10 10 10 8 5

9 Big Inverted Bowl 1 2 3 8 12 15 34 34 15 12 8 3 2 1

10 Descending 34 34 15 15 12 12 8 8 3 3 2 2 1 1

11 Most of the buffers to the front 137 1 1 1 1 1 1 1 1 1 1 1 1 1

Table no: 2 Different allocation pattern of 150 Buffers capacity

Irfan Zia Page 31

4.1.1 Case1: simulation settings This case study is modeled in plant simulation. The model building is done as

shown in figure number 13. There are total 15 workstations and between each

two workstation there are inter-station buffers. The total capacity of buffers is 70

and in one set of experiment are 150. At the beginning of the line the first

workstation is KANBAN type that pushes in the material in the line as soon as

there is place available in front of this workstation; so called the production

control mechanism is PUSH type. The processing time of each proc is lognormal.

This type of processing time has five attributes, the first one is stream it sets the

random number the source uses when MU selection is random in this case the

stream value is not important. The second attribute is the mean value and the

next attribute is standard deviation (sigma). The last two are the limits of the

processing time as lower bound and upper bound. The settings of these

parameters are written in experiment details that are coming in next section. The

buffers processing time is set to zero in all cases.

Irfan Zia Page 32

Figure no: 13 Model of production line with 15 workstation and 14 inter-station buffers

Irfan Zia Page 33

4.2 Case 2 Unbalanced flow line with variability imbalance

The first part of this case is subject to the variability imbalance of workers in line

with different buffer allocation patterns and different arrangement of workers in

production line to detect the bottleneck and to study their effect on the

performance measures like through put (TH), cycle time (CT) and work in

progress (WIP). There are workers of three different grades and the grading of

the worker is subject on their processing time capability. The worker that work

fast they are named senior ‘S’, the one who work slow are junior ‘J’ and the

workers that are in between the said two are named as medium ‘M’. The

arrangements of these three types of workers in line play a major role on the

performance of the line. Different arrangements of workers in line that are going

to study are shown in table no: 3.

Pattern 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Bowl J J M M M M S S S M M M M J J

Ascending S S S M M M M M M M M J J J J

Descending J J J J M M M M M M M M S S S

Inverted Bowl S S M M M M J J J J M M M M S

Table no: 3 Different arrangements of workers in production line

In here the steady state time and number of replication is calculated by arranging

the workers in bowl pattern with balanced buffer allocation pattern and the sum of

buffer 70 is only tested in this case.

The second part of this case is to conduct the experiments based on multi-

objective optimisation by applying NSGA-II. The experiments has been run with

four different production control mechanisms Push, CONWIP, DBR and KANBAN

and each production control mechanism run is performed with four different

workers allocation patterns Bowl, Ascending, Descending and Inverted-Bowl.

This case study can also give indication help the decision makers to select the

Irfan Zia Page 34

appropriate PCM and give a clear sign to arrange the workers in a better way to

attain the desired results.

4.2.1 Case2: simulation settings This case is being studied in FACTS Analyser. In the first part of this case PUSH

production control mechanism is modeled with different workers arrangement

patterns; in figure no: 14 the bowl arrangement of workers with the balanced

buffer allocation pattern is figured. All processing time are lognormal. The facts

analyser has four attributes for this. The first one is mean value, the next one is

sigma, and the last two are lower bound and upper bound value for the mean.

The buffers transport time is set to zero in all experiments run. The simulation is

run for 200 hours. The steady state time and number of replication are counted

as described in appendix A. the steady state time in here is 23 hours and number

of replications are 28.

Figure no: 14 PUSH Production Control Modeled in FACTS As the second part of this case is to conduct the experiments based on multi-

objective optimisation by applying NSGA-II, here the most important is to write

the detail of those parameters along the rest simulation settings. The input and

outputs for the optimisation are shown in table number 4. The total buffer

capacity is 70 so the limits for each buffer are from 1 to 70. The constrain of input

variable is also a required parameter here. The outputs are Cycle Time,

Throughput and work in process. There are two objectives one is to minimize the

cycle time and the other is to maximize the throughput, as shown in table no: 5.

Irfan Zia Page 35

Inputs Name Type Lower Bound Upper Bound

B1_Capacity Discrete 1 70 B2_Capacity Discrete 1 70 B3_Capacity Discrete 1 70 B4_Capacity Discrete 1 70 B5_Capacity Discrete 1 70 B6_Capacity Discrete 1 70 B7_Capacity Discrete 1 70 B8_Capacity Discrete 1 70 B9_Capacity Discrete 1 70 B10_Capacity Discrete 1 70 B11_Capacity Discrete 1 70 B12_Capacity Discrete 1 70 B13_Capacity Discrete 1 70 B14_Capacity Discrete 1 70

Outputs Throughput Lead time WIP Bottleneck (Text output)

Table No: 4 Advanced Inputs and Outputs for the optimisation settings

Objective

Name Formula Goal CT Lead Time Minimize TP Throughput Maximize Input constraint Formula (B1_Capacity+B2_Capacity+B3_Capacity+B4_Capacity+B5_Capacity+B6_Capacity+B7_Capacity+B8_Capacity+B9_Capacity+B10_Capacity+B11_Capacity+B12_Capacity+B13_Capacity+B14_Capacity)<=70

Table No: 5 Objective functions for the optimisation The optimisation algorithm and its corresponding several attributes are shown in

table number 6. The number of iteration are 5000 and each will replicate as the

number of replication specified in simulation setting window that are 28 and the

simulation time for this is 200 hours out of which 23 hours are warm-up time.

Irfan Zia Page 36

Optimisation settings Algorithm MME NSGA-II Name Value Total Number of Evaluations 5000 Max Number of Parallel Evaluations 20 Mutation Size 0.1 Crossover Frequency 0.5 Crossover Operator Uniform Population Size 100 Child Population Size 100 Number of Candidates 500 Reproduction Selection Operator Tournament Significant Domination Confidence 0.9

Table No: 6 Optimisation algorithm and corresponding parameters

The optimisation experiments have also been performed with CONWIP,

KANBAN and DBR. The model building of these PCM is shown respectively in

figure number 18A, 18B and 18C.

Irfan Zia Page 37

Figure No: 18A CONWIP Production control mechanism

Figure No: 18B KANBAN Production control mechanism

Irfan Zia Page 38

Figure No: 18C DBR Production control mechanism

Irfan Zia Page 39

5. Experiments, Results and Analysis

5.1 Experiment No: 1 Simple unpaced flow line The experiment has performed to calculate the warm up time and number of

replication in a simple unpaced flow line. There are total 15 machines and all

machines have average processing time of 240 seconds per part. The proc time

has lognormal distribution where the standard deviation is 120 seconds and the

upper bound limit is set to infinity (∞) and lower bound limit is set to zero.

Between each two workstations there is a buffer that has finite capacity of 5 to

hold the parts temporarily; the buffers have 0 in processing time. The first

machine can always pull in material, and the last one can always push finished

parts to the drain. The simulation length is 200 hours.

Steady State Analysis Result

Figure No: 19A steady state analysis of experiment no: 1

After the transient state the system is seems to be stable, the transient time is 26

hours as shown in figure no: 19A.

Moving Avg

0,00

2,00

4,00

6,00

8,00

10,00

12,00

14,00

16,00

1 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196

Moving Avg

Irfan Zia Page 40

Replication Analysis

Repl. MEAN STDEV Std. error 95%

% (utr) Absolute precision



10 13,7 0,06981 0,05 THP 0,70% 0,1 2,4393 10 217,3 11,73 8,39 CT 2,30% 5 28,1644 10 49,61 2,676 1,91 WIP 2,00% 1 36,6619 10 49,6 2,724 1,95 Little_WIP 2,00% 1 37,9884 Run 2

37 13,69 0,07871 8,39 THP 0,70% 0,1 2,548 37 216,3 9,327 3,11 CT 2,30% 5 14,3123 37 49,38 2,173 0,72 WIP 2,00% 1 19,4185 37 49,35 2,156 0,72 Little_WIP 2,00% 1 19,1215

Run 3 19 13,69 0,0747 0,04 THP 0,70% 0,1 2,4656 19 218,3 10,04 4,84 CT 2,30% 5 17,9709 19 49,87 2,316 1,12 WIP 2,00% 1 23,6774 19 49,82 2,364 1,14 Little_WIP 2,00% 1 24,669 Run 4


Run 5 20 13,7 0,074 0,03 THP 0,70% 0,1 2,395 20 218 9,849 4,61 CT 2,30% 5 16,994 20 49,81 2,27 1,06 WIP 2,00% 1 22,5656 20 49,77 2,313 1,08 Little_WIP 2,00% 1 23,44295 Run 6




21 13,69 0,075 0,03 THP 0,70% 0,1 2,4397

Irfan Zia Page 41

21 217,6 9,774 4,45 CT 2,30% 5 16,6258 21 49,69 2,276 1,04 WIP 2,00% 1 22,54021 21 49,66 2,308 1,05 Little_WIP 2,00% 1 23,168

Figure No: 19B Replication analysis of experiment no: 1

The repeated number is 23 after nine simulation runs so the required numbers of

replications are 23 in here as shown in figure no: 19B.

The simulation run output values with the calculated warm-up time and number

of replications are shown here.

Target value avgTHPerHr avgCTInMin avgWIP Littles_WIP

Exp 1 13.69

217.4

49.64

49.62

5.2 Experiment No: 2 The effect of a non-balanced line The experiment has performed to calculate the warm up time and number of

replication in a non-balanced flow line. Keeping the same settings except the

bottleneck experiments has been performed. The machine M8 has little longer

processing time than all others the processing time of machine M8 is 360

seconds and standard deviation is 180 seconds.

Steady State Analysis Moving Avg

0,00

2,00

4,00

6,00

8,00

10,00

12,00

1 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196

Moving Avg

Figure No: 20A steady state analysis of experiment no: 2

Irfan Zia Page 42








10 10 0,10920 0,08 THP 1,00% 0,1 6,102262 10 288,8 2,8873 2,07 CT 1,70% 5 1,70643 10 48,1 0,1693 0,12 WIP 2,10% 1 0,1466 10 48,14 0,191 1,95 Little_WIP 2,10 % 1 37,9884 Run 2

6 9,96 0,11070 0,12 THP 1,00% 0,1 8,097633 6 289,8 3,091 3,24 CT 1,70% 5 2,52518 6 48,06 0,05 0,05 WIP 2,10% 1 0,0164 6 48,1 0,0995 0,72 Little_WIP 2,10 % 1 19,1215

Run 3 8 9,99 0,1116 0,09 THP 1,00% 0,1 6,963902 8 288,9 3,244 2,71 CT 1,70% 5 2,3538 8 48,04 0,064 0,05 WIP 2,10% 1 0,0226 8 48,08 0,0889 1,14 Little_WIP 2,10% 1 24,669




The repeated number is 8 after five simulation runs so the required numbers of

replications are 8 in here.




Exp 1 9.9887

288.9

48.04

48.08

Irfan Zia Page 43

5.3 Experiment No: 3A The effect of coefficient variation on simulation analysis at CV1 The experiment has performed to calculate the warm up time and number of

replication in a simple unpaced flow line with a coefficient variation of 1. The proc

time is set to 240 and standard deviation is also 240. The machine M8 which is

the bottle neck having processing time 360 seconds and standard deviation 360

seconds. The rest settings are the same settings as experiment number 5.1.


0,00

2,00

4,00

6,00

8,00

10,00

12,00

1 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196

Moving Avg

Figure No: 21A steady state analysis of experiment no: 3A After the transient state the system is seems to be stable, the transient time is 26


Irfan Zia Page 44










Figure No: 21B Replication analysis of experiment no: 3A

The repeated number is around 10 after four simulation runs so the required

numbers of replications are 10 here shown in figure no: 21B.




Exp 1 9.604

300.2

48.08

48.04

5.4 Experiment No: 3B The effect of coefficient of variation on simulation analysis at CV 1.5 The experiment has performed to calculate the warm up time and number of

replication in a simple unpaced flow line with a coefficient variation of 1.5. The

proc time has lognormal distribution where the proc time is 240 seconds standard

Irfan Zia Page 45

deviation is 360 seconds and the upper bound limit is set to infinity (∞) and lower

bound limit is set to zero, the machine M8 which is the bottle neck having

processing time 360 seconds and standard deviation 540 seconds and the upper

bound limit is set to infinity (∞) and lower bound limit is set to zero. The

simulation length is 200 hours.

Steady State Analysis

Moving Avg

0,00

1,00

2,00

3,00

4,00

5,00

6,00

7,00

8,00

9,00

10,00

1 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196

Moving Avg

Figure No: 22A steady state analysis of experiment no: 3B

After the transient state the system is seems to be stable, the transient time is 26 hours. Replication Analysis


% (utr)

Absolute precision




76 8,3 0,23070 0,05 THP 1,20% 0,1 21,12119 76 342,9 16,41 3,75 CT 1,50% 5 42,74648

Irfan Zia Page 46

76 47,38 2,022 0,46 WIP 2,10% 1 16,22984 76 47,43 1,9885 0,45 Little_WIP 2,10% 1 15,69186


33 8,3 0,1862 0,07 THP 1,20% 0,1 14,3851 33 345,8 13,7 4,86 CT 1,40% 5 31,1497 33 47,76 1,796 0,64 WIP 2,10% 1 13,38489 33 47,81 1,719 0,61 Little_WIP 2,10% 1 12,26042 Run5 31 8,31 0,1886 0,07 THP 1,20% 0,1 14,83579 31 346,2 13,81 5,07 CT 1,40% 5 31,81813 31 47,89 1,753 0,64 WIP 2,10% 1 12,81422 31 47,91 1,6641 0,61 Little_WIP 2,10% 1 11,55011 Run 6



Figure No: 22B Replication analysis of experiment no: 3B


numbers of replications are 32 here, shown in figure no:22B.




Exp 1 8.3059

346.3

47.86

47.91

By comparing the simulation result of experiment no: 3A and 3B it can be

concluded that the increase of coefficient variation cause decrease of throughput

and increase in cycle time, and work in process is almost same by the increase

of coefficient variation.

Irfan Zia Page 47

5.5 Experiment No: 4A The effect of upper and lower bound in the processing time distribution at CV 1 The experiment has performed to calculate the warm up time and number of

replication in a simple un-paced flow line with a coefficient variation of 1. The

proc time has lognormal distribution where the standard deviation is 240 seconds

and the upper bound limit is set to 960 and lower bound limit is set to 120, the

machine M8 which is the bottle neck having processing time 360 seconds and

standard deviation 360 seconds, the upper bound limit is set to infinity 1440 and

lower bound limit is set to 180. The simulation length is 200 hours.


0,00

1,00

2,00

3,00

4,00

5,00

6,00

7,00

8,00

9,00

1 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196

Moving Avg

Figure No: 23A Replication analysis of experiment no: 4A


hours, shown in figure 23A.

Irfan Zia Page 48



% (utr)

Absolute precision






Figure No: 23B Replication analysis of experiment no: 4A


numbers of replications are 9 here, shown in figure 23B.




Exp 1 8.2077

352.9

48.25

48.27

5.6 Experiment No: 4B The effect of upper and lower bound in the processing time distribution at CV 1.5 The experiment has performed to calculate the warm up time and number of

replication in a simple unpaced flow line with a coefficient variation of 1.5. The

proc time has lognormal distribution where the proc time is 240 seconds,

standard deviation is 360 seconds and the upper bound limit is set to 960 and

lower bound limit is set to 120, the machine M8 which is the bottle neck having

processing time 360 seconds and standard deviation 540 seconds, the upper

bound limit is set to infinity 1440 and lower bound limit is set to 180.

Irfan Zia Page 49

Steady State Analysis

Moving Avg

0,00

2,00

4,00

6,00

8,00

10,00

12,00

1 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196

Moving Avg

Figure No: 24A Steady state analysis of experiment no: 4B


hours.








Run 3 11 7,76

0,1301 0,09 THP 1,30% 0,1

8,403091

Irfan Zia Page 50

11 372,8 5,533 3,72 CT 1,30% 5 6,0803 11 48,19 0,257 0,17 WIP 2,10% 1 0,3268 11 48,18 0,296 0,2 Little_WIP 2,10% 1 0,4358 Run 4



8 7,76 0,1511 0,13

THP 1,30% 0,1 12,76595

8 372,4 6,234 5,21 CT 1,30% 5 8,69224 8 48,2 0,286 0,24 WIP 2,10% 1 0,4567 8 48,15 0,341 0,29 Little_WIP 2,10% 1 0,6505

Figure No: 24B Replication analysis of experiment no: 4B


numbers of replications are 13 here.




Exp 1 7.7398

373.3

48.15

48.14

The comparison of experiment no 4A and 4B shows that by the increase of CV

(coefficient variation) throughput decrease slightly by the increase of cycle time,

and work in progress more or less remains same in the line. Comparing the

result of 4A and 3A shows that by limiting the processing time limits it decrease

the throughput and increase the cycle time and the same results has been come

out from experiment 4B and 3B.

Irfan Zia Page 51

5.7 Experiment No: 5A The effect of buffer allocation on the performance of the line at CV 1 The experiment has performed to evaluate the different buffer allocation patterns.

Here the value of coefficient variation is 1. There are total 15 machines and all



upper bound limit is set to 960 and lower bound limit is set to 120, except the


standard deviation 360 seconds, the upper bound limit is set to 1440 and lower

bound limit is set to 180. Between each two workstations there is a buffer that

has finite capacity to hold the parts temporarily; the buffers capacity table is

shown in table no: 1. The total buffer capacity is 70. The buffers have 0 in

processing time. The first machine can always pull in material, and the last one

can always push finished parts to the drain.

The simulation length is 200 hours whereas steady state time is 26 hrs and 32

numbers of replications has been run so far. The results of the simulation runs

are plotted and shown in figure no: 25A, 25B and 25C. In the diagrams the X-axis

represents the different buffer patterns the number of the patterns are the same

as in table above. The Y-axis is representing two output values. Two values are

plotted in each diagram making a total of three diagrams covering all possible

combinations. This makes it possible to compare any two values against each

other.

Irfan Zia Page 52

Throughput versus Cycle-Time

Buffer Allocation Pattern vs. ThPerHour and CT

7,4

7,5

7,6

7,7

7,8

7,9

8

8,1

8,2

8,3

1 2 3 4 5 6 7 8 9 10

Patterns

ThPerHour

0

200

400

600

800

1000

1200

CT ThPerHour

CT

Figure No: 25A The graph of throughput versus cycle-time Throughput versus Work in Process

Buffer Allocation Pattern vs. ThPerHour and WIP

7,4

7,5

7,6

7,7

7,8

7,9

8

8,1

8,2

8,3

1 2 3 4 5 6 7 8 9 10

Pattern

ThPerHour

0

20

40

60

80

100

120

140

160

WIP ThPerHour

WIP

Figure No: 25B The graph of throughput versus work in process

Irfan Zia Page 53

Cycle-Time versus Throughput Buffer Allocation pattern vs. CT and WIP

0

200

400

600

800

1000

1200

1 2 3 4 5 6 7 8 9 10

Pattern

CT

0

20

40

60

80

100

120

140

160

WIP

CT

WIP

Figure No: 25C The graph of cycle-time versus work in process

5.8 Experiment No: 5B The effect of buffer allocation on the performance of the line at CV 1 UB and LB are zero The experiment has performed to evaluate the different buffer allocation patterns.

Here the value of coefficient variation is 1. Having the same settings as in

experiment 5A except the upper bound limit and lower bound limit are changed

here, that are 0 for all stations. The machine M8 which is the bottle neck the

upper bound limit is set to 1440 and lower bound limit is set to 180. The buffer

allocation patterns are shown in table no: 1.

The results of the simulation runs are plotted and shown in figure no: 26A,

26Band 26C. In the diagrams the X-axis represents the different buffer patterns

the number of the patterns are the same as in table above. The Y-axis is

representing two output values.

Irfan Zia Page 54

Throughput versus Cycle-Time Buffer Allocation Pattern vs. ThPerHour and CT

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10

Patterns

ThPerHour

0

200

400

600

800

1000

1200

CT ThPerHour

CT



0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10

Pattern

ThPerHour

0

20

40

60

80

100

120

140

160

WIP ThPerHour

WIP


Irfan Zia Page 55


0

200

400

600

800

1000

1200

1 2 3 4 5 6 7 8 9 10

Pattern

CT

020

406080

100120

140160

WIP

CT

WIP


Results The data obtained from the 10 simulation runs of each with different buffer

allocation pattern from experiment 5A and 5B shows that buffer allocation pattern

ascending that is number 2 in allocation pattern table stands out in terms of

highest throughput per hour, lowest cycle time and lowest work in process

making it the best choice for the buffer capacities.

However, if any specific output value is of particular interest (e.g. lowest possible

WIP) another buffer pattern might be more efficient in meeting that special

demand but will cause a decrease in the other performances.

5.9 Experiment No: 5C The effect of buffer allocation on the performance of the line at CV 1.5 The experiment has performed to evaluate the different buffer allocation patterns.

Here the value of coefficient variation is 1.5. There are total 15 machines and all



upper bound limit is set to 960 and lower bound limit is set to 120, except the


standard deviation 540 seconds, the upper bound limit is set to infinity 1440 and

lower bound limit is set to 180. Between each two workstations there is a buffer

Irfan Zia Page 56

that has finite capacity to hold the parts temporarily; the buffers capacity table is

shown in table number: 1. The total buffer capacity is 70. The buffers have 0 in

processing time. The first machine can always pull in material, and the last one

can always push finished parts to the drain.





as in table above. The Y-axis is representing two output values.


6,9

7

7,1

7,2

7,3

7,4

7,5

7,6

7,7

7,8

1 2 3 4 5 6 7 8 9 10

Patterns

ThPerHour

0

200

400

600

800

1000

1200

CT ThPerHour

CT

Figure No: 27A The graph of throughput versus cycle-time

Throughput versus Work in Process Buffer Allocation Pattern vs. ThPerHour and WIP

6,9

7

7,1

7,2

7,3

7,4

7,5

7,6

7,7

7,8

1 2 3 4 5 6 7 8 9 10

Pattern

ThPerHour

0

20

40

60

80

100

120

140

160

WIP ThPerHour

WIP


Irfan Zia Page 57

Cycle-Time versus Throughput

Buffer Allocation pattern vs. CT and WIP

0

200

400

600

800

1000

1200

1 2 3 4 5 6 7 8 9 10

Pattern

CT

020

406080

100120

140160

WIP

CT

WIP


5.10 Experiment No: 5D The effect of buffer allocation on the performance of the line at CV 1.5 UB and LB are zero The experiment has performed to evaluate the different buffer allocation patterns.

Here the value of coefficient variation is 1.5. The settings of the experiment are

the same as of experiment 5C, only by changing the upper bound limit and lower

bound limit of proc time with the buffers capacity table shown in table number: 1

the experiment has been performed again.





as in table above. The Y-axis is representing two output values.

Irfan Zia Page 58


012345

6789

10

1 2 3 4 5 6 7 8 9 10

Patterns

ThPerHour

0

200

400

600

800

1000

1200

CT ThPerHour

CT



0123456789

10

1 2 3 4 5 6 7 8 9 10

Pattern

ThPerHour

0

20

40

60

80

100

120

140

160

WIP ThPerHour

WIP


Irfan Zia Page 59


0

200

400

600

800

1000

1200

1 2 3 4 5 6 7 8 9 10

Pattern

CT

020

406080

100120

140160

WIP

CT

WIP

Figure No: 28C The graph of cycle-time versus work in process Results The data obtained from the 10 simulation runs of each with different buffer








By the increase of CV (coefficient variation) the throughput decrease slightly by

the increase of cycle time and work in progress more or less remains same in the

line.

Irfan Zia Page 60

5.11 Experiment Number: 6A The effect of buffer allocation on the performance of the line at CV 1 and total buffer capacity 150 The experiment has performed to evaluate the different buffer allocation patterns.

Here the value of coefficient variation is 1 and the buffer capacity is 150. The rest

settings of the experiments are the same as in experiment 5A.

The results of the simulation runs are plotted and shown in figures 29A, 29B and

29C. In the diagrams the X-axis represents the different buffer patterns the

number of the patterns are the same as in table above. The Y-axis is



7,4

7,5

7,6

7,7

7,8

7,9

8

8,1

8,2

8,3

1 2 3 4 5 6 7 8 9 10 11

Patterns

ThPerHour

0

500

1000

1500

2000

2500

CT ThPerHour

CT


Throughput versus Work in Process Buffer Allocation Pattern vs. ThPerHour and WIP

7,4

7,5

7,6

7,7

7,8

7,9

8

8,1

8,2

8,3

1 2 3 4 5 6 7 8 9 10 11

Pattern

ThPerHour

0

50

100

150

200

250

300

350

WIP ThPerHour

WIP


Irfan Zia Page 61


0

500

1000

1500

2000

2500

1 2 3 4 5 6 7 8 9 10 11

Pattern

CT

0

50

100

150

200

250

300

350

WIP

CT

WIP


5.12 Experiment Number: 6B The effect of buffer allocation on the performance of the line at CV 1, UB and LB are Zero, total buffer capacity 150 The experiment has performed to evaluate the different buffer allocation patterns.

Here the value of coefficient variation is 1 and the buffer capacity is 150. The

rest settings of the experiments are same as in experiment 5B.

The results of the simulation runs are plotted and shown in figure no: 30A, 30B

and 30C. In the diagrams the X-axis represents the different buffer patterns the



Irfan Zia Page 62


0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11

Patterns

ThPerHour

02004006008001000

12001400160018002000

CT ThPerHour

CT



0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11

Pattern

ThPerHour

0

50

100

150

200

250

300

350

WIP ThPerHour

WIP


Irfan Zia Page 63


0200400600800

100012001400160018002000

1 2 3 4 5 6 7 8 9 10 11

Pattern

CT

0

50

100

150

200

250

300

350

WIP

CT

WIP









5.13 Experiment Number: 6C The effect of buffer allocation on the performance of the line at CV 1.5 and total buffer capacity 150 The experiment has performed to evaluate the different buffer allocation patterns.

Here the value of coefficient variation is 1.5 and the buffer capacity is 150. The

rest settings of the experiments are that same as in experiments 5C.





Irfan Zia Page 64


6,9

7

7,1

7,2

7,3

7,4

7,5

7,6

7,7

7,8

1 2 3 4 5 6 7 8 9 10 11

Patterns

ThPerHour

0

500

1000

1500

2000

2500

CT ThPerHour

CT



6,9

7

7,1

7,2

7,3

7,4

7,5

7,6

7,7

7,8

1 2 3 4 5 6 7 8 9 10 11

Pattern

ThPerHour

0

50

100

150

200

250

300

350

WIP ThPerHour

WIP


Irfan Zia Page 65


0

500

1000

1500

2000

2500

1 2 3 4 5 6 7 8 9 10 11

Pattern

CT

0

50

100

150

200

250

300

350

WIP

CT

WIP


5.14 Experiment Number: 6D The effect of buffer allocation on the performance of the line at CV 1.5, UB and LB are Zero, total buffer capacity 150 The experiment has performed to evaluate the different buffer allocation patterns.

Here the value of coefficient variation is 1.5 and the buffer capacity is 150. The

rest settings of experiments are the same as in experiment 5D.





Irfan Zia Page 66


0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11

Patterns

ThPerHour

0

500

1000

1500

2000

2500

CT ThPerHour

CT


Throughput versus Work in Process


0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11

Pattern

ThPerHour

0

50

100

150

200

250

300

350

400

WIP ThPerHour

WIP


Irfan Zia Page 67


0

500

1000

1500

2000

2500

1 2 3 4 5 6 7 8 9 10 11

Pattern

CT

0

50

100

150

200

250

300

350

400

WIP

CT

WIP


allocation pattern from experiment 6C and 6D shows that buffer allocation pattern

ascending that is number 2 in allocation pattern table and small bowl that is

number 3 stands out in terms of highest throughput per hour, lowest cycle time

and lowest work in process making it the best choice for the buffer capacities.




By the increase of CV (coefficient variation) the throughput decrease slightly by

the increase of cycle time and work in progress more or less remains same in the

line.

Irfan Zia Page 68

5.15 Experiment Number: 7 Variability Imbalance The experiment has performed with different buffer allocation patterns and

workers variability imbalance to locate the bottleneck and analyze some more

performance measures. The simulation settings are described in previous

chapter. The steady state analysis graph and replication analysis are shown

below in figure no: 33A and 33B.

Moving Avg

0.00

2.00

4.00

6.00

8.00

10.00

12.00

1 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196

Moving Avg

Figure No: 33A steady state analysis of experiment no: 7 After the transient state the system is seems to be stable, the transient time is 23 hours.





10 9.3619 0.10810 0.08 THP 1.10% 0.1 5.97994 10 272.7 30.49 21.81 CT 5.50% 15 21.143 10 43.09 5.3664 3.84 WIP 7.00% 3 16.374

Irfan Zia Page 69

10 42.57 4.996 3.57 Little_WIP 7.00% 3 31.94382 Run 2

21 9.37 0.09892 0.05 THP 1.10% 0.1 4.2577 21 286.7 36.08 16.42 CT 5.20% 15 25.174 21 44.8 6.065 2.76 WIP 6.60% 3 17.784 21 45.26 5.572 2.62 Little_WIP 6.70% 3 40.38331

Run 3 25 9.37 0.0946 0.04 THP 1.10% 0.1 3.8152 25 290.9 38.66 15.96 CT 5.20% 15 28.295 25 46.11 6.477 2.67 WIP 6.50% 3 19.856 25 45.43 6.102 2.52 Little_WIP 6.60% 3 42.5233 Run 4

28 9.36 0.09069 0.04 THP 1.10% 0.1 3.4626 28 289.9 39.08 15.15 CT 5.20% 15 28.576 28 45.9 6.553 2.54 WIP 6.50% 3 20.084 28 45.25 6.157 2.39 Little_WIP 6.60% 3 42.38375 Run 5

29 9.36 0.0907 0.03 THP 1.10% 0.1 3.448 29 290.1 38.39 14.6 CT 5.20% 15 27.484 29 45.93 6.436 2.45 WIP 6.50% 3 19.314 29 45.26 6.046 2.3 Little_WIP 6.60% 3 42.5233 Run 6

27 9.36 0.09171 0.04 THP 1.10% 0.1 3.5537 27 290.9 38.39 15.19 CT 5.10% 15 27.675 27 46.24 6.416 2.54 WIP 6.50% 3 19.323 27 45.56 6.046 2.39 Little_WIP 6.60% 3 42.38375


The repeated number is around 28 after six simulation runs so the required

numbers of replications are 28 here.

The PUSH production control mechanism is modeled to analyze the performance

measures with different buffer allocation patterns and workers arrangement

patterns. Here are the detailed variability imbalance experiments with their

graphical results.

5.16 Experiment No: 7A Ascending Workers Arrangement The workers are arranged here in ascending pattern with this worker

arrangement the buffer allocation patterns shown in table no: 3 are all run one by

one and the simulation results are plotted here shown in figure number 34A, 34B

and 34C.

Irfan Zia Page 70


0

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Keeping the workers in ascending order and running the simulation with said

settings gives through put minimum of 8.6 parts per hour and maximum of10.5

parts per hour, with a lowest average cycle time of 9380 seconds and maximum

of 30516 seconds at the same time keeping the average lowest work in process

of 17.6 parts to the maximum of 74 parts in line. It shows that buffer allocation

pattern have strong effect on the performance measures. Thus in this case the

best pattern in sense of highest throughput is moving the most buffers to the end

of line keeps low cycle time and work in process at the same time. The second

best choice is keeping the most buffers around the bottleneck also gives highest

throughput with low cycle-time and work in process. The worst buffer allocation

pattern is keeping the most buffers to the front of the line.

The bottleneck position in different patterns is different but all the time among the

junior workers a worker is found as bottleneck. That is some time the first junior

in line (M12J) and some time the last junior line (M15J), as shown under the

each pattern in figure no: 34.

Irfan Zia Page 72

5.17 Experiment No: 7B Descending Workers Arrangement The workers are arranged here in descending pattern with this worker

arrangement the buffer allocation patterns shown in table no: 3 all run one by one

and the simulation results are plotted here shown in figure number 35A, 35B and

35C.


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Placing the workers in descending order and running the simulation with said




of 22.6 parts to the maximum of 79 parts in line. Thus in this case the best

pattern in sense of highest throughput is ascending that keeps low cycle time and

work in process at the same time. The second best choice is keeping the buffers

in big inverted bowl also gives highest throughput with low cycle-time and work in

process. Again the worst buffer allocation pattern is keeping the most buffers to

the front of the line.


junior workers a worker is found as bottleneck except in case of ascending buffer

allocation pattern whereas a medium worker (M11M) is found as bottleneck. The

first worker in line that is M1J and last junior in line M4J are this time found as

bottleneck as shown under the each pattern in figure no: 35.

Irfan Zia Page 74

5.18 Experiment No: 7C Bowl Workers Arrangement The workers are arranged here in bowl pattern with this worker arrangement the

buffer allocation patterns shown in table no: 3 are all run one by one and the

simulation results are plotted here shown in figure number 36A, 36B and 36C.


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Now arrange the workers in descending order and running the simulation with

said settings gives through put minimum of 8.9 parts per hour and maximum

of10.6 parts per hour, with a lowest average cycle time of 7716 seconds and

maximum of 31060 seconds at the same time keeping the average lowest work

in process of 19.5 parts to the maximum of 77.3 parts in line. Thus in this case

the best pattern in sense of highest throughput is ascending that keeps low cycle

time and work in process at the same time. The second best choice is keeping

the most buffers around the bottleneck also gives highest throughput with low

cycle-time and work in process. Again the worst buffer allocation pattern is

keeping the most buffers to the front of the line.


junior workers a worker is found as bottleneck except in case of big inverted bowl

buffer allocation pattern whereas a medium worker (M6M) is found as bottleneck.

The first worker in line that is M1J and last junior in line M15J are this time found

as bottleneck as shown under the each pattern in figure no: 36.

Irfan Zia Page 76

5.19 Experiment No: 7D Inverted-Bowl Workers Arrangement The workers are arranged here in bowl pattern with this worker arrangement the

buffer allocation patterns shown in table no: 3 are all run one by one and the

simulation results are plotted here shown in figure number 37A, 37B and 37C.


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Placing the workers in descending order and running the simulation with said




of 20.8 parts to the maximum of 75.8 parts in line. Thus in this case the best

pattern in sense of highest throughput is ascending that keeps low cycle time and

work in process at the same time. The worst buffer allocation pattern is all the

time keeping the most buffers to the front of the line.


junior workers a worker is found as bottleneck. That is most off the time last

junior (M10J) in line and sometimes the other junior found as bottleneck, as

shown under the each pattern in figure no: 38.

Irfan Zia Page 78

5.20 Experiment No: 8 Comparison of Production Control Mechanisms based on MOO This set of experiment is performed to compare different PCMs so far discussed

in detail in literature review part. Four different PCMs (Push, CONWIP, DBR and

KANBAN) are going to compare with four different workers arrangement patterns

(Bowl, Ascending, Descending and Inverted-Bowl). The objective of this set of

experiment is to find the optimal PCM, workers arrangement pattern and buffer

allocation pattern that can achieve maximum throughput at lowest cycle-time.

The simulation is run for 200 hours, the steady state time and replication analysis

made in experiment number 7 are applied here, that is 23 hours warm up time

and 28 replication in each iteration. In each optimisation 5000 iteration has been

run and optimisation is replicated five times as output measures have some

variability, it is not recommended any given course of action based on result of a

single replication [16]. The optimisation algorithm NSGA-II is applied as far as

this has been described in detail in literature review part.

Figure No: 39A KANBAN PCM with different workers arrangement patterns

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Figure No: 39B CONWIP PCM with different workers arrangement patterns

Figure No: 39C PUSH PCM with different workers arrangement patterns

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Figure No: 39D DBR PCM with different workers arrangement patterns

The data collected from five replications of each PCM is plotted in graphs as

shown in figure number 39A to 39D. The figure no: 39A shows that workers

arrangement as descending and bowl are quite close to each other, ascending

and inverted-bowl are also much alike in senses of performance when the PCM

is KANBAN. In the lower region the ascending pattern is worst than all but in

upper region is not worst than inverted-bowl. In lower region bowl and ascending

has big difference at the same cycle time in throughput, bowl produce more than

ascending and in upper region this difference is not that big.

The figure no: 39B is drawn by taking all workers patterns data when PCM is

CONWIP concern. Again in here the performance of descending and bowl; and

ascending and inverted-bowl are quite close to each other in the graph. In lower

region and around the center region the descending pattern has more

throughputs at same cycle time than all other patterns. In the upper region it’s not

true for descending, bowl take place here.

Irfan Zia Page 81

The figure no: 39C is push control strategy with different workers arrangement

pattern. Having push PCM and arranging workers in inverted-bowl pattern gives

really bad throughput than all others workers arrangement patterns. In lower

region descending pattern is superior choice and in upper region bowl gives

prolific results. In lower region there is immense difference in throughput of all

patterns at same cycle time that decrease slightly as through put increase

further.

The performance of DBR production control mechanism with different workers

arrangement patterns is shown in figure no: 39D. Here bowl pattern is worst in

lower region. There is no through put at cycle time less than 7000 seconds in this

case but in the upper region bowl has more throughput than all other patterns at

the same cycle time. Inverted bowl and ascending patterns have almost same

effect on performance in upper and lower region.

All figure of different PCM shows that in lower region by the increase of cycle

time there is slightly big increase in throughput as compare to the upper region

where by the increase of cycle time the throughput is not increased enough. So it

helps the decision makers that what they want to scarify, if they really interested

in more throughput than they have to scarify cycle-time on the other way around

if the matter is to keep low cycle-time than the options are also clear.

Irfan Zia Page 82

Figure No: 40A Ascending arrangement of workers with different PCMs

Figure No: 40B Descending arrangement of workers with different PCMs

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Figure No: 40C Bowl arrangement of workers with different PCMs

Figure No: 40D Inverted-Bowl arrangement of workers with different PCMs

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The graphs in figure no: 40A to 40D is drawn by keeping the workers

arrangement pattern to compare at the same time with different PCMs. In figure

no: 40A the graph is showing the performance of ascending workers

arrangement with four different PCMs. It is very clear that push mechanism

produce parts at very high cycle time and DBR produce parts in very less time. In

lower region DBR mechanism performance is deliberate and push is the worst

option here. On the other way in the upper region push give more throughput

than rest mechanisms. Near the center of the curve KANBAN seems to be good

choice so the matter is again here the priority set by the decision makers.

Keeping the workers in descending order and having the KANBAN production

control mechanism is a good option when the task is to produce the parts in

small number of quantity but when the issue is concern with bulk production this

choice is no longer true than any other choice among the conferred four will be

good one as the graph in figure no: 40B shows this fact from the experiments.

In this graph the attainment surfaces of all PCMs near the center region is very

close to each other. In upper region only KANBAN is shorten and the rest three

are almost give same results but in lower region every PCM have different

performance.

The arrangement of workers in a bowl pattern with different PCMs is shown in

figure no: 40C. In the lower region the first choice will be KANBAN and the

second best choice will be CONWIP mechanism. In the medium region the

attainments surfaces are very close to each other they overlap almost all the time

close to the center of the curve. If the throughput increase further by the increase

of cycle time KANBAN is not good enough option here, the other three

mechanism still produce almost same at same cycle-time.

The last workers arrangement pattern here is inverted-bowl. The performance of

this arrangement with PCMs is understandable in figure no: 40D graph. It is clear

that all PCMs produce different number of parts at the same cycle-time. The DBR

choice subject on the objective function is the significant choice in lower region

and near the center region. In the lower region push is the worst option however

Irfan Zia Page 85

as far as the throughput increase further it manage very good even at the upper

region push produce more parts than all other mechanisms.

By comparing all mechanisms together with workers arrangements discussed so

far the bowl workers arrangement pattern gives satisfactory results in upper

region and in lower region besides the bowl pattern descending pattern is as well

a healthy choice. To produce maximum through put KANBAN is not a good

option with any workers arrangement pattern, to produce maximum throughput

with lowest cycle time CONWIP, DBR and push has to be consider. If the matter

is to keep very low cycle time the DBR is seems to be a better option among

others.

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6. Conclusions and Further Work This thesis work has investigated the performance of different production control

mechanisms (PCM) comparison using multi-objective simulation optimization and

with Push PCM workers variability imbalance has also been studied. In the first

part of the thesis, the effect of buffer allocation patterns with different simulation

settings has been investigated. A simple linear production line, which is

consisted of fifteen work stations with processing time in lognormal distribution

and a space buffer between every two workstations, has been used for the

investigations and comparisons. Using the Welch method, the warm-up time has

been determined for different experiments when their simulation settings

changed according to the number of replications calculated by using the method

introduced in [15].

The different set of experiments to evaluate the effect of coefficient of variation

and processing time limits have shown that the increase of coefficient of variation

would induce the increase of cycle time and the decrease of throughput of the

system. By limiting the processing times upper bound limit and lower bound limit

would also give less throughput and cause the increase of cycle time. This effect

is apparent when comparing with those experiments in which the limits of upper

bound is set to infinity and lower bound is set to zero.

The results of buffer allocation patterns experiments with different simulation

parameters revealed in all experiments have shown that the ascending

(1,1,2,2,3,3,4,4,…..) buffer allocation pattern stands out in term of the highest

throughput and at the same time by keeping minimum cycle time and work in

process; no matter what value of the coefficient of variation and processing time

bound limits. The worst buffer allocation pattern is moving all buffers to the front

of line gives really bad results in the sense of low throughput with longer cycle

time and higher work in process. This set of experiment has studied with two

buffer capacities 70 and 150 total buffers in the line. The increased buffer

capacity didn’t help to increase the throughput consequently it causes to increase

the cycle time and work in process in the line.

Irfan Zia Page 87

The workers variability imbalance with different allocation patterns and different

buffer allocation patterns gives a clear insight of arranging workers of different

capability in line to attain the desired system performance (i.e. the goal of

experiments is to attain maximum throughput by keeping minimum cycle time

and work in process). From the point of view of proposed four different

arrangements of workers, it is found that the descending workers arrangement by

keeping buffers in ascending order gives truly good results although keeping

workers in bowl pattern have almost results like descending pattern but keeping

in mind the said goal descending is better than others. In the same experiments,

the bottleneck detection shows that mostly the junior workers are the bottleneck.

Simulation based multi-objective optimisation experiments with four different

PCMs and four different workers variability imbalance gave clear insight of each

PCM to facilitate decision makers in which region they perform best with which

workers arrangement pattern. Considering the objective function of the

experiments, it is found that Push PCM performs better than others in upper CT-

TP region but at the same time this is worst choice in lower CT-TP region. DBR

is a better choice for the upper CT-TP region. For the lower CT-TP region the

KANBAN is a significantly better choice among the studied PCMs and the

second best choice for the lower region is CONWIP. The bowl workers

arrangement appears as best option in the upper CT-TP region with all PCMs,

the same way in the lower CT-TP region descending pattern is better than

others.

In continuation of this thesis, it is recommended that more experiments have to

be made for other production control mechanisms with different variability

imbalance patterns as well as with different objective functions of experiments

which can be taken into account in the decision-making process of designing

production systems.

Irfan Zia Page 88

References [1] Amos H.C. Ng, Jacob svensson and Matias Urenda Moris “Multi-Objective Simulation Optimisation for Production Systems Design using FACTS Analyser” Proceedings of the 2008 Winter Simulation Conference [2] http://www-new.mcs.anl.gov/otc/Guide/OptWeb/opt.html [3] Kalyanmoy deb “Multi-Objective Optimisation Using Evolutionary Algorithms” John Wiley & Sons Ltd, 2004. [4] Q. Wang and C.R Chatwin “Key issues and developments in modeling and simulation-based methodologies for manufacturing systems analysis, design and performance evaluation” International Journal Advance Manufacturing Technology (2005) [5] Jay April, Fred Glover, James P. Kelly and Manuel Laguna “Practical Introduction to Simulation Optimisation” Proceedings of the 2003 Winter Simulation Conference [6] Averill M. Law “Simulation and Modeling Analysis” McGraw Hill fourth edition [7] M. Stevenson, L. C. Hendry and B. G.Kingsman “A review of production planning and control: the applicability of key concepts to the make-to-order industry” International Journal of Production Research March 2005 [8] S.G. Koh and R. L. Bulfin “Comparison of DBR with CONWIP in an unbalanced production line with three stations” International Journal of Production Research January 2004 [9] George Liberopoulos and Yves Dallery “A unified framework for pull control mechanisms in multi-stage manufacturing systems” Annals of Operations Research 93 (2000) 325–355 [10] W. H. Ip · Min Huang · K. L. Yung · Dingwei Wang · Xingwei Wang “CONWIP based control of a lamp assembly production line” Journal Intelligent Manufacturing Technology (2005) [11] Sean M. Gahagan and Jeffrey W. Herrmann “Improving Simulation Model Adaptability with a Production control framework” Proceedings of the 2001 Winter Simulation Conference [12] Richard P. Marek, Debra A. Elkins and Donald R. Smith “Understanding the Fundamentals of KANBAN and CONWIP Pull System using Simulation” Proceedings of the 2001 Winter Simulation Conference

http://www-new.mcs.anl.gov/otc/Guide/OptWeb/opt.html

http://www.amazon.com/exec/obidos/search-handle-url/ref=ntt_athr_dp_sr_1?%5Fencoding=UTF8&search-type=ss&index=books&field-author=Kalyanmoy%20Deb

Irfan Zia Page 89

[13] Amos Ng, Matias Urenda Moris, Jacob Svensson, Anders Skoog and Björn Johansson “FACTS Analyser: An Innovation Tool for Factory Conceptual Design Using Simulation” Proceedings of the Swedish Production Symposium, 2007 [14] Goldberg, D. “Genetic algorithms in search, optimization, and machine learning”. Addison-Wesley: (1989) [15] Christopher A. Chung “Simulation Modeling Handbook” CRC press 2003

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