system dynamics of the manufacturing supply chain

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Manufacturing Supply Chain Project Team: Serdar Benderli, Raluca Eftimoiu, Lyla Fadden, Michal Leszczynski

Systems Engineering 5220 – Systems Dynamics

Final Project

December 04, 2012

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Contents

Purpose ................................................................................................................................ 3

Base Model Description ...................................................................................................... 3

Inventory Model .............................................................................................................. 4

Key Variables .................................................................................................................. 4

Reference Mode Graphs .................................................................................................. 5

Production Starts ............................................................................................................. 6

Work In Process Inventory .............................................................................................. 7

Customer Orders ............................................................................................................. 8

Desired Production .......................................................................................................... 9

Model Improvements ...................................................................................................... 9

Feedback Loops............................................................................................................. 11

System Dynamics .......................................................................................................... 12

Labor Model ...................................................................................................................... 13

Key Variables ................................................................................................................ 13

Increased Demand Impact ............................................................................................. 14

Backlog Model .................................................................................................................. 14

Key Variables ................................................................................................................ 15

Increased Demand Impact ............................................................................................. 15

Outcomes ....................................................................................................................... 17

Raw Materials Model ........................................................................................................ 19

Key Variables ................................................................................................................ 19

Calculation of the desired material delivery rate .......................................................... 20

Material delivery rate policy ......................................................................................... 20

Calculation of the feasible production starts ................................................................. 20

Basic behavior of the raw materials inventory model ................................................... 21

Raw Materials Replenishment Policies ......................................................................... 22

Threshold Policy ....................................................................................................... 22

Fixed Policy............................................................................................................... 24

Comparison ................................................................................................................... 24

Conclusion ......................................................................................................................... 24

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Purpose

The purpose of this project is to simulate various policies of inventory management. The company

maintains a Finished Goods Inventory and fulfills customer orders as they arrive. Customer orders or

demand is an exogenous variable. Customer orders may be modeled as sporadic or user defined, over a

period of time.

Ideally:

1) Product Shipment Rate equals the Customer Order Rate over a period of time

2) Desired Labor equals the Actual Labor over a period of time

3) Throughput or production completion rate equals the Desired Throughput

4) Desired Inventory equals actual Inventory over a period of time

Challenges include:

1) Inventory Management: Filling customer orders based on adequacy of inventory, while taking

backorder into account

2) Production Scheduling: Determining the rate of Production Starts based on Demand Forecast

and Labor and Inventory availability.

The following Inventory Management and Production Scheduling policies may be simulated:

1) Fixed replenishment point / Fixed replenishment quantity – when the inventory level on-hand

falls below a replenishment threshold point, the site will generate a replenishment order for a

fixed predetermined quantity.

2) Complex policy – adequate inventory levels are calculated taking backorders into account.

Base Model Description

The starting point for the project was the information presented in Chapter 18-Manufacturing Supply

Chain in John Sterman’s book Business Dynamics. The model presented in this chapter is available in

from AnyLogic, as an example model named Inventory Workforce Model. The model models the

interaction between the inventory management sector and the labor supply chain. This project aims at

improving the existing Inventory Model, simulating various inventory management policies and

simplifying the existing Labor Supply Chain model.

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Inventory Model

Key Variables

Key Variables Behavior:

1) WIP is increased by Production Starts and decreased by Throughput

2) Raw Materials Inventory is increased by Raw Materials Inventory-Order Rate and decreased by

Production Starts. Finished goods Inventory is increased by Throughput and decreased by Shipment

Rate

3) Desired Raw Materials Inventory and Raw Materials Inventory influence the Raw Materials-Order

Rate

4) Raw Materials-Delivery Rate influences Raw Materials Inventory

5) Raw Materials Inventory and Labor influence Production Starts

6) Yield Loss influences Throughput

7) Raw Materials Order Rate influences Yield via materials purity

8) Customer Order Rate influences the Desired Shipment Rate

9) Customer Order Rate influences the Demand Forecast

10) Demand Forecast influences Production Scheduling

11) WIP influences Production Scheduling

12) Inventory influences the Order Fulfillment, which influences Shipment Rate

13) Desired Throughput influences Production Starts

Component Type Units

Raw Materials Inventory Stock Units/period

Raw Materials-Order rate Flow Units/period/period

Raw Materials-Delivery Rate Flow Units/period/period

Desired Raw Materials Inventory Auxiliary Units/period

Available Labor Stock Units/period

Desired Labor Auxiliary Units/period

Production Starts Flow Units/period/period

Desired Starts Auxiliary Units/period

Throughput Flow Units/period/period

Yield Loss Constant Units/period

Desired Throughput Auxiliary Units/period/period

Work In Process Inventory-WIP Stock Units/period

Desired WIP Auxiliary Units/period

Yield Loss Constant Units/period

Manufacturing Cycle Time Auxiliary Units/period

Finished Goods Inventory Stock Units/period

Desired Finished Goods Inventory Auxiliary Units/period

Shipment rate Flow Units/period/period

Desired Shipment Rate Auxiliary Units/period/period

Customer Order Rate Flow Units/period/period

Order Fulfillment Flow Units/period/period

Demand Forecast Auxiliary Units/period

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Reference Mode Graphs

Demand

Forecast -

Sporadic

Time

Raw

Materials

Inventory

Time

WIP

Inventory

Time

Time

Finished

Goods

Inventory

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Production Starts

The production start rate is driven by the feasible prod starts from raw materials, and is

constrained by the component of the model (workweek, productivity, and the labor stock).

Feasible production starts represent the constraint on resources and is driven by the desired

production start rate. The production start rate also determines the production rate – which

determines how quickly products in the WIP inventory are moved into finished product

Inventory.

The following formulas are used to determine the production start rate:

Production_start_rate=min(Feasible_Prod_Starts_from_Materials,Labor * Workweek * Productivity)

Productivity=0.25

Workweek=40

The feasible production starts from materials represents the rate at which production can be

begun and is calculated in the Raw Materials Inventory model. This will be explained in the

“Raw Materials Model” section of this report.

Constrains from the

Labor Model.

Constrains from the

Raw Material

Model.

Primary driver is the desired

production start rate, which

governs the raw materials.

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Work In Process Inventory

The work in process inventory is increased by production starts, and depleted by the production

rate, as products are finished and moved to inventory. This rate is equal to the production starts,

however, a 3rd order delay is included to realistically represent the factory’s work process.

The production rate is defined to be:

Production_rate=delay3( Production_Start_Rate, Manufacturing_Cycle_Time )

d(Work_In_Process_Inventory)/dt=Production_Start_Rate-Production_rate

Initial value of Work_In_Process_Inventory=Desired_WIP

The desired WIP reflects the rate of production that will satisfy customer orders, taking under

consideration the cycle time.1

The Adjustment_For_WIP constant modifies production starts to keep the WIP inventory in line

with the desired level. Desired_WIP is set to provide a level of work in process sufficient to yield

the desired rate of production given the current manufacturing cycle time.

WIP_Adjustment_Time=6 weeks

Adjustment_For_WIP= ( Desired_WIP - Work_in_Process_Inventory ) / WIP_Adjustment_Time

Desired_WIP=Manufacturing_Cycle_Time * Desired_Production

Desired_Production=max(0,Expected_Order_Rate + Production_Adjustment_from_Inventory)

Desired_Inventory= Desired_Inventory_Coverage * Expected_Order_Rate

Desired_Inventory_Coverage= Minimum_Order_Processing_Time + Safety_Stock_Coverage

1 John D. Sterman, Business Dynamics (McGraw-Hill Companies 2010) p. 714.

Calculated to meet

customer orders

and maintain a

certain level of

inventory

To Inventory

Desired production

rate governs both

the labor and raw

material

inventories.

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Safety_Stock_Coverage=2 weeks

Desired production is determined by the Expected Order Rate, modified by the

Production_Adjustment_from_Inventory. Desired production is constrained to be non-negative.

To provide adequate inventory as a buffer against unexpected variations in demand or

production, the firm seeks to maintain a certain coverage of expected demand. Desired inventory

coverage is composed of two components. First, the firm must maintain enough coverage to ship

at the expected rate, requiring a base coverage level equal to the minimum order processing time.

Second, to ensure an adequate level of service, the firm maintains additional safety stocks. The

higher the coverage provided by the safety stock, the greater the service level. 2 However, there

is a tradeoff as too much safety stock can result in inventories that are too high and which

provide financial disadvantages.

Customer Orders

As orders come in, the model calculates the shipping rates based on not only current orders, but

also the backlog. The maximum order rate is also accounted for, by dividing the inventory by the

minimum order processing time. This rate is then used in conjunction with the desired shipping

rate in order to arrive at order fulfillment rate – found by using a lookup table.

Minimum_Order_Processing_Time=2 weeks

Shipment_Rate= Desired_Shipment_Rate * Order_Fulfillment_Ratio

Order_Fulfillement_Rate=Table_for_Order_Fulfillment(Maximum_Shipment_Rate/Desired_Shipment_R

ate)

Maximum_Shipment_Rate= Inventory / Minimum_Order_Processing_Time

Desired_Shipment_Rate= Backlog/Target_Delivery_Delay

The Backlog stock is explained in the “Backlog Model” section of this report.

2 John D. Sterman, Business Dynamics (McGraw-Hill Companies 2010) p. 714.

To calculate the

desired shipment

rate, backorders

must be calculated

in the Backorder

part of the model

…desired shipment

rate, with backorders

taken under

consideration.

The customer order

rate also influences

the expected order

rate, which then

drives the rest of

the model.

In this part of the model,

the maximum order

fulfillment ratio is

determined.

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Desired Production

The desired production is an output of the forecasted order rate (expected order rate), combined

with the adjustment that is needed to bring the inventory in line with safety stock requirements.

Model Improvements

The following weaknesses were identified in the model presented in Chapter 18:

1. Orders not immediately filled are assumed to be lost forever. Desired shipment rate

equals the customer order rate and order backlogs are not being modeled.

2. Production start rate always equals the desired production start rate, implying that raw

materials resources are always ample. Raw materials are assumed to be exogenous

The improvements presented in this report are:

1. The existing Labor Model was simplified. Vacancies and their attrition rate were

disregarded. A “dislike layoffs” company policy was modeled as follows:

The speed of layoff versus hiring is differentiated so that the Labor_Adjustment_Time

depends on whether there is excess or insufficient labor:

Labor_Adjustment_Time equals 100 weeks if Desired_Labor is greater or equal to actual

Labor. Labor Adjustment_Time equals 200 weeks if Desired_Labor is smaller than actual

Labor. Since the Labor_Adjustment_Time is smaller in the first case than in the second

one, this ensures that the “dislike layoffs” policy is simulated.

This part of the model

determines how much

safety stock should be

kept in inventory

The expected order rate

determines what the rate of

production is necessary to

keep u[p with future

demand.

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2. Order Backlogs were modeled and taken into account when adjusting the desired

production rate. Unfulfilled sales are no longer assumed to be lost.

3. Raw Materials Inventory model was defined and modeled.

4. Two Raw Materials Replenishment Policies were defined and modeled. A Threshold

Policy that keeps raw materials inventory at a threshold at all times and a Complex

Policy where raw materials order rate is determined by desired production start rate,

taking backlogs into account.

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Inven

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Yield Loss

Desired

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Finished

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Inven

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Shipment

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Desired

Shipment Rate

Customer Order

Rate

Order

Fulfillm

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Sy

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Labor Model

The labor resource was modeled as follows:

Key Variables

The main stock is Labor and the flows rates are Hire_Rate and Quit_Rate. The model allows for

negative Labor.

Quit Rate=Labor/Avg. Employment Duration

Hire Rate= (Desired_Labor-Labor)/Labor_Adjustment_Time

Labor Adj.Time= 150-50*signum(Desired_Labor-Labor)

If Desired_Labor>=Labor, Labor Adj. Time = 100 weeks

If Desired_Labor<Labor, Labor Adj. Time = 200 weeks

Firm dislikes layoffs

Desired_Labor= Desired_Production_Start_Rate / (Workweek * Productivity)

Productivity=0.25

Workweek=40 hours

Avg. Employment Duration=200 weeks

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Increased Demand Impact

With a step increase in order rate, Desired Labor rises above actual Labor, and Actual Labor

catches up in time:

Backlog Model

The backlogs were modeled as follows:

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Key Variables

The main stock is the Backlog and its flows are the Order_Rate and the Order_Fulfillment_Rate.

To ensure that the model begins in balance equilibrium, the initial backlog must equal the target

delivery delay’s worth of incoming orders:

Backlog Initial value = Target_Delivery_Delay * Order_Rate

Desired shipment rate is the rate of shipments that will ensure orders are filled within the target

delivery delay:

Desired_Shipment_Rate= Backlog/Target_Delivery_Delay

The goal for the interval between placement and receipt of orders is the target delivery delay:

Target_Delivery_Delay=2 weeks

Using Little’s Law, the Avgerage Delivery Delay at any moment is modeled to be equal to:

Delivery_Delay= Backlog/Order_Fulfillment_Rate

Order_Rate=Customer_Order_Rate

Order_Fulfillment_Rate=Shipment_Rate

Increased Demand Impact

With a step increase in order rate, desired shipments exceed actual shipments as the firm works

off excess backlog

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A gradual Production increase can be observed:

With backlogs:

Without backlogs:

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Outcomes

Outcome #1:

Backlog Inventory buffers orders and shipments. Therefore, Desired Shipments rise more

gradually than without backlogs. Decline in Inventory is more gradual, as can be observed in the

two graphs below.

With backlogs:

Without backlogs:

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Outcome #2:

Orders are no longer lost forever. Therefore, Shipment Rate rises above the Customer Order Rate

as the firm works off its excess backlog inventory, as can be seen below:

With backlogs:

Without backlogs:

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Raw Materials Model

Key Variables

Key Variables Behavior:

1) Desired production start rate (from Inventory model) increases Desired Material usage rate.

2) Material Usage per Unit increase Desired Material usage rate

3) Desired Material usage rate increases Material Usage Ratio and Material Usage Rate.

4) Material Usage Ratio increases Material Usage Rate.

5) Material Usage Rate increases Feasible Production Starts from Materials.

6) Feasible Production Starts from Materials increases Production Start Rate.

7) Desired Material Inventory increases Adjustment for Material Inventory

8) Material Inventory Adjustment time increases Adjustment for Material Inventory.

9) Adjustment for Material Inventory increases the Desired Material Delivery Rate.

10) Desired Material Delivery Rate increases Material Delivery Rate.

11) Material Delivery Rate flow increases the stock of Material Inventory.

12) The Material Inventory stock decreases the Adjustment for Material Inventory and the Maximum

Material Usage Rate.

13) The Material Inventory stock is depleted by the Material Usage Rate.

14) The Maximum Material Usage Rate increases Material Usage Rate.

15) The minimum material inventory coverage decrease the Maximum Material Usage Rate

The original model assumed that raw materials were infinitely plentiful and accessible. In

our Supply Chain Management and Design of Manufacturing Systems courses, we learned that

raw materials are a critical consideration when designing a manufacturing operation. Therefore,

we opted to integrate a raw materials sub-model with the rest the inventory model.

The raw materials model was created on the bases on the WIP components of the

inventory model. As the desired production rate controlled the desired production start rate,

which directly increased the WIP stock, so too does the desired production start rate now affect

Component Type Units

Feasible Production Starts from Materials Auxiliary Units/period

Material Usage per Unit Constant Unit/period

Desired Material Usage Rate Auxiliary Units/period/period

Material Usage Ratio Flow Ratio

Table for Material Usage Auxiliary Units/period [lookup]

Material Safety Stock Coverage Auxiliary Units/period

Desired Material Inventory Auxiliary Units/period/period

Desired Material Inventory Coverage Constant Units/period

Minimum Material Inventory Coverage Constant Units/period

Maximum Material Usage Rate Auxiliary Units/period/period

Materials Inventory Stock Units

Adjustment for Material Inventory Auxiliary Units/period

Material Inventory Adjustment Time Auxiliary Units/period

Desired Material Delivery Rate Auxiliary Units/period/period

Material Delivery Rate Flow Units/period/period

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the material delivery rate, which feeds the raw materials into the system. The material usage rate

now controls the original production start rate.

The primary parts of the raw material model include (1) the calculation of the desired

material delivery rate, which determines how quickly the system intends to consume raw

materials, taking safety stocks under account, (2) the material delivery policy that determines

how the material delivery rate is actually met, and (3) the feasible production start rate at

which raw materials move into the WIP in the original model.

Calculation of the desired material delivery rate

Once the inventory model determines a suitable desired production start rate for the

WIP, it is then passed onto the raw materials model. Here, it is converted to raw materials

(number of raw materials per product, in our simulation, it was a one-to-one relationship). Next,

a desired material inventory coverage time frame is calculated by adding the number of time

periods that current inventory should cover and the amount of time periods representing a certain

safety stock. The sum of these is multiplied by the current desired materials usage rate to arrive

at the desired materials inventory. This is how much raw materials are expected to be in the stock

in order to allow the system to perform optimally, without taking into account current demand.

Just as in the work in process part of the inventory model, an adjustment is calculated based on

the difference between actual and desired material inventory. It is adjusted for the time it takes to

complete an inventory adjustment cycle (essentially the lead time to wait for the materials to

arrive at the factory, combined with preparing it for storage). Finally, the adjustment and the

desired production start rate are combined to form the desired material delivery rate.

Material delivery rate policy

Once the desired material delivery rate is calculated, one of two policies is applied to

the rate, and this is finally fed into the material inventory stock.

Calculation of the feasible production starts

Orders increase the materials inventory stock, material usage depletes it. The usage rate

is calculated by considering the current inventory, and dividing it by the minimum material

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coverage time period. This will indicate the amount of materials that can be used at a given point

in time, considering current inventory. A materials usage ratio determines the usage of materials

based on the availability of the inventories to sustain the desired rate. This is achieved by

creating a look–up table, as in the case of the WIP. In essence, this ratio indicates that as long as

the inventory stock is adequate, the actual material usage rate will fulfill the desired need.

However, if this stock falls, the usage ratio will fall below the desired rate.

This ratio is then combined with the desired material usage rate to arrive at the actual

materials usage rate, which depletes the stock. Before being able to use this rate in the

inventory model to feed the WIP, it needs to be converted back into the production units, from

materials, by dividing by the material usage per unit constant. The final rate is stored in the

feasible production starts.

Basic behavior of the raw materials inventory model

With a step increase in demand, the desired materials rate is communicated to the raw

material model quickly, and the raw materials inventory catch up quickly to the demand, soon

surpassing it. This is mostly due to the fact that there are no delays in the raw materials inventory

model, and the lead times are short.

The amplified response of material deliveries to the demand is visible below. This occurs

because with the step increase in demand, not only is the inventory stock depleted faster, but the

system must replenish it to a higher level than before in order to meet customer demand.

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As the amplified response allows of inventory levels to return to normal, the desired

production starts level off, as does the resultant desired material delivery rate.

Raw Materials Replenishment Policies

We decided to implement two policies in order to further enhance the model and

demonstrate the shortfalls of ignoring dynamics in a system. AnyLogic allowed us to implement

a policy control pane. The policy types implemented are:

Fixed Policy

� Order Amount = PolicyInputRate

� When the materials inventory falls below a

certain threshold (user defined), the factory

replenishes raw materials at a fixed rate

(user defined)

Complex Policy –

� Order Amount =

desired_material_delivery_rate

� Desired Material Delivery rate is

determined through the raw materials model

Threshold Policy

In our Design of Manufacturing Systems course, a

capacity-driven safety method was presented. This

method specifies that a target inventory for a given type

of material is set, and that the system should strive to

order enough items to either meet the target level, or

order up to a certain capacity. We implemented a

simple threshold policy to demonstrate a method of

maintaining raw material inventory. The policy dictates that if the raw materials inventory drops

below a certain threshold, the system will submit orders at a user-defined replenishment rate.

The order amount determines how the material inventory stock is fed:

If PolicyType == 0 Then

If(materials_inventory < PolicyInputThreshold) Then PolicyInputRate

Else 0

Else desired_material_delivery_rate

The shortcomings of this policy are easy to demonstrate. The success of this policy is dependent

on the difference between the order rate and the replenishment rate. If the replenishment rate

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falls below the order rate, the system will not have

enough raw materials, unless the initial threshold is

high enough to maintain and adequate raw

materials inventory stock, and the spike in demand

is temporary. In the accompanying figure, it the

difference between the demand and the actual raw

rate is shown – the system uses up all raw

materials.

The raw materials inventory can only

recover when the daily replenishment rate is greater

than the order rate, and the threshold is set to an

amount higher than the demand. In this case, the

raw materials inventory recovers, and overshoots

the desired amount. This leads to inefficiencies, as

the system is incurring holding costs.

The implifcations of this threshold policy

were observed further downstream – in the WIP. It

was assumed that the raw materials inventory

would be replenished if the stock fell below 4000

units, at a rate of 2000 per day. The customer order

rate was set to 8000. To amend this, the threshold

had to be raised to the level of the customer order

demand rate, and the order rate was amended to be

equal or greater than the customer order rate.

Following a step increase in demand, the inventory

plummets and the gap between desired and actual

inventory grows.

The implication of this is that the

production start rate is throttled by the lack of raw

materials. The feasible production start rate rises

slightly, but due to the poorly chosen threshold and

reorder rate limitations, it does not allow the

system to fulfill orders.

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Fixed Policy

This policy allowed the desired material usage rate to be passed through directly to the

desired materials delivery rate. By analyzing a step increase demand, the response of this policy

can be observed.

The change in demand triggers an increase

in the desired production rate. Both labor and raw

material stocks begin to rise. Given that there are

no lead times when ordering raw materials, the

raw material inventory responds very quickly, and

the actual inventory remains high, the production

rate overshoots the customer order rates. Once the

backlog of orders begins the clear and the

inventory coverage recovers, the production start

rates being to approach the order rates again.

Comparison

The two policies were compared; the

simulation was run for 50,000 days under each scenario. The threshold policy resulted in a 0.002

fulfillment rate, while operating under the assumption that the threshold should be equal to the

mean demand of 10,000, and that the system is capable of replenishing material at a rate double

that of the threshold (20,000).

The complex policy resulted in a 0.397 fulfillment rate.

Conclusion

Adding in the raw material model into the inventory model has demonstrated the fallacy

of ignoring the dynamics in a system. To further enhance the model, we recommend combing the

two policies, and creating new ones. The fixed policy is simplistic and limited, and reacting to

change in the system often resulted in poor results. The complex policy, meanwhile, did not

account for the fact that the holding capacity of raw materials may be limited in the real world,

and that there is a limit of materials that can be ordered (and processed upon arrival) during one

day. A combination of both policies can be developed to better reflect real-world processes. A

further extension to this is to take the costs into account when running the model – such as

holding costs and expedited shipping costs, and combining these with real-world constraints

(minimum batch size, etc.), to understand the performance of the supply chain from the financial

side.

system dynamics of the manufacturing supply chain

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