systems thinking term project: scheduling a fleet of road tankers
TRANSCRIPT
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
1/31
MIDDLE EAST TECHNICAL UNIVERSITY
I E 3 9 8 - S Y S T E M S T H I N K I N G
Term Project:
Scheduling a Fleet of Road
Tankers
May 2011, Ankara
Burcu Yzak - 1627884
Fato lbi - 1535459
Onur Ylmaz - 1627868
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
2/31
1
Table of Contents
PAGE
Table of Contents .............................................................................................................. 1
1. INTRODUCTION .. 2
1.1. Project .............................................................................................................. 2
1.2. Related Issues ........................................................................................................ 2
1.3. Approach ............................................................................................................ 2
1.4. Recommendations ................................................................................................ 2
2. REPORT .... 3
2.1. Statement of the Problem....................................................................................... 3
2.2. Analysis of Specific System...................................................................................... 5
2.3. Scale Decisions and Critiques.................................................................................. 8
2.4. Major Steps of Analysis and Findings...................................................................... 9
2.5. Alternative Actions.................................................................................................. 14
2.6. Recommendations................................................................................................... 16
3. CONCLUSION .................................................................................................................. 17
4. GLOSSARY . 18
5. APPENDIX .... I
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
3/31
2
1. INTRODUCTION
1.1. Project
This project is related to planning the fleet size and its content; and scheduling the
fleet of Transport Department of Asit Kimya in order to meet the next periods demand. This
project is not only based on managerial trade-offs and decisions but also includes engineering
approaches like planning and scheduling considering the limitations and objectives.
1.2. Related IssuesIn this project, not all the operations of the Asit Kimya or Transport Department are
considered. Scheduling the current fleet, changing the size and its content are the main
concerns of this study; on the other hand, maintenance operations, purchasing operations and
limitations of these operations are not considered in the concept of this study. In addition,
assumptions are made on the unknown or unspecified details of the operations while
considering the main structure of the problem situation.
1.3. Approach
The manager is not willing to clean the tankers since it is hazardous to cleaning
workers. He finds the cleaning decision reasonable only when he will need to buy a new
tanker in order to meet the demand of the next year.Thus, his approach to cleaning and
purchasing decisions will be reflected to the solution approach by using step by step
approach. At each step, cleaning or buying one more additional tanker options will be
compared. In addition to these, alternative actions will also be introduced.
1.4. Recommendations
It is recommended that Transport Department of Asit Kimya should proceed with a
preliminary analysis of the transportation operations in detail by its costs and critical
requirements. The analysis would develop a model for finding optimal scheduling scheme as
well as optimal fleet size, i.e. exact numbers specifically for every type of tanker, via
indicating number of cleanings at the beginning of the year and new tankers to be bought.
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
4/31
3
According to this model, reliable estimates of the potential savings in operating costs should
be computed in order to justifying the results of the model.
In the next parts of the report, firstly, problem situation is described and then specific
system which is going to be studied is given. Following these, boundary of the system is
determined by declaring assumptions on the system. Then, major steps of analyzing this
system are shown in detail and findings and comments on these findings given in the
subsequent section. Considering these findings, alternative actions that can be taken are
mentioned and the final recommendations are made in the last section.
2. REPORT
2.1. Statement of the Problem
In this part, problem which will be solved in the next parts will be defined with
presenting different aspects and different roles of people which are involved in the problem.
Firstly, dividing the problem into smaller subsets will make it easier to analyze andrealize their effects on each other and the whole.
Since this is a business environment, whether to implement the solutions provided will
be the decision of the manager of the Transport Department of Asit Kimya and thereafter he
will be mentioned shortly as manager. Since this project aims to solve a problem, there will
be an objective or some objectives. In this manner, the managers objective is to operate the
Transport Department successfully by the means of its measurable and immeasurable aspects.
In order to control how well the main objective is reached, this one objective can be
divided into more specific goals on different areas which would provide rather small
environment to consider for a more focused study. First of these goals is the minimizing the
total costs which is the sum of transportation costs, procurement costs and operating costs.
Second is to minimize number of cleanings and damage of this cleanings on the cleaning
workers. As the third goal, it is aimed to minimize the spare time of trucks throughout the
year. For the last, it is aimed to minimize the possible threats to public safety caused by
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
5/31
4
accidents etc. These specified goals will determine how well the solutions satisfy the main
objective.
These objective and goals should be measured by some means, in order to compare
different actions. These means could include numerical measurements like total transportation
cost, procurement cost, operating cost; or in short overall total costs, or rates and counts such
as number of cleanings and proportion of the spare time to the all available time. On the other
hand there are some aspects which are difficult to assign numeric values but reveals the
performance of the solutions, like amount of damage given to cleaning workers and amount
of damage caused by tanker accidents
In order to derive a proper solution to the problem, there shall be different actions to
be taken in this problem environment, and those can be listed as the following; determining
number of tankers to buy and sell, number of compartments to clean and finally allocation of
tankers to route. These actions, individually or as a group, will shape the solution provided to
this problem.
Finally, there is an environment in which this problem is emerged and needed to be
solved. Therefore, context of the problem which affects the situation must be presented. There
are some direct relationships that no one has control on them, such as cleaning operations
effects on health problems; also, some legal and operational limitations which cannot be
changed, like the limitation of 16.5 tons for any type of material stated by law and
minimum/maximum level of materials to be delivered to a depot due to the capacities of these
depots. In addition to these, costs of new tankers or salvage, taxes, insurance and
transportation cost per kilometer are taken as given. Since the problem is about planning the
succeeding year, and the manager stated so, demand forecasts of the next year are counted as
completely reliable. Moreover, due to security issues, maintenance operations and their time
requirements, which is 40 % of the total annual time, are also included in the problem
environment.
Secondly, presenting the different roles of individuals which are included in the
problem situation would make the problem statement more clear. The owner of this problem,
who has the full responsibility of the possible consequences of this problem, is the manager ofthe Transportation Department. When the problem is solved, people who are going to execute
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
6/31
5
the decisions are the tanker drivers, cleaning and maintenance workers. In addition, there are
the ones who would benefit or would be victim of the consequences of these implemented
decisions. They are other depots which are in Asit Kimyas transportation network, cleaning
and maintenance workers and publicity, due to the possible threats. This problem will be
solved and recommendations will be provided by the analysts in OR Department of the Asit
Kimya.
To conclude, in this part, problem is divided into parts and each part is described in
detail. Following that, different roles of individuals are mentioned in order to provide a full
explanation of the problem statement. In the following part, specific system which this
problem is emerged will be explained.
2.2. Analysis of Specific System
In the previous section, the problem is stated and in this following section, system in
which the problem is emerged is going to be studied and the point of view will be fixed for
the next phases of providing solution.
In this manner, if we consider the Transport Department as a black box then it will
transform existing routes, tankers and workers; with the possible new additions/removals into
a new route scheduling for the following year. In order to accomplish this transformation,
some sub-components of the system; namely, cleaning system, maintenance system, fleet of
tankers, factory and pre-determined routes; are used.
Considering this system as a black box it is convenient to look out for some inputsand outputs. First of all, these inputs can be gathered into two subsets as the ones which are
not in the control of the system and the ones which are going to be decided. The first set
consists of demand forecast, number of on-hand tankers and their types, number of current
workers and wages, costs of procurement, mileage cost, taxes and insurance, limits of other
depots, security limits of carriage, maintenance time limit, current compartment allocation of
tankers, existing routes and capacity of tankers and compartments. And the second set
includes the inputs which could be decided; explicitly, number of new tankers, number of
tankers salvaged, number of cleanings and capacity usage of compartments.
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
7/31
6
Besides these controllable and uncontrollable inputs, there should be some outputs of
the system. Although, some of them are difficult to measure; these expected outputs of the
system could be listed as; total cost (transportation cost, procurement cost, operating cost),
damage given to cleaning workers, spare time of tankers, damage caused by tanker accidents
and a new schedule of tankers.
All aspects of the system mentioned could be summarized by the given diagram which
shows the narrow system of our interest specifically:
Diagram 2.2: Narrow system of interest
As summarized in the influence diagram below, controllable inputs are shown with
rectangular and uncontrollable ones are shown with clouds. The different situations of the
system, which are formed by taking these inputs and processing them, are indicated by
circles. Outputs which are shown with ovals should be mentioned according to their
importance in the objective of the system. This system is trying to accomplish its objective by
minimizing total costs, number of cleaning operations, spare time of tankers, damage given to
cleaning workers and damage caused by tanker accidents.
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
8/31
7
Diagram 2.3: Influence diagram
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
9/31
8
2.3. Scale Decisions and Critiques
Having settled the system to be studied in the last section, assumptions and critiques
will be presented with their justifications before going any further in analyzing the system, in
the following part of this report.
First of all, as mentioned before, demand forecasts are taken as given for the planning
of next years operations without any concern. As known, Transportation Department
Manager implied that there are negligible deviations in the numbers when previous years
forecasts considered. Therefore, it is reasonable to assume that forecasts are totally true for
next year.
Secondly, being a decision maker, Transportation Manager is presumed that has some
authority limitations and relaxations. Although there are any clear evidence; Transportation
Manager is counted as having the power of buying and selling tankers without any restrictions
like smooth level of resources or monetary issues. On the other hand, manager has some
restrictions, for instance; it is regarded as he has no chance to change the other depots
load/unload demands and capacities.
Thirdly, there are some assumptions about operations of the factory and its sub-
departments. All considerations are made in an environment such that the workforce is fixed.
That is because, any cost of hiring new drivers or workers for maintenance when new tankers
are bought is given; in addition to these, also any cost for firing employees when the size of
fleet is decreased is mentioned. Considering all of these, workforce is taken as constant for
the following year or there would be no effect of changing the level of workforce for our
concern. The second issue about operations is the currently used routes. Routes which are
currently using will be used without any change in the following year. This assumption would
not only will ease the analysis of the recommendations, but also, fix the focus of the study to
more important aspects of the situation. Finally, since it is mentioned that, due to security
issues, any change is considered on the maintenance checks, therefore, total available time of
one tanker is taken as 5240 hours annually.
Fourthly, there are some assumptions about types and assignments of tankers. It is
assumed that when the manager wants to buy new tankers, the only available tankers are the
ones which are mentioned in the question text, i.e. A, B, C, D; and there is no other option. In
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
10/31
9
addition, it is assumed that any type of tanker could be assigned to any of the routes without
any restriction like road conditions, insurance restrictions etc.
Fifthly, there are some immeasurable aspects which cannot be directly included in the
cost calculations. For instance, there is no assigned cost of cleaning one tanker and more
importantly there is no fixed cost of the damage given to the cleaning workers. Therefore, it is
assumed that minimizing the number of cleanings could minimize both of these and it will
satisfy the concerns of the manager.
Finally, in this project it is tried to give a scheduling output which only includes
assignment of one type of tanker to one route and this approach is undertaken in order to
avoid combining or dividing routes throughout the next planning horizon. Since this approach
of assignment seems to ignore idle time of the tankers by not assigning them to other routes in
their idle times, and since spare time of the tankers are tried to be minimized, at all steps of
analysis, idle time percentages are checked prior to making any recommendations.
Considering these assumptions and decisions made to fix the scale of our view, our
solution approach to the problem will be presented in the following part.
2.4. Major Steps of Analysis and Findings
First of all, the main thing that should be focused on, while constructing the model of
the system, is the trade-off between the number of cleanings and the number of new tankers to
be bought. If a tanker is cleaned, it will not affect the total cost considerably but the harm that
will be given to the cleaning workers must be taken into consideration. On the other hand, if a
new tanker is bought, only the high level of cost will be considered; however, the
responsibility on the health of the cleaning workers is not so easy to consider. So the manager
is willing to undertake the cleaning if he can see that it will save him from purchasing another
vehicle to transport the forecast of the coming year.
Due to the trade-off explained above, it is thought that solving the problem using one
model will not be effective on finding a solution. Therefore, to solve the problem different
models; in fact modified models, are used in each step. Note that the number of tankers
allocated to routes, number of tankers cleaned and the number of new tankers bought are
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
11/31
10
defined as integer numbers in the models in order to find a logically valid solution. However,
number of times a tanker completes its route is assumed to be a real number to make the
solver of the problem, GAMS, solve efficiently. Moreover, salvaging the unnecessary tankers
is also considered in each step.
The major steps followed in order to reach the best solution to the problem are
summarized below:
a) First Step:
In this step, the aim of the model is to be acquainted with the system and to see
whether the tankers on hand will be sufficient to meet the demand of the next year without
cleaning the existing ones. The model is constructed using the idea that depots are covered byroutes. It means that if the demand of the depot is going to be satisfied then there must be at
least one tanker which is assigned to the routes covering that depot.
The idea behind this model is to assign types of tankers (A,B,C,D) to the routes. So an
assumption made here is that this assignment is done at the beginning of a year and it does not
change during the year. Decision variables are defined for each route and each tanker type
indicating the number of tankers of given type assigned to the given route. In addition to
these, there are also decision variables for each tanker type indicating the number of salvaged
tankers and one more decision variable for number of times a tanker completes its given
route. The model includes constraints mentioned by the manager of the company. First of all,
there are demand satisfaction constraints to satisfy the demands of the next year. Moreover,
maintenance constraints saying that 40% of a year a tanker should be in maintenance, legal
restrictions obligating a delivery amount no more than 16,5 tons and the restrictions of the
depots on the delivery amounts are also included.
The details of the model and brief explanations of the constraints can be found in
Appendix A.
Findings: In this step, it is expected to find out whether or not the current situation is
sufficient for the next periods. Solving the model explained in the first step of analysis, it is
found that it is not possible to meet the demands of the next year without changing the
number of on hand tankers. Therefore, the manager should take any actions like either
existing tankers should be cleaned or the manager should buy new tankers. Details of thesolution are given in Appendix B showing that the solution is infeasible.
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
12/31
11
b) Second Step:
In the last part, it is shown that it is impossible to meet the demand of the next
planning horizon with the current number of tankers. Since manager is willing to undertake
cleaning only if it saves him from buying a new tanker, and current number of tankers is not
enough, it is thought that, what would happen if the model gives full permission to cleaning
operation?
With this reasoning, firstly, new decision variables are added in order to determine
whether or not a cleaning operation is undertaken, how many of tankers are cleaned and
combining these with the current level of the tankers, number of tankers is updated. Secondly,
some constraints related to change in the number of tankers due to cleaning operation are
added and one more constraint related to assigning number of cleaned tankers is added.Thirdly, since there is no determined cost of the cleaning, and this step only checks whether
cleaning is a solution to infeasibility of the first step, no cleaning related cost is added to
objective function. Finally, it is thought that only cleaning between A-B types and C-D types
considered since, for instance, A-D cleaning exceeds the 16,5 tons of legal carriage amount.
Changes described above are made to the model of the first step and it is provided in
the Appendix C.
Findings: By solving the model of the second step, it is found that it is impossible to
meet the demand of the next period even with the restrictions on cleanings are removed. This
result means that there should be an increase in the total numbers of tankers because in this
step all operationally feasible compartment combinations of the currently available trucks are
tested. As given in the Appendix D, relaxing the considerations on cleaning will also yield an
infeasible solution.
c) Third Step:
In the last part, it is shown that it is impossible to meet the demand of the next
planning horizon with the current number of tankers even if the cleaning operations are
undertaken. Therefore, this step is focused on what would happen if we let manager buy any
number of tankers which yields the minimum cost. This step will going to be a base step for
the following steps, because this will provide a direction on the type and number of tankers tobuy and trade-offs between new tankers and cleanings will be made on this direction.
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
13/31
12
With this reasoning, some changes are made to the model in the first step. First of all,
number of tankers and their types are added to decision variables and this will determine the
total number of tankers with their types. Secondly, a constraint added to ensure that the new
bought tankers are added to the number of the related tankers. Thirdly, objective function is
updated to include new purchase cost.
Changes described above, which are made to the model in the first step, are given in
the Appendix E in detail.
Findings: In this step, it is expected to find the optimal number of trucks with the
minimum total cost. Because, since in the last two steps yield infeasible solutions, in this step
purchase is allowed with no number limitation. As given in the Appendix F, this step has a
minimum cost level of $ 110.846,73 and route-tanker assignments with related numbers can
be seen from the Table 2.5 below:
As tabulated above, result of this step shows that the minimum cost is attained when 4
new D type tankers are purchased and shown assignments are made. As mentioned in the last
parts related step above, since this step creates a basis for the direction ofthe following steps,
in the next steps trade-offs will be made considering this 4 new D type tankers.
It is shown that it is impossible to meet the demand of the next planning horizon
without any purchase. In addition, it is found that if all new purchases made on type D and no
cleaning is made then the minimum cost will be attained. Therefore, in the next steps,
purchasing one more D type tanker and cleaning trade-off will be compared. With this
reasoning, in the next steps, 8000 of new purchase cost will be added to total cost function
and on hand D type tanker will be increased by one in each step. Then it is checked whether
or not the model is feasible without buying any additional tanker and cleaning the on hand
tankers. This iterative controls are made for considering that we have one, two and three D
types of tankers on hand, because if were to buy 4 D type tankers, considering any cleaning
R O U T E S TOTAL
TANKERS
1 2 3 4 5 6 7 8 9 10 11 12
TANKERS A 1 1
B 3 3
C 1 1 1 1 1 1 6
D 1 1 2 4
Table 2.5.1: Information gathered from Appendix F
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
14/31
13
will be unnecessary since the manager wants to undertake cleaning only if it saves him from
buying any additional tanker.
d) Fourth Step:
In this step, it is checked whether or not it is possible to purchase one D type tanker
and undertake cleaning operations to meet demand. With this approach, changes made to
model of the Second Step are provided in Appendix G.
Findings: By solving this model, it is found impossible to meet demand with one
additional D type tanker and letting cleaning operation if there is any need.
e) Fifth Step:
In this step, it is checked whether or not it is possible to purchase two D type tankers
and undertake cleaning operations to meet demand. With this approach, changes made to
model of the Second Step are provided in Appendix H.
Findings: By solving this model, it is found impossible to meet demand with two
additional D type tankers and letting cleaning operation if there is any need.
F) Sixth Step:
In this step, it is checked whether or not it is possible to purchase three D type tankers
and undertake cleaning operations to meet demand. With this approach, changes made to
model of the Second Step are provided in Appendix J.
Findings: By solving this model, it is found impossible to meet demand with three
additional D type tankers and letting cleaning operation if there is any need.
Considering the fourth, fifth and sixth steps, it is found that the manager cannot use cleaning
to save himself from buying additional D type tankers.
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
15/31
14
2.5. Alternative Actions
As explained above, the first feasible solution to this problem is found in the third step
in which the cleaning option is not considered and buying new tankers is taken into
consideration only. The decision was to buy 4 new type D tankers. Then in order to reflect the
trade-off between cleaning decision and buying decision, the model including cleaning in
second step is modified to reach a feasible solution by increasing number of type D tankers on
hand by one in each step up to three type D tankers. In these steps, it is found that cleaning
cannot overcome the need for type D tankers. So it is concluded that the best solution to that
problem is to buy 4 new type D tankers. However, some alternative scenarios are also found.
While deciding on each scenario, the idea was to see whether other tanker types can be
bought instead of type D tankers when the cleaning is also considered. To be able to compare
each scenario easily all combinations of options are shown by using tables. Since buying a
type B tanker will result in cleaning them and increasing the number of type A tankers due to
larger demand for acidic than for caustic and larger acidic capacity of type A tankers than of
type B tankers; while tabulating only purchase of type A tankers are combined with purchase
of type C tankers. Each feasible scenario has the cost value and the number of cleaning donein that scenario. Moreover, some of the scenarios are cancelled since they include buying
more than four tankers, which will directly be more costly than buying four new type D
tankers.
Number of type A tankers bought
Number of
type C
tankers
bought
0 1 2 3
0Fourth Step
Infeasible Infeasible Infeasible
Cost:
116.204,48
# of Cleanings:
2 (C type)
1 Infeasible Infeasible
Cost: 111.646,73
# of Cleanings:
3 (C type)
-
2 Infeasible
Cost: 111.646,73
# of Cleanings:3 (C type) 1 (B Type)
- -
3
Cost: 111.646,73
# of Cleanings:
3 (C type)
- - -
Table 2.5.2 : Number of A and C type tankers ara compared when number of on hand D type tankers is 1
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
16/31
15
Number of type A tankers bought
Number of
type C
tankers
bought
0 1 2 3
0Fifth Step
InfeasibleInfeasible
Cost: 111.646,73
# of Cleanings:
2 (C type)
-
1 Infeasible
Cost: 111.646,73
# of Cleanings:2 (C type) 1 (B Type)
- -
2
Cost: 111.646,73
# of Cleanings:
3 (C type)
- - -
3 - - - -
Table 2.5.3 : Number of A and C type tankers ara compared when number of on hand D type tankers is 2
Number of type A tankers bought
Number of
type C
tankers
bought
0 1 2 3
0Sixth Step
Infeasible
Cost: 111.646,73
# of Cleanings:
2 (C type)
- -
1
Cost: 111.646,73
# of Cleanings:
2 (C type)
- - -
2 - - - -
3 - - - -
Table 2.5.4 : Number of A and C type tankers ara compared when number of on hand D type tankers is 3
Above tables show the options when one, two and three type D tankers are bought
respectively. The options are elected by comparing the costs first, then number of cleanings
done is considered and the ones having larger number of cleanings are omitted. Thereafter,
options having larger caustic capacity are ignored since caustic demand is not high. Finally,
two alternative actions are found which are shown in Table 2.5.5 below. GAMS outputs of the
models for Option 1 and Option 2 are in Appendix K and L respectively.
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
17/31
16
Third Step Option 1 Option 2
Total Cost 110.846,73 111.646,73 111.646,73
# of cleanings - 2 ( C type ) 2 ( C type )
# of type A tankers 1 3 2
# of type B tankers 3 3 3
# of type C tankers 6 4 4
# of type D tankers 4 4 5
Table 2.5.5: Alternative Actions and Third Step Compared
2.6. Recommendations
As seen in Table 2.5.5 the cost value of buying four type D tankers is the optimal one.
Therefore, it will be better to choose this option. Moreover, in these two alternative options,
number of type A tankers are increased by buying new ones. However, buying type D tankers
is always more meaningful than buying type A tankers. The reason for that is that type D
tankers have extra caustic capacity compared to type A tankers. In addition to that, they
have the same price, 8000TL.Therefore, buying four new type D tankers is again the optimal
policy when looked from that point of view.
As mentioned before, outputs of the system are schedule of the tankers which is given
in Appendix F for the optimal case, number of cleanings done which is zero, total cost
including procurement, operating and transportation cost minus salvages, which is found to be
110,846.73TL. In addition to these, Table 2.6.1 below shows the spare time percentages of a
tanker assigned to each route for the optimal policy.
Route 1 Route 2 Route 3 Route 4 Route 5 Route 6
% spare time of tankers 0 0 45 36 66 0
Route 7 Route 8 Route 9 Route 10 Route 11 Route 12
% spare time of tankers18 31 0 69 90 96
Table 2.6.1: Spare time of tankers
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
18/31
17
As it can be seen from the above table some tankers assigned to specific routes have a
large amount of spare time. The reason for that is the assumption made which says that if a
tanker is assigned to a route at the beginning of the year, then it will not be assigned to
another route. If this assumption is considered again, then the number of tankers needed to
meet the requirements of the following year could be less than 14 since the tankers would be
assigned to different routes at their spare times.
3. CONCLUSION
In this project, scheduling the fleet of Transport Department of Asit Kimya is
analyzed. The problem is stated with all its sub-components and then the system which this
problem is emerged is described in this report. Making related assumptions, a step-by-step
solving approach is undertaken with considering the managers approach to cleaning and
purchasing. At each step, cleaning or buying one more additional tanker options are
compared. In addition, considering business environment and its future, alternative actions are
introduced. Considering all alternative actions, it could be stated that buying four D type
tankers and increasing fleet size without any cleaning is recommended and this results with
the total cost of $ 110.846,73. This is found to be the best alternative since it considers the
effect of cleanings on workers health without comparing it with any financial gain. In
addition considering the compartment sizes of D type tankers and currently having no D type
tankers on hand, it is the recommended action for manager.
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
19/31
18
4. GLOSSARY
In this part, technical expressions which are used in the report will be explained.
Mathematical model: Mathematical model is a description of a system using
mathematical concepts and language.
Decision variable: Decision variables are the variables within a mathematical model
that one can control. They are not random variables and they are related to the managers
decisions in this content.
Constraint: Constraints are the conditions in an optimization environment which are
needed to be satisfied.
Infeasible: A mathematical model is said to be infeasible if it cannot satisfy all or
some of the constraints it contains.
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
20/31
Appendix - I
5. APPENDIX
PAGE
Appendix A - Mathematical Model of the First Step Analysis ............................................ II
Appendix B - GAMS Output of the First Step ..................................................................... IV
Appendix C - Mathematical Model Changes for the Second Step Analysis V
Appendix D - GAMS Output of the Second Step ................................................................ VI
Appendix E - Mathematical Model Changes for the Third Step Analysis ........................... VII
Appendix F - GAMS Output of the Third Step .................................................................... VIII
Appendix G - Mathematical Model Changes for the Fourth Step Analysis ........................ IX
Appendix H - Mathematical Model Changes for the Fifth Step Analysis ........................... IX
Appendix J - Mathematical Model Changes for the Six Step Analysis ................................ X
Appendix K - GAMS Output of the Option 1 ...................................................................... XI
Appendix L - GAMS Output of the Option 2 ....................................................................... XII
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
21/31
Appendix - II
Appendix A - Mathematical Model of the First Step Analysis:
Sets:
i : Type of tankers {A, B, C, D}
r: Routes defined in the question {1, 2, , 12}
j: Depots {1, 2, , 11}
Parameters:
Ni : Number of on hand tankers of type i
CAi : Capacity of type i tankers for acidic
CCi : Capacity of type i tankers for caustic
Dr : Duration of route r
DTr : Distance of route r
Tj : Total demand of depot j
Decision Variables:
Xir :
{
Yir : Number of type i tankers assigned to route r
Lr : Number of times a tanker assigned to route r completes its assigned route
Si : Number of type i tankers salvaged
Objective function:
min Z = DTr * Lr *0.1 + Yir * 200 - Si * 3000Constraints:
Yir Ni * Xir ( If type i is not assigned to route r, number of total tankers assigned to
route r should be zero )
Yir Ni for all i (Sum of all type i tankers assigned to a route is smaller than its onhand amount)
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
22/31
Appendix - III
Yir * CCi * 5240 / Dr 53000 (Caustic demand of Tepe) Yir * CCi * 5240 / Dr Tj for all j ( Acidic demand of all depots )Lr ( 5240 / Dr )
*
Yir for all r ( Maintenance restriction on total number of
times a tanker assigned to route r completesthe route)
Si Ni - Yir for all i ( Number of unnecessary tankers of each typeis salvaged )
16,5 for all j
( Legal restriction on acidic )
16,5 for all j
( Legal restriction on caustic )
5,5 for all j
( Delivery amount of at most 5,5 for Hanya )
5,5 for all j
( Delivery amount of at most 5,5 for Maras3 )
15for all j except Hanya and
Mara3
( Delivery amount of at least 15 tons for
depots )
Xir , Yir , Lr , Si 0 Xir , Yir integer
THE ROUTES
1: {Tepe, Hanya}
i.e: Tepe-Hanya-Tepe
2: {Tepe, Bor}
3: {Tepe, Bor, Hanya}
i.e: Tepe-Bor-Hanya-Tepe
4: {Tepe, Hanya, Mara1}
i.e: Tepe-Hanya-Mara1-Tepe OR
Tepe-Mara1-Hanya-Tepe OR
Tepe-Mara1-Tepe
5: {Tepe, Hanya, Mara2}
6: {Tepe, Hanya, Mara3}
7: {Tepe, Hanya, eme}
8: {Tepe, Hanya, Koru}
9: {Tepe,Lara}
10: {Tepe, Lara, Hanya}
11: {Tepe, Geyve}
12: {Tepe, Hora}
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
23/31
Appendix - IV
Appendix B - GAMS Output of the First Step
GAMS Rev 227 x86/MS Windows 05/19/1120:49:34 Page 5G e n e r a l A l g e b r a i c M o d e l i n g S y s t e mSolution Report SOLVE system_1 Using MIP From line 162
S O L V E S U M M A R Y
MODEL system_1 OBJECTIVE zTYPE MIP DIRECTION MINIMIZESOLVER CPLEX FROM LINE 162
**** SOLVER STATUS 1 NORMAL COMPLETION**** MODEL STATUS 10 INTEGER INFEASIBLE**** OBJECTIVE VALUE 0.0000
RESOURCE USAGE, LIMIT 0.140 1000.000ITERATION COUNT, LIMIT 0 10000
ILOG CPLEX May 1, 2008 22.7.2 WIN 4792.4799 VIS x86/MSWindowsCplex 11.0.1, GAMS Link 34Cplex licensed for 1 use of lp and barrier.
Problem is integer infeasible.
No solution returned
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
24/31
Appendix - V
Appendix C - Mathematical Model Changes for the Second Step Analysis:
Additions
Decision Variable:
Mi : New number of tankers of type i
Ti : {
Ci : Number of type i tankers cleaned
Costraints:
Ci 10* Ti ( If there is not any cleaning on type i, the number of cleaned tankers
should be zero)MA = NA - CA + CB ( Change in tanker numbers due to cleaning )
MB = NB + CA + CB ( Change in tanker numbers due to cleaning )
MC = NC - CC + CD ( Change in tanker numbers due to cleaning )
MD = ND - CD + CC ( Change in tanker numbers due to cleaning )
Ci , Mi 0 Ti, Ci integer
Changes Made
Old:
Si Ni - Yir for all i ( Number of unnecessary tankers of each type is salvaged )New:
Si Mi - Yir for all i ( Number of unnecessary tankers of each type is salvaged )
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
25/31
Appendix - VI
Appendix D - GAMS Output of the Second Step
GAMS Rev 230 WIN-VIS 23.0.2 x86/MS Windows 05/21/1117:41:38 Page 5G e n e r a l A l g e b r a i c M o d e l i n g S y s t e mSolution Report SOLVE system_1 Using MIP From line 188
S O L V E S U M M A R Y
MODEL system_1 OBJECTIVE zTYPE MIP DIRECTION MINIMIZESOLVER CPLEX FROM LINE 188
**** SOLVER STATUS 1 NORMAL COMPLETION**** MODEL STATUS 10 INTEGER INFEASIBLE**** OBJECTIVE VALUE 0.0000
RESOURCE USAGE, LIMIT 0.093 1000.000ITERATION COUNT, LIMIT 0 10000
...
Problem is integer infeasible.
No solution returned
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
26/31
Appendix - VII
Appendix E - Mathematical Model Changes for the Third Step Analysis:
Additions
Decision Variable:
Ji : Number of bought tankers of type i
Mi : New number of tankers of type i
Costraints:
Mi = Ni + Ji for all i ( Updating the total number of tankers )
Ji , Mi 0 Ji integer
Changes Made
Old:
Objective function:
min Z = DTr * Lr *0.1 + Yir * 200 - Si * 3000
New:
Objective function:
min Z = DTr * Lr *0.1 +( Yir ]- Ji ) ) * 200 - Si * 3000+ Ji * 8000
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
27/31
Appendix - VIII
Appendix F - GAMS Output of the Third Step
S O L V E S U M M A R Y
MODEL system_1 OBJECTIVE zTYPE MIP DIRECTION MINIMIZESOLVER CPLEX FROM LINE 174
**** SOLVER STATUS 1 NORMAL COMPLETION**** MODEL STATUS 8 INTEGER SOLUTION**** OBJECTIVE VALUE 110846.7273
RESOURCE USAGE, LIMIT 0.557 1000.000ITERATION COUNT, LIMIT 33 10000
MIP status(102): integer optimal, toleranceFixed MIP status(1): optimalSolution satisfies tolerances.
MIP Solution: 110846.727273 (31 iterations, 0 nodes)Final Solve: 110846.727273 (2 iterations)
Best possible: 106318.938883Absolute gap: 4527.788390Relative gap: 0.040847
---- VAR Y Number of type i tankers assigned to route r
LOWER LEVEL UPPER MARGINAL...A.route8 . 1.000 100.000 3200.000...B.route1 . 3.000 100.000 -3088.000...C.route3 . 1.000 100.000 3200.000...
C.route5 . 1.000 100.000 3200.000C.route6 . 1.000 100.000 143.333...C.route10 . 1.000 100.000 3200.000C.route11 . 1.000 100.000 3200.000C.route12 . 1.000 100.000 3200.000...D.route3 . 1.000 100.000 3200.000D.route4 . 1.000 100.000 3200.000...D.route7 . 2.000 100.000 3200.000...
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
28/31
Appendix - IX
Appendix G - Mathematical Model Changes for the Fourth Step Analysis:
Old:
Objective function:
min Z = DTr * Lr *0.1 + Yir * 200 - Si * 3000New:
Objective function:
min Z = DTr * Lr *0.1 + Yir * 200 - Si * 3000 + 8000
On hand number of type D tankers is increased to one from zero.
Appendix H - Mathematical Model Changes for the Fifth Step Analysis:
Old:
Objective function:
min Z = DTr * Lr *0.1 + Yir * 200 - Si * 3000New:
Objective function:
min Z = DTr * Lr *0.1 + Yir * 200 - Si * 3000 + 16000
On hand number of type D tankers is increased to two from one.
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
29/31
Appendix - X
Appendix J - Mathematical Model Changes for the Six Step Analysis:
Old:
Objective function:
min Z = DTr * Lr *0.1 + Yir * 200 - Si * 3000New:
Objective function:
min Z = DTr * Lr *0.1 + Yir * 200 - Si * 3000 + 24000
On hand number of type D tankers is increased to three from two.
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
30/31
Appendix - XI
Appendix K - GAMS Output of the Option 1
GAMS Rev 230 WIN-VIS 23.0.2 x86/MS Windows 05/21/1118:04:52 Page 5G e n e r a l A l g e b r a i c M o d e l i n g S y s t e mSolution Report SOLVE system_1 Using MIP From line 188
S O L V E S U M M A R Y
MODEL system_1 OBJECTIVE zTYPE MIP DIRECTION MINIMIZESOLVER CPLEX FROM LINE 188
**** SOLVER STATUS 1 NORMAL COMPLETION**** MODEL STATUS 8 INTEGER SOLUTION**** OBJECTIVE VALUE 111646.7273
RESOURCE USAGE, LIMIT 0.046 1000.000ITERATION COUNT, LIMIT 34 10000
MIP Solution: 111646.727273 (32 iterations, 0 nodes)Final Solve: 111646.727273 (2 iterations)
R O U T E S TOTAL
TANKERS
1 2 3 4 5 6 7 8 9 10 11 12
TANKERS A 1 1 1 3
B 3 3
C 1 1 1 1 4
D 1 1 2 4
Table Appendix K-1: Information gathered from the related GAMS Output
-
7/31/2019 Systems Thinking Term Project: Scheduling a Fleet of Road Tankers
31/31
Appendix L - GAMS Output of the Option 2
GAMS Rev 230 WIN-VIS 23.0.2 x86/MS Windows 05/21/1118:18:02 Page 5G e n e r a l A l g e b r a i c M o d e l i n g S y s t e mSolution Report SOLVE system_1 Using MIP From line 188
S O L V E S U M M A R Y
MODEL system_1 OBJECTIVE zTYPE MIP DIRECTION MINIMIZESOLVER CPLEX FROM LINE 188
**** SOLVER STATUS 1 NORMAL COMPLETION**** MODEL STATUS 8 INTEGER SOLUTION**** OBJECTIVE VALUE 111646.7273
RESOURCE USAGE, LIMIT 0.062 1000.000ITERATION COUNT, LIMIT 35 10000
MIP Solution: 111646.727273 (33 iterations, 0 nodes)Final Solve: 111646.727273 (2 iterations)
Best possible: 110681.488289
Absolute gap: 965.238984Relative gap: 0.008645
R O U T E S TOTAL
TANKERS
1 2 3 4 5 6 7 8 9 10 11 12
TAN
KERS A 1 1 2
B 3 3
C 1 1 1 1 4D 1 1 2 1 5
Table Appendix L-1: Information gathered from the related GAMS Output