The Effect of Semi-Rational Supply C hain Members on the Decision
Parameters Used in Managing the Stock of an Echelon’
Mert Edali
Industrial Engineering Department
Yildiz Technical University
Besiktas - Istanbul 34349 - Turkey
medali@yildiz.edutr
Hakan Yasarcan
Industrial Engineering Department
Bogazici University
Bebek - Istanbul 34342 - Turkey
hakan.yasarcan@boun.edu.tr
Abstract
A supply-chain is a series of connected stock management structures. Therefore, the
structure of a supply-chain consists of many cascading inventory management problens. It
is shown that the optimal inventory control parameter values suggested by the literature
are also valid for a supply-chain. The motivation for this study is to investigate the effect of
the literature suggested optimal values of the decision parameters in the presence of semi-
rationally managed supply-chain echelons. We use a soft coded version of The Beer Game
as an experimental platform to carry out the study. According to the results of the
simulation experiments, it is not rational to continue to use the optimal parameters when
other echelons’ inventories are managed sub-optimally, especially if the time horizon is
long.
Keywords: anchor-and-adjust; beer game; stock adjustment time; stock management;
supply chain management; weight of supply line.
1 This research is supported by a Marie Curie Intemational Reintegration Grant within the 7th European
Community Framework Programme (grant agreement number: PIRGO7-GA-2010-268272) and also by
Bogazici University Research Fund (grant no: 6924-13A03P1).
Introduction
A supply-chain is a series of connected stock management structures. Therefore, the
structure of a supply-chain consists of many cascading inventory management problems.
Supply chains are known for their interesting rich dynamics such as oscillations, bullwhip
effect, and chaotic behavior and, thus, subject to many scientific studies (Mosekilde and
Laugesen , 2007; Sterman, 1989; Thomsen et al., 1991). In his famous Beer Game paper,
Sterman (1989) suggests a stock control ordering policy, namely the anchor-and-adjust
heuristic, to be used in managing the level of a stock. Accortling to the results reported in
that paper, the proposed heuristic is a good representation of the decision making processes
of the participants who were managing inventories on a supply chain. Therefore, we
represent the decision making processes of the computer simulated participants (i.e., the
echelon of concem and the rest of the three echelons) using the anchor-and-adjust
heuristic. In this study, the parameters of the anchor-and-adjust heuristic are called
“decision parameters” and the variables of the same heuristic are called “decision
variables”. We optimize the parameters of the anchor-and-adjust heuristic for the selected
echelon by keeping the parameters of the anchor-and-adjust heuristic constant for the rest
of the three positions. We carry out this optimization process for each one of the four
echelons of the game, selecting them one by one. To observe the long-term effects of the
parameters on the dynamics, the time horizon is selected as 520 weeks for the simulations.
The Echelons in the Beer Game
In this study, we use a soft coded version of The Beer Game as an experimental
platform to carry out the simulations (Edali, 2014; Edali and Yasarcan, forthcoming). The
Beer Game is a four echelon supply chain consisting of a retailer, wholesaler, distributor,
and factory; there is an inventory control problem for each one of these echelons. During
the game, every participant in a group of four is responsible for one of the four echelons
and manages the associated inventory by placing orders. A supply chain can be modeled as
a series of connected stock management structures. Therefore, the structure of the game
consists of four cascading stock management problems. The orders flow from downstream
echelons towards upstream echelons and cases of beer flow in the opposite direction. The
aim of the game is to minimize the accumulated total cost obtained by the participants of a
group managing each echelon. The accumulated cost generated by each individual echelon
is calculated at the end of the game by adding up all inventory holding and backlog costs
obtained at the end of each simulated week (Sterman, 1989). A representative stock-flow
diagram for only a single echelon is given in Figure 1.
Retailer's Desired Retailer's Stodk Retailer's Weight of
Inventory Adjustrert Time Supply Line
Figure 1. A representative stock- flow diagram for the retailer echelon
The Decision Parameters and Their Values
Stock adjustment time (sat; 1/a, in Sterman, 1989), weight of supply line (wal; # in
Sterman, 1989), desired inventory (I*; S* in Sterman, 1989), and smoothing factor (0; also
@ in Sterman, 1989) are the main decision parameters of the anchor-and-adjust heuristic.
Stock adjustment time (sat) determines the intended time to close the gap between the
desired level of the stock and the current stock itself. In The Beer Game, sat represents the
number of weeks in which a decision maker wants to bring his current inventory level to
the desired level. Smaller values of sat results in aggressive corrections while higher values
correspond to mild corrections. According to Sterman (1989), the optimum value of this
parameter is one unit of time (i.e, a week). Therefore, sat is taken as one week for the
echelon of concem.
Weight of supply line (wsl) represents the relative importance given to the supply line
compared to the main stock. In other words, wsl is the fraction of supply line considered in
the control decisions (i.e., order decisions). When wel is taken as one, the main stock and
its supply line will be effectively reduced to a single stock that cannot oscillate (Barlas and
Ozevin, 2004; Sterman, 1989 and Chapter 17 in 2000; Yasarcan and Barlas, 2005a and
2005b). However, a zero value of wsl means that supply line is totally ignored in decision-
making process and it may potentially create an unstable stock behavior. According to
Stenman (1989), the optimum value of this parameter is unity. Therefore, wsl is taken as
unity for the echelon of concem.
Tt is known that the aforementioned optimal values of sat and wel are also valid for a
single isolated inventory control problem. This study focuses mainly on the values of sat
and wsl. Accordingly, the motivation for this study is to investigate the optimality of the
literature suggested optimal values of sat and wsl in the presence of semi-rationally
managed supply-chain echelons. The sat and wsl values for the semi-rationally managed
supply-chain echelons are taken as 3.85 weeks and 0.34, respectively. These values are the
averages of the estimated parameter values of the participants of The Beer Game (Sterman,
1989).
Desired inventory (I*) is another parameter of the anchor-and-adjust heuristic and it
simply represents the target inventory level. In The Beer Game, the cost function is
asymmetric; unit backlog cost is $1.00/(case week) while unit inventory holding oost is
$0.50/(case week). Therefore, it is usually less costly to have a positive on-hand inventory
than having a backlog. Comparatively speaking, a better control decreases the requirement
for large values of I* while a worse control increases this requirement. The value of I* is
assumed to be 0 for all echelons. The reason for selecting P* =0 is that if inventory and
backlog are both zero for an echelon in a simulated week, that echelon produces no costs in
that week. In this study, we do not experiment with the selected value of this parameter.
Smoothing factor (9) is the main parameter of exponential smoothing forecasting
method and it represents the weight given to recent observations in the forecasting process.
Although smoothing-factor is one of the parameters of the anchor-and-adjust heuristic, its
optimization is out of the scope of this study. Theoretically, @ can take a value between 0
and 1. A zero value of 6 means no corrections in the forecasted values. On the other hand,
when it is taken as one, the exponential smoothing method will be equivalent to a naive
forecast. It may not be practical to use a randomly selected smoothing factor value, even if
that value fall in the theoretical range. According to Gardner (1985), the smoothing factor
of a simple exponential smoothing forecasting method should be between 0.1 and 0.3 in
practice. As a reasonable value, we suggest using a smoothing factor of 0.2 in forecasting,
which is the middle point of the range suggested by Gardner (1985). This value of
smoothing factor also falls in the range of 0.01 and 0.3 that is suggested by Montgomery
and Johnson (1976). Therefore, 0 is taken as 0.2 for the echelon of concem. The value of 0
for the semi-rationally managed supply-chain echelons is taken as 0.36 per week. This
value is the average of the estimated @ value of the participants of The Beer Game
(Sterman, 1989). In this study, we do not experiment with the selected value of this
parameter.
Results for the Optimal Values of satand wal
In these experiments, the optimal value of sat that is one week and the optimal value
of wel that is unity are used as the decision parameter values of the selected echelon only.
The sat and wsl values of the other three echelons (i.e. the semi-rationally managed
supply-chain echelons) are taken as 3.85 weeks and 0.34, respectively. The results are
reported in Table 1. The experiment is repeated for all the echelons by changing the
echelon of concem for each simulation nm. Note that we focus on the supply-chain
dynamics in the long run. Accordingly, the length of simulation runs is taken as 520 weeks
(ie. ten years).
Table 1. Total cost values generated by changing the echelon of concem
The echelon Total Total Cost of | Total Cost of | Total Cost of | Total Cost
of concem | TeamCost Retailer Wholesaler Distributor | of Factory
Retailer 4715.0 701.0 1056.5 1603.0 1354.5
Wholesaler | 34684.5 6909.5 9611.0 9955.0 8209.0
Distributor 33302.0 4919.5 9162.5 10192.5 9027.5
Factory 32987.5 4401.0 8094.5 11808.0 8634.0
Extremely high costs are obtained when the echelon of concem is the wholesaler, the
distributor, or the factory. The reason behind these high cost values is the oscillations in
the dynamics as it can be observed from figures 2, 3, and 4.
Inventory Dynamics
2 Retailer
3 4 — Wholesaler
= = Distributor
— Factory
e 4
8
Si.
z
5
Se
2 84
= ‘
Sia
&
o |
o 4 d
T T
400 500
Figure 2. The dynamics of the inventories, when only the wholesaler is using the literature
suggested optimum values and the rest are semi-rational supply chain members
Backlog Dynamics
Backlog
Figure 3. The dynamics of the backlogs, when only the wholesaler is using the literature
suggested optinium values and the rest are semi-rational supply chain members
Dynamics of Orders
84 = + Retailer
— Wholesaler
— — Distributor
34 — Factory
Order
T
y 100 200 300 400 500
Weeks
Figure 4. The dynamics of the orders, when only the wholesaler is using the literature
suggested optimum values and the rest are semi-rational supply chain members
Results for the Re-O ptimized Values of satand wal
In these experiments, the optimal value of sat that is one week and the optimal value
of wel that is unity are not used as the decision parameter values of the selected echelon.
Instead, they are re-optimized for each echelon. Similar to the experiments in the previous
section, the sat and wsl values of the other three echelons (i.e., the semi-rationally managed
supply-chain echelons) are taken as 3.85 weeks and 0.34, respectively. The results are
reported in Table 2.
Table 2. The re-optimized parameter values and the corresponding total cost values
ag (1/sat) | wsl of the
Total Total
The echelon of the echelon Total Cost | Total Cost of | Total Cost of
Team Cost of
of concem | echelon of of of Retailer | Wholesaler | Distributor
Cost Factory
concem | concan
Retailer 0.8 1.0 4681.5 695.0 1042.0 1584.0 1360.5
Wholesaler O01 0.2 7495.0 1258.0 2094.0 2096.5 2046.5
Distributor 0.5 1.0 8081.5 1121.5 1870.0 2606.5 2483.5
Factory 0.8 0.6 7108.0 1137.0 1787.5 2679.5 2104.0
The extreme oosts reported in Table 1 are eliminated when the re-optimized
parameter values are used (see Table 2). Remember that the parameter values used in
obtaining the results reported in Table 2 are not valid if the other supply-chain members
use literature suggested optimal values. The reason behind the decrease in the costs values
is caused by the damping oscillations as it can be observed from figures 5, 6, and 7.
Inventory Dynamics
= Distributor
Inventory
10 20 30 40 50 60 70 80 90
i)
p=
Figure 5. The dynamics of the inventories, when only the wholesaler is using the
re-optimized parameter values and the rest are semi-rational supply chain members
Hands-On Modeling United States Energy Policy: Achieving
Emissions Targets and Exploring Scenarios
Jeffrey Rissman
Senior Analyst
Energy Innovation: Policy and Technology LLC
Workshop Date and Time
Thursday, July 23, 2015
10:30 am - 12:00 pm
Workshop Description
This workshop is a follow-up to my presentation earlier in the System Dynamics
Conference, titled “A Model of Energy Policy Impacts on Pollutant Emissions, Costs, and
Social Benefits Developed for China’s Central Government.” In that presentation, I describe
a System Dynamics model that Energy Innovation LLC developed to assist the Chinese
central government in selecting policy measures that will allow China to achieve its
emissions reduction goals. The model simulates the effects of 35 policies over years 2013-
2030 and covers the Transportation, Electricity Supply, Buildings, and Industry sectors.
For more details, please see the uploaded conference paper associated with that
presentation.
This workshop will give conference attendees a chance to use two versions of this model
(the Energy Policy Simulator):
e The version created for China, adapted for a web application interface that users
interact with via a web browser
e An improved version, loaded with a complete set of U.S. data and tuned to represent
the United States. This is a Vensim download and can be used in Vensim Model
Reader or Vensim DSS.
The model is user-friendly for beginners, but it also includes powerful features to enable
more advanced analysis to be done. The workshop will have two main sections.
First, I will demonstrate the online web application we have constructed that allows the
model to be run on a webserver and results to be visualized in a web browser. This
application was built by Todd Fincannon in the Ruby programming language and relies on
a multi-user version of Vensim running behind the scenes. China has specified emissions
Backlog Dynamics
eg == Retailer
= — Wholesaler
eo I = Distributor
= — Factory
34
o 4
a 84
= ox,
3 8
2 «©
34
2 4
e4
ae
4
orl ‘Age
T T T T T T
a 100 200 300 400 500
Weeks
Figure 6. The dynamics of the backlogs, when only the wholesaler is using the
re-optimized parameter values and the rest are semi-rational supply chain members
Dynamics of Orders
Order
Figure 7. The dynamics of the orders, when only the wholesaler is using the
re-optimized parameter values and the rest are semi-rational supply chain members
-10-
Conclusions
According to the results of the simulation experiments conducted in this study, it is
not rational to continue to use the optimal parameter values when other echelons’
inventories are managed sub-optimally. In fact, using optimal values suggested by the
literature produces approximately 3-4 times more cost compared to the re-optimized
parameter values reported in Table 2. Therefore, one can claim that the optimal values
suggested by the literature are valid only if all echelons’ inventories are managed with
these same optimal parameter values. More work is necessary to understand this counter-
intuitive result.
References
Banas, Y. and M.G. Ozevin, 2004, “Analysis of Stock Management Gaming Experiments
and Altemative Ordering Formulations”, Systems Research and Behavioral Science,
Vol. 21, No. 4, pp. 439-470.
Edali, M., 2014, Decision Making Inplications for a Selected Echelon in the Beer Game,
MS. Thesis, Bogazici University.
Edali, M. and H. Yasarcan, forthooming. A Mathematical Model of The Beer Game.
Journal of Artificial Societies and Social Simulation.
Gardner, E.S., 1985, “Exponential Smoothing: The State of the Art’, Journal of
Forecasting, Vol. 4, No. 1, pp. 1-28.
Montgomery, D.C. and L.A. Johnson, 1976, Forecasting and Time Series Analysis,
MoGraw-Hill, New Y ork.
Mosekilde, E. and J.L. Laugesen, 2007, “Nonlinear Dynamic Phenomena in the Beer
Model”, System Dynamics. Review, Vol. 23, No. 2-3, pp. 229-252.
Stenman, J.D., 1989, “Modeling Managerial Behavior: Misperceptions of Feedback in a
Dynamic Decision Making Experiment”, Management Science, Vol. 35, No. 3, pp.
321-339,
Sterman, J.D., 2000, Business Dynamics: Systems Thinking and Modeling for a Complex
Wodid, Irwin/McGraw- Hill, Boston, MA.
-l1l1-
Thomsen, J.S., E. Mosekilde and J.D. Sterman, 1991, “Hyperchaotic phenomena in
dynamic decision making”, in: E. Mosekilde, L. Mosekilde (Eds.), Complexity,
Chaos, and Biological Evolution, Plenum Press, New Y ork, pp. 397-420.
Yasarcan, H. and Y. Barlas, 2005a, “A Generalized Stock Control Formulation for Stock
Management Problems Involving Composite Delays and Secondary Stocks”, System.
Dynamics Review, Vol. 21, No. 1, pp. 33-68.
Yasarcan, H. and Y. Barlas, 2005b, “Stable Stock Management Heuristics when the
Outflow is Proportional to the Control Stock’, In: System Dynamics Society,
Proceedings of the 23"? Intemational System Dynamics Conference. Boston, MA.
-12-
targets as part of a bilateral agreement with the United States and in its submission to the
UNFCCC for the upcoming conference in Paris. Workshop participants will be asked to
design policy scenarios inside the web application that enable China to achieve these
emissions targets, as well as other non-emissions targets, such as cost minimization. This
will provide a user-friendly introduction to the model and its capabilities, without relying
on locally installed software on participants’ computers. I will also answer questions about
the development of this web application, to help any attendees who might be interested in
deploying their own Vensim models online using custom web-based software.
Web Server — App Server
Web Service Web App
Vensim Interface Rails 4
JavaScript App Vensim Library Ruby
Web Browser Database Server t- Linux Server
Figure 1: Architecture of the Energy Policy Simulator web application
Second, I will show the model inside Vensim and demonstrate the use of a Python script we
have developed to control the software and automatically test thousands of different policy
combinations, searching for ones that meet particular criteria (for example, those that have
emissions below a specified carbon cap, ordered from lowest to highest monetary cost).
Workshop participants will be invited to download the Vensim model. All participants can
download the free Vensim Model Reader, in which they can run and use the model and
obtain detailed output. Any participants who own Vensim DSS (the version of Vensim that
supports scripting) can use the Python script to perform runs in an automated manner. I
will answer questions about the functionality of the model and the Python script. This will
help teach users both how to use this model and how to perform automated runs and
subsequent analysis for their own Vensim models.
The goals of this workshop are to give attendees knowledge of the technical workings of
the Energy Policy Simulator, an understanding of the support tools we have created (the
Ruby web application and Python scripts), and to help them come away with ideas and new
skills that they can apply to their own System Dynamics modeling projects.
What to Bring
No equipment is required if you simply desire to watch and listen. To use the model via the
web interface, you will need an internet-connected laptop. To use the Vensim model, you
will need a copy of the free Vensim Model Reader. To use the Python script, you will need a
copy of Vensim DSS (the version of Vensim that supports scripting).
What to Read Beforehand
Although not required, it is strongly recommended that you either attend my presentation
earlier in the conference titled “A Model of Energy Policy Impacts on Pollutant Emissions,
Costs, and Social Benefits Developed for China’s Central Government” or read the uploaded
conference paper associated with that presentation.
