Research on the Optimization of Retailer Inventory Strategy based on System Dynamics Simulation

Yang Lin, Hou Kaihu, Zhong Jinyuan Department of Industrial Engineering

Kunming University of Science and Technology Kunming, P. R. China

yanglinwolf@163.com,Kaihu_kmustie@163.com

Abstract—Aiming at a satisfying inventory strategy, simulation was put into use in a dynamic system. In this paper, we focused on a simply two-stage supply chain inventory management system. The model of inventory system was simplified rationally, and we assumed that it was primarily consisted of a manufacturer and a retailer. The study based on the theory of System Dynamics and vensim software was used to optimize variable parameters in the supply chain inventory system. The retailer inventory strategy was optimized under uncertain environment and the variable parameters of adjustment production time, demand production delay time and demand sale time were reset, and then a rational inventory management project was selected in this system. Finally, an example was come up with and it showed that the method was feasible and a better retailer inventory strategy was proposed.

Keywords- System Dynamics; Supply chain; Retailer inventory; Vensim; Optimization

I. INTRODUCTION The supply chain inventory management aims at meeting

customers' demands, reducing inventory cost and increasing enterprise profit. We need place an order and replenish productions when the inventory is under safety stock quantity. We can appropriately combine with historical records and product sale reports through a dynamic simulation analysis, and then provide variable parameters which are similar to the reality operation situation. So a simulation model is established and it must meet customers' demands, operate smoothly and use up the inventory in time. Therefore, we can use the method of system dynamic simulation to optimize the variable parameters in a two-stage supply chain inventory system. We simplify the model actually and assume that it is primarily consisted of a manufacturer and a retailer. Moreover, it can describe the process of supplying an order directly from a manufacturer to a retailer. The model should meet the customers' demands primarily, and we need reset the variable parameters of adjustment production time, demand production delay time and demand sale time to get a better retail inventory strategy ultimately.

II. SYSTEM DYNAMICS AND VENSIM SOFTWARE System dynamics (SD) was created during the mid-1950s

by Professor Jay Forrester of the Massachusetts Institute of Technology. A system is integrated by multiple elements, such

as constraint conditions, inputs, outputs and feedbacks. They are all included in the complex of systems and the environment. The theory foundation of system dynamics consist of classical fluid mechanics and feedback control theory. It is a discipline that focuses on cognizing and solving system problems, connecting with natural science and social science as well. It is widely used within the company, between businesses and businesses, among regions and even in cross-border strategy decisions. System dynamics is usually called “strategic decision laboratory” [1].

Vensim software is a kind of visual modeling tool. When a system dynamics model is established, we can use this software to conceive it, simulate it, analyze it and optimize it, and the documents are created at the same time. The specialties of vensim software are as follows: It uses graphical programing language to establish a simulation model. And it can run under Windows environment. In other words, its requirement of operating system and hardware environment is lower than some other simulation software. We can use a variety of analytic methods to analyze the model (including structural analysis, data analysis, causes and effects feedback analysis and graph analysis, etc.) and we can also make a reality check. We can check whether the existing models following given rules or not by putting the necessary constraints into the simulation model. In this way, we may make a judgment whether the model is rational and realistic or not. If the result is not rational, we should adjust structure or reset the parameters to the previous model until a better conclusion is acquired.

III. THE ESTABLISHMENT OF THE INVENTORY MANAGEMENGT SYSTEM MODEL

A. The establishment of two-stage supply chain simulation model First, we established the balance score card (BSC) of

supply chain systems and confirmed supply chain performance indicators and ascertained the boundary of system model. Then, we analyzed the cause and effect relationship among each indicator and established the system dynamics flow maps of supply chain performance evaluation on the basis of indicators which were established above. Finally, we could clearly describe the working process of the two-stage supply chain system in a system dynamics flow maps [2, 3].The stock and flow maps were shown in Fig.1 below.

978-1-4577-2025-3/12/$26.00 ©2012 IEEE

Work inprocess

inventory（ ）WIP

Retail store（ ）inventory RI

（ ）Production rate Pr（ ）Reorder rate Ror

（ ）Retail sales rate Rsr

Adjustmentproduction

（ ）time AptAdjustmentproduction

（ ）rate Apr

Demandproduction

（ ）rate Dpr

Adjustment order rate（ ）Aor

Demandsales time（ ）Dst

Demand sales rate（ ）Dsr

Demand production（ ）delay time Dpd

Entering warehouse（ ）time Et

Transport（ ）time Tt

Shipment（ ）time St

Replenishment（ ）time Rt

-

+

++

+

+

++

- +

+

+

+

Inventorywaste（ ）rate IwrDemand

function（ ）Df

（ ）Replenishment rate Rr-

+

Fig.1 The system dynamics flow maps of two-stage supply chain system

B. The analysis of flow maps The system dynamics flow maps of the two-stage supply

chain system was established above. Then we analyzed the model and gave some explanations to it. Working in process inventory (WIP) and retail store inventory (RI) were variables related to time. We assumed that the number of products in process was “r”, and products were supplied directly from a manufacturer to a retailer inventory. So we could define WIP as the integral of difference between reorder rate (Ror) and production rate (Pr). We assumed that the number of retail store inventory was “k”, it's not difficult to understand that not only selling, but also transporting, handing and depreciation all wasted part of products. So we defined retail store inventory as the integral of difference about replenishment rate (Rr), retail sale rate (Rsr) and inventory waste rate (Iwr). Demand production rate (Dpr) was defined as the quotient between WIP and demand production delay time (Dpd). Production rate was defined as the moving average process related to adjustment production time (Apt) between adjustment production rate (Apr) and demand production rate (Dpr).In vensim software, the average process was expressed as exponent information delay function (SMOOTH). Replenishment time (Rt) was defined as the sum of entering warehouse time (Et), transport time (Tt) and shipment time (St). Reorder rate was related to production rate and replenishment time, and it was defined as delay function. We assumed that no matter how many products were ordered one time, the products must be provided once and split delivery is not allowed. Demand sale rate (Dsr) was defined as the moving average process related to retail sale time (Rst) and demand sale time (Dst). Reorder rate was the sum of demand sale rate and adjustment order rate (Aor).At the same time, we assumed that the demand function was integrated by step function and random function. Step function means the demand change indefinitely from “e” to “f” during the simulation time. Random function means that the variables change randomly in an interval from “m” to “n”. The functions among variable parameters were shown as follows.

WIP = r + dt; (1)

RI= k + dt; (2) Dpr= WIP/Dpd; (3) Pr= SMOOTH (Dpr+Apr, Apt); (4) Rt= ET+Tt+St; (5) Rr= DELAY FIXED (Pr, Rt: Pr); (6) Dsr= SMOOTH (Rsr, Dst); (7) Ror= Dsr+Aor; (8) Df= INT (STEP (e, f) +RANDOM (m, n)). (9)

IV. MODEL SIMPLIFICATION AND SYSTEM DYNAMICS SIMULATION

A. Model simplification The flow maps were shown as Fig.1. For the convenience

purpose, the simulation model necessarily needed to be simplified. On the premise of system function not changing, we cut down some of the information flow (including adjustment order rate (Aor), inventory waste rate (Iwr) and replenishment time (Rt), etc.)The new simplified model was shown as Fig.2.In this model, auxiliary variable consisted of demand sale rate (Dsr), demand function (Df) and demand production rate (Dpr) .Auxiliary constants included demand sale time (Dst), demand production delay time (Dpd) and adjustment production time (Apt) and they could be regarded as exogenous variables, for their changing in a period was specified in advance.

Wok inprocess

inventory（ ）WIP

（ ）Reorder rate Ror （ ）Production rate Pr

Retail store（ ）inventory RI

（ ）Retail sales rate Rsr

Demand Sales）rate (Dsr

Demand sales（ ）time Dst Demand production

（ ）delay time Dpd

Demand production（ ）rate Dpr Adjustment

production（ ）rate Apr

Adjustmentproduction

（ ）time Apt

（ ）Replenishment rate Rr

Demand（ ）function Df

Fig.2 Inventory management system model (simplified)

B. Example analysis A manufacturing enterprise M products car components

and it supplies production directly to a retailer. Production process needs a high requirement on batch production and continuous manufacturing. Due to the existing of information delay and it is always inevitable, so complete JIT inventory management is difficult to achieve [4]. We assumed that the number of products in process was 190 each week, the number of retail store inventory was 275, the adjustment production time (Apt) was 4 weeks, the demand production delay time (Dpd) was 2 weeks and the demand sale time (Dst) was 1 week. In addition, we simplified the demand function into a step function. According to the market forecast, the demand of previous 10 weeks was 100 each week, and 10 weeks later, it

changed into 120 each week until the simulation time was over. System dynamics often focused on the nonlinear system, the step function was appropriate for the system, and it could get a good output ultimately.

In reality, factory production can't change with the increase of order immediately, but there is a delay process which is mainly used to change the personnel and equipment [5]. Demand production rate (Dpr) adjusts the actual factory production, but manufacturing delay is inevitable. We set manufacturing delay as a constant and define it as demand production delay time(Dpd).In order to make our study more convenient, we assumed that the production process keep the same without any improvement. At the same time, we assumed that retailer reorder rate (Ror) was equal to demand sale rate (Dsr). We set the time step as 0.25 as usual, and set the simulation time as 50 weeks (For the convenience purpose, assuming that there are 50 weeks in a year).

C. The establishment of the system dynamics equation. After constructing the simulation flow maps of the system

dynamics, according to enterprise actual situation and production logistics data, we used the formula editor which provided by vensim to establish the two-stage supply chain performance evaluation simulation model. The system dynamics equations of inventory management system were as follows:

Dsr= SMOOTH (Rsr, Dst); (10) Dpr= WIP/ Dpd; (11) WIP= INTEG (Ror-Pr, 190); (12) Apr=SMOOTH (Dpr, Apt); (13) RI= INTEG (Rr- Rsr, 275); (14) Rsr= Test input=Demand function; (15) Ror= Dsr; (16) Demand function=100+STEP (20, 10); (17) Apt=4 weeks; (18) Dpd=2 weeks; (19) Dst=1 week; (20) INTIAL TIME=0; (21) FINAL TIME=50; (22) TIME STEP=0.25; (23) SAVEPER=TIME STEP. (24)

D. Analysis of the simulation results The purpose of the System dynamics simulation was to

compare with the performance of the system in different states, so that we could optimize the system. The simulation results could be calculated by the simulation software, but in most cases, the data which outputted by the computer couldn’t reflect the performance of the system directly. Only by analyzing and disposing the data, can we clearly cognize the performance of the system in different projects [6, 7, 8]. Using the simulation function of SyntheSim which was provided in vensim software, we got graphs in different conditions by changing the value of Apt, Dpd, Dst and other parameters.

Setting the first project adjustment production time as 4 weeks (shown as graph.1)and 13 weeks as the other project (shown as graph.2),we got the appropriate parameters and

selected the better project by observing the graphs of retailer store inventory. The graphs of RI were shown as Fig.3.

Fig.3 The influence of changing the Apt on RI

If the production adjustment time (Apt) was set as 13 weeks, namely a quarter of a year. Although the ordering cost was decreased, the retailer would be often in certain condition of inventory rising and falling widely, so that it was difficult to cope with the stable market demand in a period of time. However, if the production adjustment time (Apt) was set as 4 weeks, the retailer would keep in a stable inventory in the whole simulation time. Replenishment rate (Rr) also tended to be stable, which would guarantee the demand of the market effectively. When we changed Apt, the causal and effect relationship of RI and Rr were shown as Fig.4.

Fig.4 The causal and effect relationship of RI and Rr

Setting the demand production delay time (Dpd) as 2 weeks

in the first project (shown as graph.1), 3 weeks as the second project (shown as graph.2) and 4 weeks as the third project (shown as graph.3), we got the appropriate parameters of Dpd and selected the appropriate project by observing the graphs of retailer store inventory in these three different cases. The influence of changing Dpd on RI was shown as Fig.5.

Through observing the graphs we knew that in the condition of the first project, the RI kept in a high amount, it did not seem to be helpful to the retailer for it produced some overstock cost. In the condition of the second project, the RI was relatively appropriate and it was keeping in a relatively low number, which would save the unnecessary inventory cost and made the retailer obtain more profits. In the condition of the third project, though the demand productions delay time (Dpd) was changed into 4 weeks, and that would save manufacturing cost for a producer. But this project was not rational because of it would lead to a phenomenon of stock out for RI. So we made a conclusion that setting 3 weeks as production adjustment time (Apt) was more rational by comparing with different projects above.

Fig.5 The influence of changing Dpd on RI

We set the demand sale time (Dst) of the first project as 1

week (shown as graph.1), the second project as 2 weeks (shown as graph.2) and the third project as 3 weeks (shown as graph.3).The retailer order quantity changed with the demand forecasting. When the retail sale rate was increasing, demand sale rate (Dsr) presented a rising trend, so as to the reorder rate (Ror). When the retail sale rate was decreasing, demand sale rate (Dsr) would reduce, so as to the reorder rate (Ror). The influence of changing Dst on RI was shown as Fig.6.

We knew that the RI decreased constantly along with the Dst increasing by observing the graphs. When setting the Dst as 3 weeks (as the graph 3 showed), the inventory was relatively appropriate and it was more conducive to the retailer.

Fig.6 The influence of changing Dst on RI

V. CONCLUSION Supply chain inventory management system is an

integrated system, and the operation process of the supply chain is much more complex in reality than a simulation model. This paper focused on a two-stage supply chain inventory management system and it was simplified rationally. We used vensim software to establish models and simulate the system and provided some better supply chain inventory operation projects by adjusting the value of Apt, Dpd, Dst and other parameters. And the retailer inventory storage strategy was optimized under uncertain environment ultimately. We made a conclusion that the method was feasible through analyzing an example. And a better inventory storage strategy was given to the retailer. For the simulation model which we researched on was a simplified one, so it couldn't react the whole storage operation process of the supply chain system roundly and objectively. Since the theory of system dynamics is integrated and complex, the subject needs a further study, only in this way can we use these theories and methods to solve more practical problems.

ACKNOWLEDGMENT This research is partially supported by the project of

Yunnan province scientific and technological innovation (Project No. 2008AA011). Special thanks for staffs in Integrated Management Department of FAW-GM Hongta Yunnan Automobile Manufacturing Co., Ltd.

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