Dynamic Simulation of the Supply Chain with VMI Policy

Dynamic Simulation of the Supply Chain with VMI Policy
XU Minli, JIAN Huiyun
School of Business, Central South University, Changsha, P.R. China, 410083
[email protected]
Abstract: Based on the traditional vendor managed inventory (VMI) policy, the third-party logistics
(TPL) is introduced to the supply chain. A dynamic simulation model is established by using system
dynamics for the supply chain with VMI policy. By analyzing the key parameters, the influences of
system stability and the average total inventory of the supply chain with VMI policy caused by order
time, transporting time and expected inventory are studied. Reducing the order time T1 can help the
supply chain with VMI policy to be more stable and reduce the average inventory of whole system.
When the other variables keep constant, on the condition of T1<δ (critical value), transporting time T2
can not change the average stock of the supply chain with VMI policy, and the system will still keep
stable. But when T1>δ, the increasing of T2 will push the system from stable to unstable. When the
other variables keep constant, reducing the expected inventory EI can reduce the average inventory of
the system. No matter the expected inventory EI is, after some days the curve of total inventory will
become stable at last. These conclusion will help companies to operate the supply chain with VMI
policy better.
Keywords: Supply chain, System dynamics, Vendor managed inventory (VMI), Vensim_PLE software.
1 Introduction
Sunil and Meindl [1] define that “a supply chain is dynamic and involves the constant flow of
information, products and funds between different stages. Each stage of the supply chain performs
different processes and interacts with other stages of the supply chain.” After Maggee [2] brought up the
framework of vendor managed inventory (VMI), VMI has been focused by academic researcher and
enterprises managers. Vendor-managed inventory (VMI) was first successfully applied to Wal-Mart and
Procter & Gamble in the late 1980s. Then many companies like Shell Chemical, Campbell Soup, and
Johnson & Johnson followed them. VMI is a tool used to satisfy customer service and decrease
inventory cost. It is a supply chain strategy where the supplier is given the responsibility of tracking and
replenishing the customer’s inventory. In a VMI system, the suppliers quick respond to the customers’
inventory needs of quantities to replenish. Because the suppliers get more accurate information of the
customer’s needs, the replenishments will be more accurate and meet the true demand. It then can
effectively minimize the so-called bullwhip effect that tends to amplify demand fluctuations [3]. It can
also increase the inventory turns and decrease the safety stock [4]. Gerbert [5] found that VMI can achieve
better than JIT and zero-inventory management. Waller [6] found that VMI can reduce production cost
and stock cost. Burke [7] and Cottrill [8] believe that VMI will implement to the industry more widely.
Disney etc. [9] and Lee etc. [10] found VMI can mitigate bullwhip effect and reduce the cost of whole
supply chain. Disney and Towill gave an Overview of VMI scenario showed in Fig. 1[11]. In the supply
chain system with VMI policy, the third-party logistics company will help provide logistics service.
Fig2 is the operation model of supply chain with VMI policy.
In 1960s Forrester founded the Systems Dynamics Group at MIT. System dynamics takes
companies as systems with six types of flows, namely materials, goods, personnel, money, orders, and
information. It assumes that managerial control is realized through the changing of rate variables.
System dynamics is one of the best methods for analyzing complex systems [12]. It has been applied to
various fields of natural and social sciences [13]. Shapiro [14] believes, “systems dynamics is a
well-elaborated methodology for deterministic simulation.” Forrester [15] built a system dynamics
model of the three-echelon supply chain using system dynamics. Paich and Sterman [16] simulated a
.
Project (No. 70471048) supported by National Natural Science Foundation of China
216
new product diffusion process. Ashayeri and Keij (1998) [17] use SD to study the distribution chain of
Edisco, which is the European distributor of the US company Abbott Laboratories. Otto and Kotzab
(2003) [18] reviewed SD simulation of SCM. And. System dynamics has proven its worth in supply
chain simulation. Computer simulations are divided into two types, static and dynamic. Ballou [19]
pointed out that supply chain is too complex for mathematical analysis and is usually studied with the
aid of computer simulation. Because it is interactive and incorporates hierarchical feedback processes,
dynamic simulations are properly used to study the supply chain [20]. We used the Systems Dynamics
software, Vensim_PLE, as a tool to build our supply chain model with VMI policy and simulate the
supply chain. It can analyze the movements of dynamic systems and simulate the impacts of causal
relationships that have feedback loops.
This paper explores some of the underlying factors that might affect the effectiveness of supply
chain with VMI policy. It is organized as follows. Section 2 introduces the dynamic model of supply
chain with VMI policy. Section 3 is the analysis of the simulation results, and Section 4 gives the
conclusion.
Fig 1 Overview of VMI scenario [8]
The third-party logistics
Replenishment
Delivery
Order information
Suppliers
Retailers
Fig 2 VMI model with the third-party logistics company
2 Dynamic model of supply chain with VMI policy
2.1 Assumption
(1) Fix-order quantity model is used;
(2) The production line is stable;
217
(3) Capacity of the warehouse is big enough;
(4) Receipt of inventory is not instantaneous;
(5) Logistics service is adequate to distribute the goods;
(6) Delay is permitted. For an example, after an order has been placed, supply builds up over a
period of time. We take into account the order rate, distributing rate and receiving rate.
2.2 Dynamic model structure
Causal loop diagram of supply chain with VMI policy is showed in Fig.3. The stock-flow diagram
of our model is exhibited in Fig. 4. The diagram is constructed using building blocks (variables)
categorized as stocks.
The variables that will appear in the chain are the following:
DT: The simulation period
T1, Order time: the time spent in which the supplier provides the goods to the third party company
T2, transportation time: the time spent in which the third party company transports the goods to
retailer
T3: Distributors stock adjusting time
I1: stock in supplier’s warehouse
I2: The stock in third-party logistics company
I3: real stock in retailer’s warehouse
EI, expected stock of retailer
DI, the stock difference between I3 and EI: EI-I3
OR: Order rate. OR=DI/T3
DR: Supply rate DR=I1/T1
RR: Receiving rate RR=I2/T2
SR: sale rate
AI: the whole stock of the VMI system;
；
；
；
；
；
；
；
；
；
；
；
；
RR
+
+
I3
I2
EI
+
+
DR
DI
+
+
I1
+
OR
Fig. 3 Causal loop diagram of supply chain with VMI policy
218
EI
DI
AI
I1
I2
I3
OR
SR
(DR)
RR
T1
T3
T2
Fig.4 Stock-flow diagram of VMI
，
According to Fig.4 the equations in the simulation model are the following:
L
I3.K = I3.J + (RR.JK-SR.JK)*DT
R
RR.KL= I2.K/T2
L
I2.K = I2.J + (DR.JK-RR.JK)*DT
R
DR.KL= I1.K/T1
L
I1.K = I1.J + (OR.JK-DR.JK)*DT
R
OR.KL= I3.K/T3
3 Results Analysis
The simulation has been developed by using the Vensim PLE software. This section will analyze
the simulation results.
3.1 The effect of order time T1 on the supply chain with VMI policy
The other variables keep stable, only change the order time T1, we find a critical value
When
T1< δ
δ
exists.
, the quantity (AI) of whole VMI system inventory vibrates weakly (Attenuated
concussion). But when T1> δ , the quantity (AI) of whole VMI inventory vibrates strongly (becoming a
diffused concussion). Fig.5 is the simulation result diagram.
15,000
6
6
11,500
1
2 3 4 5
2
3
5 6
1
4
2 3 4
5
1
2 3
5
6
4
4 5
2 3
5
4
1 2 3
1
5 6
4
1 2 3
1
2
3 4 5
1
1
0
AI : T1=5
AI : T1=9
AI : T1=10
AI : T1=11
AI : T1=16
AI : T1=20
6
2 3 4
5
8,000
6
6
60
120
1
1
2
5
6
5
6
5
6
6
2
3
4
5
1
2
3
4
360
1
2
3
4
300
1
2
3
4
5
6
1
2
3
4
240
1
2
3
4
5
1
2
3
180
Time (Day)
3
4
5
6
4
5
6
5
6
6
Fig.5 the effect of Order time T1on the total inventory
Attenuated concussion means that the quantity of whole VMI inventory tends to be stable by its
self-regulation. Diffused concussion tells us that the VMI system is unstable. In practice, diffused
concussion means products overstock or stock-out. From the simulation result we can get the first
conclusion: reduce the order time T1 can make the supply chain with VMI policy more stable and
reduce the average inventory of whole system.
3.2 The effect of transporting time T2 on VMI system
219
①
When the order time T1< δ , the change of transporting time (T2) will not change the
concussion style of the total inventory. The total inventory of the supply chain keeps attenuated
concussion. Fig. 6 is the simulation result.
20,000
3
15,000
3
3
3
2 3
10,000
1 2
2
2
2
2
1
1
1
1
3
2
2
2
1
3
3
3
3
2
2
2
1
1
3
3
3
3
1 2
1
1
2
2
1
1
1
1
5,000
0
0
36
AI : T2=5
AI : T2=15
AI : T2=30
1
72
1
2
108
1
2
3
1
2
3
144
1
2
3
180
216
Time (Day)
1
2
3
1
2
3
1
2
3
252
1
2
3
288
1
2
3
1
2
3
324
1
2
3
360
1
2
3
1
2
3
3
，the effect of T2 on total inventory
Fig. 6 when T1< δ
②When the order time T1> δ , transporting time (T2) will change the total inventory. When T2
becomes larger, the total inventory will become more unstable, and the stock vibrates fiercely. The result
is showed in Fig.7.
3
30,000
3
3
21,000
3
3
3
3
12,000
3
3
1 2
1
2
1 2 3
2
1
1 2
1 2
1 2 3
1 2
1 2
1 2
1 2
1 2
1 2
3
3
3,000
1 2
1 2
3
- 6,000
0
36
AI : T2=5
AI : T2=15
AI : T2=30
1
72
1
2
108
1
2
3
1
2
3
144
1
2
3
180
216
Time (Day)
1
2
3
1
2
3
1
2
3
252
1
2
3
288
1
2
3
1
2
3
324
1
2
3
360
1
2
3
1
2
3
3
，the effect of T2 on total inventory
Fig.7 when T1> δ
Then we can get the second conclusion: when the other variables keep constant, on the condition of
T1<δ (critical value), T2 can not change the average stock of the VMI system, and it will make the
system stable. But when T1>δ, the increasing of T2 make the VMI system unstable.
3.3 The effect of expected inventory (EI) on the VMI system
When the other variables keep constant, the change of EI will not change the total inventory
style—attenuated concussion. Fig.8 is the simulation result.
25,000
3
18,750
3
3
12,500
3
1
1
2
2
2
1
1
1
1
1
3
2
2
2
1
1
3
3
3
2
2
2
1
3
3
3
2
2
2
6,250
3
3
3
1 2
2
2
1
1
1
1
0
0
36
AI : EI=4000
AI : EI=7000
AI : EI=12000
72
1
108
1
2
1
2
3
2
3
144
1
2
3
180
216
Time (Day)
1
1
2
3
1
2
3
2
3
252
1
2
3
288
1
1
2
3
324
1
2
3
2
3
360
1
1
2
3
3
Fig. 8 The effect of expected inventory on total inventory
Conclusion 3: When the other variables keep constant, reducing EI can reduce the average
220
inventory of the VMI system. No matter the expected inventory EI is, the curve of total inventory will
become stable after some days.
5 Conclusions
In the supply chain system with VMI policy, we introduced the third logistics company to manage
the distribution. A dynamic model was developed. We simulated the model by using Vensim PLE
software. We found the basic law of system stability and average total inventory of the supply chain with
VMI policy. The decreasing of the ordering time (T1) can not only increase the stability of the system,
but also cut down the average inventory of the supply chain. When the other variables keep constant,
there is a critical value δ of order time (T1). When T1<δ, the transporting time (T2) can only change the
average total inventory, but not the system stability. When T1>δ, when T2 is big enough, the system will
be unstable. When the other variables keep constant, if you decrease the expected inventory (EI), the
average total inventory of the supply chain with VMI policy will be cut down, and the system will be
more stable. These results will help us manage the supply chain with VMI policy.
References
[1] Sunil C, Meindl P. Supply chain management. New Jersey: Prentice-Hall, 2001: 4.
[2] Magee J F. Production Planning and Inventory Control [M]. New York: McGraw-Hill Book Company,
1958:80-83.
[3] H.L. Lee, V. Padmanabhan, The bullwhip effect in supply chains [J]. Sloan Management Review, 1997, 38 (3):
93–102
[4] T. Davis, Effective supply chain management [J]. Sloan Management Review, 1993, 34 (4): 35–47.
[5] Gerber N. Objective Comparisons of Consignment, Just-in-time, and stockless [J]. Hospital Material
Management Quarterly, 1991, 13(1):10-17.
[6] Waller M, Johnson M E, Davis T. Vendor-managed Inventory in the Retail Supply Chain [J]. Journal of Business
Logistics, 1999, 20(1):183-203.
[7] Burke M. It’s Time for Vendor Managed Inventory [J]. Industrial distribution, 1996, 85(2):90.
[8] Cottrill K. Reforging, the Supply Chain [J]. Journal of Business Strategy, 1997, 18(6):35-39.
[9] Disney S M, Towill D R. A Procedure for the Optimization of the Dynamic Response of a Vendor Managed
Inventory System [J]. Computers &Industrial Engineering, 2002, 43: 27-58.
[10] Lee H, Padmanabhan P, Whang S. Information Distortion in a supply Chain: the Bullwhip Effect
[J].Management Science, 1997, 43(4): 546-558.
[11] S.M. Disney, D.R. Towill, The effect of vendor managed inventory (VMI) dynamics on the Bullwhip Effect in
supply chains [J]. Int. J. Production Economics, 2003, 85: 199–215.
[12] Dinitrios V., Patroklos G., Eleftherios I. A system dynamics model for dynamic capacity planning of
remanufacturing in closed-loop supply chains [J]. Computer & Operations Research, 2007, 34: 367-394.
[13] Toru Higuchi, Marvi D.Troutt. Dynamic simulation of the supply chain for a short life cycle product-Lesson
from the Tamagotchi case [J]. Computer & Operations Research, 2004, 31: 1097-1114
[14] Shapiro JF. Modeling the supply chain [M]. California: Duxbury, 2001: 468.
[15] Forrester JW. Industrial dynamics [M]. Massachusetts: MIT Press, 1961.
[16] Paich M, Sterman JD. Boom, bust and failures to learn in experimental markets [J]. Management Science 1993;
39(12):1439–58.
[17] Ashayeri, J. and R. Keij, Global business process re-engineering: a system dynamics based approach [J].
International Journal of Operations and Production Management, 1998, 18: 817-831
[18]Otto, A. and H. Kotzab. Does supply chain management really pay? Six perspectives to measure the
performance of managing a supply chain [J]. European Journal of Operational Research, 2003, 144: 306-320
[19] Ballou RH. Business logistics management [M]. New Jersey: Prentice-Hall, 1992: 443
[20] Pidd M. Computer simulation in management science [M]. 2nd ed. Chichester: Wiley, 1984: 219.
221