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1、Inventory/distribution control system in a one-warehouse/multi-retailer supply chainChumpol Monthatipkula,1, Pisal Yenradeeb,*Abstract—This paper proposes a new inventory control system called the inventory/distribution
2、plan(IDP)control system for a one-warehouse/multi-retailer supply chain.In the system,a proposed mixed-integer linear programming model is solved to determine an optimal IDP control system,a proposed mixed-integer linear
3、 programming model is solved to determine an optimal IDP that controls the inventories of the supply chain.The efficiency of the IDP control system is compared to that of the echelon-stock R,s,S control policy,where R i
4、s a periodic review interval,s is a reorder point,and S is an order-up-to level,at various fillrates.The experimental results show that when the system faces non-stationary demands,the IDP control system significantly ou
5、tperforms the echelon-stock R,s,S control system because it can give lower total costs for all ranges of fill rates.Keywords:Inventory/distribution plan; One-warehouse/multiple retailers; Supply chain;Mixed-integer linea
6、r programming1.IntroductionIn Supply Chain Management(SCM),the inventory control problem is very complicated and challenging because the planner needs to consider several factors,for example,supply chain structures,coord
7、ination levels,and information sharing processes.The inventory control policy used by each entity is also an important factor because it affects the inventory replenishment process of the upstream entity.The upstream dem
8、and may be distorted and far from the actual demand faced by the downstream entity.This phenomenon is known as the Bullwhip Effect,which is presented in Forrester(1961).Many classical inventory control systems(s,Q,s,S,R,
9、S,R,Q,and R,s,S,etc.where s,Q,S,and R denote reorder points,reorder quantities,order-up-to levels,and periodic review periods,respectively)are still used in the supply chain environment.However,determination of their con
10、trol parameters is very difficult.For SCM,all entities in the supply chain should be planned and controlled simultaneously to obtain goodcontrol parameters and low inventory costs.The aim of this paper is to develop a ne
11、w inventory control system called the inventory/distribution plan(IDP)control system that determines optimal product flow through a one-warehouse/multi-retailer supply chain under both stationary and non-stationary uncer
12、tain demand situations.The IDP control system controls each supply chain member using the optimal IDP operating under a one-period rolling horizon planning strategy.The optimal IDP is obtained by solving a proposed mixed
13、-integer linear programming model.The performance of the proposed IDP control system is compared with that of the echelon-stock R,s,S control policy since both systems are similar in manyaspects.The main contribution of
14、this paper is the development of IDP control system thathas good performances under both stationary and nonstationary uncertain demand situations.This paper also proposes a practical way to determine appropriate safety s
15、tock factors at the warehouse and retailers that yield relatively low total costs while maintaining relativelyhigh fill rates.1.1.Literature reviewan(1999)studied a non-linear programming model which accounts for invento
16、ry and transportation costs.Solving the model by the Newton or the conjugate gradient method,the planner obtains near-optimal control parameters of the installation-stock s,Q system.Abdul-Jabar et al.(2003)studied invent
17、orycontrol systems of a one-warehouse/N-retailer network under centralized and decentralized policies.The authors obtained inventory control parameters(replenishment times and reorder quantities)by solving various types
18、of mathematical models concerning holding and ordering costs.Another determination of control parameters on a one-warehouse/N-retailer network belongs to Axsa¨ter(2003).The author proposed a technique to approximate
19、 optimal reorder points.The model considers holding costs at all locations and backorder costs at retailers.Yokoyama(2002)studied a multi-DC/multi-Retailer model controlled by the installation-stock R,S system.The targe
20、t inventory and the transportation amountare determined so as to minimize the sum of transportation,holding,and shortage costs.Tagaras(1999)considered the installation-stock R,S system in a one-warehouse/N-retailer netwo
21、rk.Order-up-to quantities are calculated by solving a mathematical model concerning holding,shortage,and transshipment costs,if the transshipment between retailers is allowed.Optimal stock levels in general divergent net
22、works under the echelon-stock R,S system was studied by Heijden(2000).The objective is to achieve target fill rates and to minimize total holdingcosts of the entire networks.Recently,control parameters of the traditional
23、 R,S system for serial supply chains were improved by Xie et al.(2006).The authors propose a two-level supply chain coordination algorithm to adjust the values of R and S,which are regularly determined by the local optim
24、ization.Some numerical experiments have been conducted and it is found that the supply chain performance is increased due to the new values of R and S.Al-Rifai and Rossetti (2007)proposed an efficient heuristic optimizat
25、ion algorithm to determine the control parameters of the s,Q system.Their model is a one-warehouse/multi-retailer supply chain.The goal is to minimize the inventory investment that is affected by average annual ordering
26、frequency and expected number of backorders.The continuous review s,Q policy were also studied by Seifbarghy and Akbari Jokar(2006).The authors study a onecentral-warehouse/multi-identical-retailer supply chain,which fac
27、es independent Poisson demands.When the batch size is given,the related reorder point at each facility is determined bya proposed approximate cost function.The remainder of this paper is organized as follows.Section 2 de
28、scribes a supply chainmodel.The IDP control system and safety stock policies are presented in Sections 3 and 4,respectively.Section 5 contains the echelon-stock R,s,S control system and an approach to determine its contr
29、ol parameters.The experimental design is shown in Section 6.Section 7 discusses the experimental results.Finally,the results are concluded in Section 8.2.A supply chain modelA supply chain under consideration comprises o
30、f one-warehouse and multiple identical retailers as depicted in Fig.1.It faces uncertain demand of a single product.When the demand is not satisfied,it is considered as a lost sale.The retailers replenish their inventori
31、es from the central warehouse,which in turn replenishes its inventory from an incapacitated vendor outside the concerned supply chain.It is assumed that all storage and transportation capacities are unlimited.Transportat
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