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1、Int. J. Production Economics 114 (2008) 119–133Inventory/distribution control system in a one-warehouse/ multi-retailer supply chainChumpol Monthatipkula,1, Pisal Yenradeeb,?aGraduate School of Management and Innovation,

2、 King Mongkut’s University of Technology, Thonburi, Bangkok 10140, Thailand bIndustrial Engineering Program, Sirindhorn International Institute of Technology, Thammasat University, Pathum Thani 12121, ThailandReceived 8

3、June 2005; accepted 24 December 2007 Available online 19 January 2008AbstractThis paper proposes a new inventory control system called the inventory/distribution plan (IDP) control system for a one-warehouse/multi-retail

4、er supply chain. In the IDP control system, a proposed mixed-integer linear programming model is solved to determine an optimal IDP that controls the inventories of the supply chain. The efficiency of the IDP control sys

5、tem is compared to that of the echelon-stock R,s,S control policy, where R is a periodic review interval, s is a reorder point, and S is an order-up-to level, at various fill rates. The experimental results show that whe

6、n the system faces non-stationary demands, the IDP control system significantly outperforms the echelon-stock R,s,S control system because it can give lower total costs for all ranges of fill rates. r 2008 Elsevier B.V.

7、All rights reserved.Keywords: Inventory/distribution plan; One-warehouse/multiple retailers; Supply chain; Mixed-integer linear programming1. IntroductionIn Supply Chain Management (SCM), the in- ventory control problem

8、is very complicated and challenging because the planner needs to consider several factors, for example, supply chain struc- tures, coordination levels, and information sharing processes. The inventory control policy used

9、 by each entity is also an important factor because it affects the inventory replenishment process of the upstream entity. The upstream demand may bedistorted and far from the actual demand faced by the downstream entity

10、. This phenomenon is known as the Bullwhip Effect, which is presented in Forrester (1961). Many classical inventory control systems (s,Q, s,S, R,S, R,Q, and R,s,S, etc. where s, Q, S, and R denote reorder points, reorder

11、 quantities, order-up-to levels, and periodic review periods, respectively) are still used in the supply chain environment. However, determination of their control parameters is very difficult. For SCM, all entities in t

12、he supply chain should be planned and controlled simultaneously to obtain good control parameters and low inventory costs. The aim of this paper is to develop a new inventory control system called the inventory/distri- b

13、ution plan (IDP) control system that determines optimal product flow through a one-warehouse/ARTICLE IN PRESSwww.elsevier.com/locate/ijpe0925-5273/$ - see front matter r 2008 Elsevier B.V. All rights reserved. doi:10.101

14、6/j.ijpe.2007.12.010?Corresponding author. Tel.: +662 986 9009x2107; fax: +662 986 9112. E-mail addresses: chumpol.mon@kmutt.ac.th (C. Monthatipkul), pisal@siit.tu.ac.th (P. Yenradee). 1Tel. +662 470 9783; fax: +662 470

15、9798.the total costs including inventory costs (order- ing, holding, and shortage costs) and transpor- tation costs (transportation and in-transit holding costs). Schneider and Rinks (1991) and Schneider et al. (1995) pr

16、ovided a good approximation for parameter setting for the echelon-stock R,s,S control policy. The model is developed based on the backlogging model of a one-warehouse multiple-stores supply chain. Ganeshan (1999) studied

17、 a non-linear program- ming model which accounts for inventory and transportation costs. Solving the model by the Newton or the conjugate gradient method, the planner obtains near-optimal control para- meters of the inst

18、allation-stock s,Q system. Abdul-Jabar et al. (2003) studied inventory control systems of a one-warehouse/N-retailer network under centralized and decentralized policies. The authors obtained inventory con- trol paramete

19、rs (replenishment times and re- order quantities) by solving various types of mathematical models concerning holding and ordering costs. Another determination of con- trol parameters on a one-warehouse/N-retailer network

20、 belongs to Axsa ¨ ter (2003). The author proposed a technique to approximate optimal reorder points. The model considers holding costs at all locations and backorder costs at retailers. Yokoyama (2002) studied a mu

21、lti- DC/multi-Retailer model controlled by the installation-stock R,S system. The target in- ventory and the transportation amount are determined so as to minimize the sum of transportation, holding, and shortage costs.

22、Tagaras (1999) considered the installation- stock R,S system in a one-warehouse/N-retailer network. Order-up-to quantities are calculated by solving a mathematical model concerning holding, shortage, and transshipment co

23、sts, if the transshipment between retailers is allowed. Optimal stock levels in general divergent net- works under the echelon-stock R,S system was studied by Heijden (2000). The objective is to achieve target fill rates

24、 and to minimize total holding costs of the entire networks. Recently, control parameters of the traditional R,S system for serial supply chains were improved by Xie et al. (2006). The authors propose a two-level supply

25、chain coordination algorithm to adjust the values of R and S, which are regularly determined by the local optimization. Some numerical experimentshave been conducted and it is found that the supply chain performance is i

26、ncreased due to the new values of R and S. Al-Rifai and Rossetti (2007) proposed an efficient heuristic optimization algorithm to determine the con- trol parameters of the s,Q system. Their model is a one-warehouse/multi

27、-retailer supply chain. The goal is to minimize the inventory invest- ment that is affected by average annual ordering frequency and expected number of backorders. The continuous review s,Q policy were also studied by Se

28、ifbarghy and Akbari Jokar (2006). The authors study a one- central-warehouse/multi-identical-retailer sup- ply chain, which faces independent Poisson demands. When the batch size is given, the related reorder point at ea

29、ch facility is deter- mined by a proposed approximate cost func- tion.The remainder of this paper is organized as follows. Section 2 describes a supply chain model. The IDP control system and safety stock policies are pr

30、esented in Sections 3 and 4, respectively. Section 5 contains the echelon-stock R,s,S control system and an approach to determine its control parameters. The experimental design is shown in Section 6. Section 7 discusses

31、 the experimental results. Finally, the results are concluded in Section 8.2. A supply chain modelA supply chain under consideration comprises of one-warehouse and multiple identical retailers as depicted in Fig. 1. It f

32、aces uncertain demand of a single product. When the demand is not satisfied, it is considered as a lost sale. The retailers replenish their inventories from the central warehouse, which in turn replenishes its inventory

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