On conflict and cooperation in a two-echelon inventory model for deteriorating items
Introduction
In practical, the four scenarios which discussed in the of the two level (ex. supplier and retail) inventory model are (1) single independent inventory model (e.g. EOQ, EPQ), (2) the retailer is dominant during negotiations with suppliers (e.g. Wal-mart Stores, Inc.), (3) the supplier is dominant during negotiations with retailers (e.g. China Steel Corporation), and (4) supplier and retailer cooperate. However, the researches were primarily focused on single independent inventory model and simple multiechelon inventory models, in classical inventory model. Fewer studies had discussed simultaneously the four above inventory scenarios. Consequently, base on the integrity and the real situation, we will discuss and analyze simultaneously the four above inventory models with deteriorating items. At the same time, we adopt the results of the supplier and retailer cooperate model from Lin and Lin (2007), and the four scenarios will be analyzed and compared simultaneously.
In order to improve the aggregated advantage for participating stakeholders in a supply chain, applied studies on supply chain systems focus on either strategic aspects or operational issues (Arcelus et al., 2006, Arshinder Kanda and Deshmukh, 2009, Aviv, 2001, Axsäter, 2005, Hosoda et al., 2008, Lin and Lin, 2006, Seo et al., 2002). Concerning operational issues, many studies primarily explore inventory control policies by proposing joint inventory models to handle cooperative activities between suppliers and retailers (Bylka, 1999, Goyal, 2000, Hall, 1996, Hill, 1997, Sharafali and Co, 2000, Viswanathan, 1998). Others (such as Cheng et al., 2010, Park et al., 2010, Ryu et al., 2009, Thomas and Griffin, 1996) survey the literature on coordinated supply chain management and suggest further research directions. Viswanathan (1998) proposes two strategies for integrated supplier–retailer inventory models, in which either the delivery quantity to the retailer is always identical, or the entire inventory held by the supplier is shipped to the retailer. Goyal (2000) improves the model proposed by Hill (1997) by generalizing for a single-supplier–single-retailer integrated production inventory model. Sharafali and Co (2000) extend the classical inventory models to demonstrate several cooperative policies regarding price changes, discount policies, and partial deliveries. Axsäter (2005) considers a two-echelon distribution inventory system with a central warehouse and a number of retailers and presents an approximation technique to solve the model. Yu, Zeng, and Zhao (2009) consider the intrinsic evolutionary mechanism of the VMI supply chains by applying the evolutionary game theories.
However, it is important to note that none of these studies consider the deterioration property of inventories, despite the fact that all items will eventually deteriorate. Some items will deteriorate significantly, such as certain types of foods, chemicals, electronic components, and radioactive substances. Intuitively, deteriorating items may require greater attention in cooperative actions between suppliers and retailers since a mutual conflict between these two sides can easily induce an over-estimated stock subject to deterioration. Thus, the loss in this case will be greater than that for general goods. The proposed approach in this study will be useful for practitioners who must deal with deteriorating items in a supply chain system. A number of papers (Cheng and Wang, 2009, Dye et al., 2007, Giri et al., 1996, Hariga and AlAlyan, 1997, Lin and Lin, 2004, Lin and Lin, 2007, Lin et al., 2000, Wee, 1995) explore the property of deterioration in EOQ models. However, none of these models permit backordering, apart from the one proposed by Sharafali and Co (2000).
By incorporating the property of deterioration into a cooperative inventory model, Andijani and Al-Dajani (1998) formulate the model as an inventory–production system, using a linear quadratic regulator technique. Their optimal production policy, however, does not consider the shortage costs. Balkhi (1999) models an integrated production system (i.e., two departments) where the rates of production, demand, and deterioration (for finished products and raw materials) are all time-dependent.
In classical inventory problems, studies usually derive an optimal solution for the supplier and retail independently. This implies that a conflict may exist between them. However, by researching mutual benefits and the facilitation of business activities, conflicts may be resolved in three different ways: (1) If the supplier has more bargaining power, then the supplier will dominate the activity, and the retailer will negotiate by providing available demand information; (2) if the retailer owns the sale channel and thus dominates the activity, as a result, the supplier is forced to negotiate by providing production information; and (3) if the bargaining power between the retailer and supplier are in balance, and neither firm dominates negotiations, both firms may provide available information to mutually solve their problems. Therefore, the model proposed in this study will examine four scenarios for cooperation between suppliers and retailers while taking into consideration the property of deterioration and complete backordering with a constant service level. These scenarios are: (1) when no information is shared; (2) supplier domination during negotiations with a retailer; (3) retailer domination during negotiations with a supplier; and (4) when the supplier and retailer cooperate, which is similar to the coordinate cases proposed by Chen and Hall (2007) in whom scheduling problems are solved for the supplier and manufacturer. For each scenario, a model is formulated to solve it. Additionally, numerical examples are presented to demonstrate the solution procedure and the characteristics of the scenario. Furthermore, we discuss three cooperative policies originally proposed in Sharafali and Co (2000) and derive their corresponding conditions. All the detailed analyses of measurement are also available from the author upon request via e-mail.
This paper is organized as follows: In Section 2, we introduce the assumptions and notations used in the model. In Section 3, the independent models for retailers and suppliers are proposed for analysis. The model in which the supplier dominates the chain and the retailer cooperates with the supplier is formulated and analyzed in Section 4. The model in which the retailer dominates the chain is explored in Section 5. In Section 6, we explore the model in which the supplier and retailer cooperate and share information with each other. Finally, sensitivity analysis is performed, and the effects of the parameters on optimality are discussed, followed by conclusions.
Section snippets
Assumptions and notations
Suppose a supplier (manufacturer) produces a product over a planning horizon H based on demand (i.e., the planning horizon of inventory problem H is finite in H time units). In general, the supplier will produce and deliver the product in an economical (small) size rather than producing the entire demand in period H at the beginning of period H (i.e., separate the demand into n production units and plan the number of replenishments over [0, H]). The relevant costs for the supplier should include
No information sharing between the retailer and supplier
When there is no collaboration and thus no information sharing between the retailer and supplier, the two sides will make decisions independently.
Supplier dominates, retailer negotiates
This scenario assumes that the retailer must provide information on future demand to the supplier, and that the supplier determines the optimal production size to satisfy the retailer’s demand. It can be formulated as follows:Based on (5), the supplier determines the optimal value for n. Let Isi(Ti), i = 1, 2, …, n be the delivery size for period i, and let the net inventory size the retailer receives be (1 − θ3)Isi(Ti
Retailer dominates, supplier negotiates
In this scenario, the total cost for the retailer over the entire time horizon H is given byHerein, the retailer determines the optimal service rate (r) and demand size for each period; while the supplier must satisfy the retailer’s demand. Henceforth, the instantaneous inventory level for the supplier will be described by
Model
In this scenario, the total cost for the retailer over the entire time horizon H is given by Eq. (15). To supply the stock of product, the reduced equations refer to Lin and Lin (2007). The total cost to the supplier over the time horizon H is thus given byTherefore, the aggregate total cost of the inventory system over the entire period is given byAn elaboration of the optimal solution for the Cooperation model will be discussed
Conclusions
Four scenarios for cooperative relationships between suppliers and the retailers are examined in this study. These scenarios capture almost all types of relationship between suppliers and retailers, for which models and corresponding optimal solutions are proposed and solved. Furthermore, comparisons between the models, in terms of cost as well as sensitivity analysis, are conducted. The results confirm that the cooperation scenario promotes concern for the other side, in terms of the total
Acknowledgements
The authors wish to thank both the Editor-in-Chief and the anonymous referees for their precious suggestions, which contributed to the improvement of the presentation of this paper. This work was partially supported by National Science Council, Taiwan, R.O.C., under Grant NSC94-2416-H-218-010- and NSC95-2416-H-006-044-MY2.
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