Coordinating supplier-retailer using multiple common replenishment epochs with retailers’ choices, To obtain competitive advantages, supply chain partners often seek coordination to improveperformance of the supply chain. As one of the most important supply chains in the modernretail industry, chain convenience stores have devoted significant efforts to improve supplycoordination. As of 2012, the three famous convenience store chains, 7-Eleven, FamilyMart,and Couche-Tard, operate around 43,000, 17,560 and 6,000 convenience stores worldwiderespectively (7-Eleven, 2012; FamilyMart, 2012; Alimentation Couche-Tard, 2012). The hugeand continuously growing number of stores in chain convenience stores creates a persistentdrive to improve their supply coordination. Often, a better coordination in the supply chainsupports the products with an enhanced competitive advantage. In practice, the retailingindustry with multiple stores would divide the distribution channels into various modules basedon geographic areas, replenishment epochs, or some other managerial considerations toenhance logistic efficiency.This paper studies a single-supplier, multiple-retailer supply chain for a single commodity. Thedemand of the commodity occurs only at the retailers with constant rates, and the supplier isresponsible for replenishing all the retailers’ requests to satisfy their demands. The supplier isthe leader of the supply chain, and it provides a sequence of prescheduled epochs for all theretailers to choose their order replenishment timings. The cost disadvantages of the retailersfor joining the replenishment timings shall be compensated by the supplier through quantitydiscounts. In addition, the costs considered in the supply chain include setup and deliverycosts of the supplier, as well as holding and ordering setup costs of the retailers. The objectiveof the supply chain is to minimize the total cost of the supplier.
The importance of coordination in the supply chain is evidenced by the ample growth in thecoordination literature. Fugate, Sahin, and Mentzer (2006) summarize the benefits ofcoordination including cost reduction, risk reduction, profit increase and competitiveadvantages enhancement. Interested readers can refer to Goyal and Gupta (1989), SarmahAcharya and Goyal (2006, 2008), Arshinder, Kandaa and Deshmukh (2008), Chan and Chan(2010), and Chan (2011) for the review of the buyer-vendor coordination models.Replenishment timing is one of the essential issues in inventory management. Heterogeneousretailers pursuing their own optimizations may order at various times. Nevertheless, thevariations on retailers’ replenishment timings significantly increase the cost of the supplier forhandling these replenishment orders. If replenishment orders can be synchronized, therelevant inventory costs can be reduced. Hence, replenishment coordination is one of the areasthat research focuses on supply chain coordination, e.g., Yao and Chiou (2004), Chen and…