انتخاب تامین کننده تحت ریسک شکست، کمیت و تخفیف حجم معاملات  Supplier Selection under Failure Risk, Quantity and Business Volume Discounts

1 Introduction Natural disasters not only cause horric human tragedies; they also shatter the economy and inuence businesses all around the globe. Japan’s 2011 “quadruple disaster” (The Economist, 2011) is one recent example of a supply chain disruption that highlights the importance to hedge supply chains against supplier outage. Multi-sourcing, i.e. having dierent suppliers for the same item, is one way of approaching this issue. However, this leads to a more complex supply chain (e.g. setting up order policies is more dicult), the contract negotiations with dierent suppliers may be rather time-consuming, or the costs per item may increase due to lower quantity discounts compared to single-sourcing. Balancing the advantages and disadvantages of multi-sourcing is a key issue when it comes to the design of the supply chain and a major challenge for production/inventory systems. When sourcing an item, a buyer has to consider the risk of a supply chain disruption, which has a certain probability. Dealing with this risk, the buyer needs to decide upon the supplier selection and the allocation of orders between suppliers. Ruiz-Torres and Mahmoodi (2006) studied a problem with multiple suppliers subject to failure risk and used an enumeration to decide about supplier selection and order allocation. Meena et al. (2011) considered disruptions due to catastrophic events and determined the optimal number of suppliers. Sawik (2014) compared single sourcing to dual sourcing strategies in make-to-order systems. Silbermayr and Minner (2016) considered multi-sourcing with dierent speeds and costs per supplier and examined the trade-o between economies of scale and supply disruptions. Tang (2006), Snyder et al. (2016) and Fahimnia et al. (2015) reviewed supply chains subject to disruptions and their risk management. Thomas and Tyworth (2006) presented a critical literature review on order splitting. Minner (2003) provided an overview of multi-sourcing problems. Individual contracts with suppliers often allow for quantity discounts, i.e. in addition to considering the disruption risk of a supplier, there are incentives for the buyer to allocate larger orders to suppliers with larger quantity discounts.Incrementaldiscounts only apply to items exceeding a certain order quantity whileall-unitsdiscounts apply to all items. Burke et al. (2008) modeled incremental quantity discounts without supplier failure risk. Munson and Rosenblatt (1998) reviewed quantity discounts and Munson and Jackson (2015) provided a more recent, extensive overview on quantity discounts. Another regularly observed price reduction comes from business volume discounts, i.e. the supplier oers a discount on the total amount of sales generated by a buyer. Sadrian and Yoon (1994) and Xia and Wu (2007) considered supplier selection under business volume discounts. An overview on multi-criteria supplier selection was presented in Ho et al. (2010).