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This paper investigates an integrated supplier selection and inventory control problems in supply chain management by developing a mathematical model for a multi-echelon system. In particular, a buyer firm that consists of one warehouse and N identical retailers procures a type of product from a group of potential suppliers, which may have different prices, ordering costs, lead times and have restriction on minimum and maximum total order size, to satisfy stochastic demand. A continuous review system that implements the order quantity, reorder point (Q, R) inventory policy is considered in the proposed model. The objective is to select suppliers and to determine the optimal inventory policy that coordinates stock levels between each echelon of the systems while properly allocating orders among selected suppliers to maximize the expected profit. The model is solved by decomposing the mixed integer nonlinear programming model into two sub-models. Numerical experiments are conducted to evaluate the model and some managerial insights are obtained with sensitivity analysis.

In today׳s increasingly globalized economy, companies are facing increasing challenges to reduce operational costs, enlarge profit margins and remain competitive. People are forced to take advantages of any opportunity to optimize their business processes and improve the performance of the entire supply chain. For most industrial firms, the purchasing of raw material and component parts from suppliers constitutes a major expense. For example, as it was pointed out by Hayes et al. (2005) and Wadhwa and Ravindran (2007), it is expected that more and more manufacturing activities will be outsourced. Hence, among the various strategic activities involved in the supply chain management, the purchase decision has profound impacts on the overall system. According to Aissaoui et al. (2007), there are six major purchasing decision processes: (1) ‘make’ or ‘buy’, (2) supplier selection, (3) contract negotiation, (4) design collaboration, (5) procurement, and (6) sourcing analysis. Among all of them, the supplier selection problem has received great attentions (Weber et al., 1991, Jayaraman et al., 1999 and Feng, 2012). Generally, the supplier selection problem is to define which supplier(s) should be selected and how much order quantity should be assigned to each selected supplier. It is a multi-criteria decision making process depending on a wide range of factors which involve both quantitative and qualitative ones (such as quality, cost, capacity, delivery, and technical potential). Another relevant problem in supply chain management is to determine appropriate levels of inventory in each echelon. It is important to determine the quantity to order, the selections of suppliers and the best time to place an order. To derive optimal inventory policies that simultaneously determine how much, how often, and from which suppliers, typical ordering costs, purchasing costs, and holding costs should be considered. Although there is a plethora of research for the supplier selection model, only limited studies focused on the inventory control policies integrated with supplier selection, especially under stochastic demand. However, considering the cost issue, supplier selection decision is actually highly correlated with some major logistics issues within a company such as inventory (stock level, delivery frequency, etc.) Incorporating the decisions to schedule orders over time with the supplier selection may significantly reduce costs over the planning horizon (Aissaoui et al., 2007). For example, in the article by Mendoza and Ventura (2010), the authors studied both supplier selection and inventory control problems under a serial supply chain system. A mathematical model was proposed to determine an optimal inventory policy in different stages and allocate proper orders to the selected suppliers. It considered the integration of supplier selection and inventory control problems in multi-level systems. However, the mathematical model built in that paper was based on a stationary inventory policy with a constant demand. Moreover, the constant lead time, no backorder allowed and the same order quantity for different suppliers were assumed in the paper. These assumptions could be restrictive in reality, and it may not be appropriate to order the same quantity each time from different suppliers due to the different ordering costs and replenishment lead times. Thus, in this paper, we consider stochastic demand and lead time for this problem, which adopts various replenishment policies for different suppliers. We investigate both supplier selection and inventory control problems in a serial supply chain system in this paper. A two-echelon distribution system with a central warehouse and N retailers is considered to procure from a set of suppliers. The supplier selection process is assumed to occur in the first stage of the serial supply chain, and the decision is made by a single decision maker (i.e., centralized control) who aims to reduce the total cost associated with the entire supply chain. Capacity, ordering cost, unit price, holding and backorder cost are considered as the criteria for the supplier selection. For the inventory control policy, a continuous review system which applies the order quantity, reorder point (Q, R) policy is adopted to determine the inventory level held at each echelon of the supply chains. The objective of the proposed integrated model is to coordinate the replenishment decision with the inventory at each echelon while properly selecting the set of suppliers which meets capacity restrictions. A mixed integer non-linear programming (MINLP) model is established to determine the best policy for the supplier selection and replenishment decisions. The main contribution of this paper is to develop a multi-echelon inventory model for supplier selection problem under stochastic demand and lead times. To the best of our knowledge, this is the first work to tackle such a problem. The remainder of this article is organized as follows. In Section 2, previous work related to the supplier selection is summarized. In Section 3, we present our problem definition and assumptions. In Section 4, the development and formulation of the proposed multi-echelon inventory model with supplier selection is presented. We implement the model by conducting numerical experiments in Section 5. Finally, a summary of our work and an outlook on future research directions are presented in Section 6.

In this paper, we investigate a supplier selection and order allocation problem in a multi-echelon system under stochastic demand. Both the supplier selection decisions among potential suppliers and inventory control policies among one warehouse and N identical retailers are considered simultaneously. Capacity, ordering cost, unit price, holding and backorder cost are considered as the criteria for the supplier selection. A mixed integer non-linear programming (MINLP) model is proposed to select the best suppliers and determine a coordinated replenishment inventory policy at each echelon of the supply chains so that the total expected profit is maximized. To solve the model more efficiently, we decompose the mathematical model into two sub-models. Our experiments demonstrate the solvability and the effectiveness of the model. Moreover, we further investigate some issues regarding the selection of long-distance suppliers. Then, sensitivity analysis for the long-distance suppliers is conducted. There are two limitations for the current work in this paper. First, we have adopted the no-order-splitting assumption, which requires ordering from a certain supplier for some continues time span. In reality, a company could use the proposed model to choose strategic suppliers (a major supplier and several backups). The model can then be applied to decide the priorities to select suppliers and estimate the size to order from such suppliers. If we were to consider order-splitting for the problem under study, different models/approaches would be needed. We adopted the widely used two-echelon inventory system assumption: i.e., the batch size and the reorder point of the warehouse are the integral number of that of the retailer. Under the order-splitting setting, different suppliers may have various replenishment lead times and ordering costs, which could require a different ordering policy for these retailers. This will inevitably violate the above integer-ratio policy. Thus, to avoid this dilemma, we have applied the no-order-splitting assumption. Nevertheless, the results in our experimental examples at Section 5.4 demonstrate similar (Q, R) polices that are assigned to the retailer for different suppliers even when we considered the no-order-splitting assumption. This implies that it is possible to apply the order splitting model at the warehouse, and implement consistent replenishment policy at retailers for all the selected suppliers. Thus, future work may focus on extending order splitting model at the warehouse and the same ordering policy for the retailer. Second, to implement the stochastic demand assumption, we mainly focus on calculating the expected values of the total ordering size. The intention to use these expected values is not for signing the contract and ordering the computed amount from the selected suppliers, but for deciding the priorities to select suppliers and estimating the size to order from each supplier. Our model offers more insights to choose suppliers and allocate orders among the suppliers when considering the integration of both the supplier selection and inventory control problems in the multi-echelon system under stochastic demand. The model has several important managerial implications. (1) Strategic partnership: the manager can use our model to select strategic suppliers based on the quantitative criteria, which provides more insights of the expected quantity to order. (2) Inventory policy: management can use the model to decide the inventory policy for the cycle, safety and transition stocks. This would give a clear indication of the amount of safety stock that needs to be hold at each location. (3) What-if analysis: the model is very flexible for sensitivity analysis for cost structures when making changes to supplier lead times, fixed ordering costs and price. Such an analysis is useful when future changes are made by the suppliers. There are several directions for the future work. First, as we mentioned above, the order-splitting model seems to be a promising direction to work on. Second, in this paper we assume the (Q, R) continuous review policy. Future work may consider a periodic review system. Moreover, our model can be extended to consider multiple products and joint replenishment costs. Finally, since the supplier selection is a typical multi-criteria decision problem, this work could be extended to multi-objective models where the trade-offs associated with these criteria can be analyzed.