مدل موجودی یکپارچه با خریدار واحد و فروشندگان متعدد به همراه تعداد متغیری از فروشندگان

Supply chain management is concerned with the coordination of material and information flows in multi-stage production systems. A closer look at the literature reveals that previous research on the coordination of multi-stage production systems has predominantly focused on the sales side of the supply chain, whereas problems that arise on the supply side have often been neglected. This article closes this gap by studying the coordination of a supplier network in an integrated inventory model. Specifically, we consider a buyer sourcing a product from heterogeneous suppliers and tackle both the supplier selection and lot size decision with the objective to minimise total system costs. First, we provide mathematical formulations for the problem under study, and then suggest a two-stage solution procedure to derive a solution. Numerical studies indicate that our solution procedure reduces the total number of supplier combinations that have to be tested for optimality, and that it may support initiatives which aim on increasing the efficiency of the supply chain as a heuristic planning tool.

Inventory management has long been treated as an isolated function solely focused on individual entities, taking into account only those cost parameters that could be directly influenced by the planning company. However, companies have realised in the last years that the management of inventories across different echelons in a supply chain is critical to increase profits, as the coordination of inventory directly influences both costs and service. Since demand is almost always uncertain, inventory is required to assure that the demand of the customer can be satisfied without interruption. Increasing inventory levels is thus a popular method to improve customer service, although every unit of a product kept in stock results in inventory holding costs. In this context, some empirical studies suggest that the present value of inventory in the United States is close to $ 1.5 trillion (Neale et al., 2003 and US Census Bureau, 2008), which illustrates the importance of efficient inventory management. Starting with Goyal (1976), a stream of research has emerged in recent years aiming at the coordination of inventory replenishment decisions among individual companies to benefit the entire supply chain, rather than a single company. The consequences of coordinating inventory replenishment decisions are regularly analysed in so-called integrated inventory models, which focus on the total costs of the system in question. So far, research was mainly concerned with single-vendor-single-buyer- and single-vendor-multiple-buyer-models, which does not adequately reflect the importance of the supply side in creating customer value and in improving the overall cost situation of the company. To close this gap, this paper focuses on a single buyer sourcing a single product from multiple suppliers. Specifically, the article analyses a situation where the buyer faces a pool of heterogeneous suppliers, and tackles the supplier selection and lot size decision with the objective to minimise total system costs. The model developed in this article may be used as a heuristic planning tool in practical situations where suppliers have been short-listed after a market study and where it has to be determined how many and which suppliers to select. One area where our model may be applied is the automotive industry, where it has been reported that buyers and vendors engage in strategic partnerships with the intention to create competitive advantages (see for example Dyer, 1996). It is obvious that if buyer and vendors decide to invest in specific assets, it is also necessary to achieve coordination at an operational level. In this case, using an integrated inventory model may help to coordinate material flows in the system. Specifically, the model developed in this article may help to determine the total costs of alternative sourcing agreements and thus provides assistance in finding a setting where a particular product can be produced and distributed at the least total cost. Incentive problems and the question of how to allocate the system profit are not considered in the model, but may be added without altering its core statements. The remainder of the paper is organised as follows: in the next two sections, the article reviews related literature and outlines the assumptions and definitions which are used in Sections 4 and 5. Accordingly, we develop a coordination mechanism and derive a solution for the supplier selection and integrated lot sizing problem. Section 5 presents a numerical example and Section 6 concludes the article.