A Mathematical Model for Coordinating Decisions in Periodic Review Inventory Systems and Sharing the Profit in a two-echelon Decentralized Supply Chain, by Considering Quantity Discount Contract

Supply chain (SC) coordination is one of the major issues which has been considered in the investigations of supply chains. In this study, a two-echelon supply chain with one retailer and one supplier is considered. Demand is stochastic and has a normal distribution and lead time is assumed deterministic. The retailer uses a periodic review inventory system for his replenishment decisions and faces partial shortages. Review period and order-up-to-level are decision variables of the retailer. First, the optimized values of the variables in both decentralized and centralized decision-making structures are obtained. Although Centralized decision making increases the whole SC’s profitability, it reduces the profitability of the retailer in comparison with the decentralized model; In order to make centralized decisions and to encourage the retailer to change his decisions, a coordination model is proposed. Quantity discount contract is used as an incentive scheme in the coordinated model. For calculating the exact value of the discount factor in this contract, the both member’s profit is considered. Furthermore, to fairly share the extra profit achieved by the coordinated model, a profit-sharing strategy, based on the bargaining power of the members, is proposed. A set of numerical experiments and sensitivity analysis, which is performed with respect to several key parameters of the study, reveal that, from economic viewpoint, the proposed coordination model for the supplier-distributor channel, can increase the channel profit up to its optimal profit level and guarantee the improvement of channel members’ profit in comparison with their profit under the decentralized model. From inventory management viewpoint, the proposed discount contract reduces the distributor’s inventory shortage risk. Moreover, results of evaluating the proposed model under high levels of demand uncertainty shows that the proposed model is capable of coordinating the SC under various conditions such as demand frequencies and high quantities of standard deviation of the demand.