Vendor managed inventory model for single-vendor multi-retailer supply chains

Vendor managed inventory is an integrated approach for retailer–vendor coordination, according to which the vendor decides on the appropriate inventory levels within bounds that are agreed upon in a contractual agreement between vendor and retailers. In this contract, the vendor usually incurs a penalty cost for items exceeding these bounds. The purpose of this paper is to develop a model for a supply chain with single vendor and multiple retailers under VMI mode of operation. This model explicitly includes the VMI contractual agreement between the vendor and retailers. The developed model can easily describe supply chains with capacity constraints by selecting high penalty cost. Theorems are established to alleviate the complexity of the model and render the mathematics tractable. Moreover, an efficient algorithm is devised to find the global optimal solution. This algorithm reduces the computational efforts significantly. In addition, numerical experiments are conducted to show the utility of the proposed model.