A novel cross-docking EOQ-based model to optimize a multi-item multi-supplier multi-retailer inventory management system

Nowadays, the retail industry accounts for a large share of the world’s economy. Cross-docking is one of the most effective and smart inventory management systems used by retail companies to respond to demands efficiently. In this study, the aim is to develop a novel cross-docking EOQ-based model for a retail company. By considering a two-stage inventory procurement process, a new multi-item, multi-supplier, multi-retailer EOQ model is developed to minimize the total inventory costs. In the first stage, the required items are received from suppliers and are held in a central warehouse. In the second stage, these items are delivered to several retail stores. The total inventory costs include four main parts, i.e., holding costs at the central warehouse, holding costs at the retail stores, fixed ordering costs from the suppliers, and fixed ordering costs from the central warehouse. The optimal inventory policy is obtained by analyzing extrema, and a numerical example is used to confirm the efficiency of the proposed model. Based on the obtained results, it is evident that the proposed model produces the optimal policy for the cross-docking system. Furthermore, the model enables managers to analyze the effects of key factors on the costs of the system. Based on the obtained results, the annual demand of each retailer, the ordering cost by the central warehouse, the ordering cost at each retail store, and the holding cost at each retail store have a direct impact on the optimal cost. Furthermore, it is not possible to describe the effects of the holding cost at the central warehouse on the optimal cost of the system generally.