Developing a two-echelon inventory model with simultaneous consideration of backorders and lost sales

One of the most important challenges in inventory control of an efficient supply chain is to minimize logistics costs for each member of the chain. This challenge is even more important when facing non-deterministic demands. In this paper, a divergent two-echelon inventory model is developed to minimize logistics costs (ordering, holding and shortage costs) both for a warehouse and retailers when facing a Poisson stochastic demand. First, a mathematical model is developed which consists of one warehouse and multiple retailers with ordering, holding and shortage costs. The warehouse, similar to the retailers, has both backorder and lost-sales shortage costs simultaneously. This simultaneous combination of backorder and lost-sales shortage costs for both the warehouse and the retailers is the main contribution of this paper towards the research field of divergent two-echelon inventory models. The mathematical model is analytically solved and then validated through simulation. Finally, validity of the model is evaluated by comparing the mathematical and simulation results which indicate the contribution of "percent of warehouse demand with lost sales" and "percent of each retailers' demand with lost sales" parameters affect the total costs of the system.