Optimal batch ordering policies for assembly systems with guaranteed service

For a supply chain modelled as a multi-echelon inventory system, effective management of its inventory at each stock is critical to reduce inventory costs while assuring a given service level to customers. In our previous work, we used the guaranteed-service approach (GSA) to design optimal echelon batch ordering policies for continuous-review serial systems with Poisson customer demand and fixed order costs. The approach assumes that the final customer demand is bounded and each stock has a guaranteed service time in the sense that the demand of its downstream stock can always be satisfied in the service time. This paper extends this work by considering more general assembly systems. We first derive an analytical expression for the total cost of the system in the long run. The problem of finding optimal echelon batch ordering policies for the system can then be decomposed into two independent sub-problems: order size decision sub-problem and reorder point decision sub-problem. We develop efficient dynamic programming algorithms for the two sub-problems. Numerical experiments on randomly generated instances show the effectiveness of the proposed approach.