Mixed backlogging and stockout models with inventory capacity

This paper addresses a dynamic lot sizing problem with mixed backlogging and stockout and bounded inventory. The stockout option means that there is outsourcing in a period only when inventory level at that period is less than or equal to 0. The production cost may include setup cost and the production level is unlimited. The holding, backlogging and outsourcing cost functions are linear. Furthermore, backlogging level at each period is limited, and outsourcing level at each period cannot exceed the demand of that period. The goal is to minimize the total cost of production, inventory holding/backlogging and outsourcing. We developed a dynamic programming algorithm with complexity O(T³logT) to solve this model, where T is the length of the planning horizon. Computational results indicate that the proposed algorithm is high performance with the number of periods in the planning horizon.