A lost-sales continuous-review inventory system with emergency ordering

While existing lost-sales continuous-review inventory models with a provision for emergency ordering under an (s,S) or (s,Q) policy assume that regular and emergency orders are placed at levels s and 0, repectively, we develop an exact model with non-unit-sized demands where orders of sizes Q1 and Q2 are placed at reorder levels s1 and s2. Using a level-crossing methodology, we derive the stationary distribution of the inventory level (stock on hand) and present explicit expressions for the average cost rate functions with/without a service level constraint. Some numerical results, in comparison with the case with no provision for emergency ordering, are presented.