Periodic review integrated inventory model with controllable lead time and setup cost in the presence of a service level constraint

The impact of lead time reduction on an integrated periodic review inventory system comprising a single vendor and multiple buyers with a step crashing cost function and service level constraints is explored in this study. Distribution free and normal distribution procedure with Lagrange multipliers is applied to determining the lead time, the common shipment cycle time, the target levels of replenishments and the number of shipments per production cycle so that the expected total system cost is minimised. The efficient algorithm is constructed to find the optimal lead time, the common shipment cycle time, the target levels of replenishments and the number of shipments per production cycle simultaneously. Moreover, the numerical example is introduced to illustrate the proposed model. Through sensitivity analysis, some observations and managerial implications are provided.