Effective Investment to Reduce Setup Cost in a Mixture Inventory Model Involving Controllable Backorder Rate and Variable Lead Time with a Service Level Constraint

This paper investigates the impact of setup cost reduction on an inventory policy for a continuous review mixture inventory model involving controllable backorder rate and variable lead time with a service level constraint, in which the order quantity, setup cost, and lead time are decision variables. Our objective is to develop an algorithm to determine the optimal order quantity, setup cost, and lead time simultaneously, so that the total expected annual cost incurred has a minimum value. Furthermore, four numerical examples are provided to illustrate the results, and the effects of system parameters are also included for decision making.