Lot size reorder point inventory model with controllable lead time and set-up cost

This paper deals with the lead time and set-up cost reductions problem on the modified lot size reorder point inventory model in which the production process is imperfect. We consider that the lead time can be shortened at an extra crashing cost, which depends on the length of lead time to be reduced and the ordering lot size. The option of investing in reducing set-up cost is also included. Two commonly used investment cost functional forms, logarithmic and power, are employed for set-up cost reduction. We assume that the stochastic demand during lead time follows a Normal distribution. The objective is simultaneously to optimize the lot size, reorder point, set-up cost and lead time. An algorithm of finding the optimal solution is developed, and two numerical examples are given to illustrate the results.