Quality improvement, setup cost and lead-time reductions in lot size reorder point models with an imperfect production process

This paper investigates the lot size, reorder point inventory model involving variable lead time with partial backorders, where the production process is imperfect. The options of investing in process quality improvement and setup cost reduction are included, and lead time can be shortened at an extra crashing cost. The objective is to simultaneously optimize the lot size, the reorder point, the process quality, the setup cost, and the lead time. We first assume that lead-time demand follows a normal distribution and develop an algorithm to find the optimal solution. Then, we relax the assumption of normality to consider a distribution-free case where only the mean and standard deviation of lead-time demand are known. We apply the minimax distribution-free procedure to solve this problem. Furthermore, two numerical examples are given to illustrate the results.