Manufacturing setup cost reduction and quality improvement for the distribution free continuous-review inventory model with a service level constraint

Over several decades, the continuous-review inventory model has been widely studied based on various assumptions and restrictions such as those related with quality improvement, service level constraint, and setup cost reduction. The proposed study investigates a continuous review inventory model with order quantity, reorder point, backorder price discount, process quality, and lead time as decision variables. 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. Two models are developed based on the probability distribution of lead time demand. The lead time demand follows a normal distribution in the first model and in the second model we apply the distribution free approach for the lead time demand. Finally, some numerical examples are given to illustrate the model.