A periodic review integrated inventory model with controllable setup cost, imperfect items, and inspection errors under service level constraint

This paper presents an integrated inventory model which consists of single vendor and buyer. The buyer managed its inventory periodically and orders products from the vendor to satisfy the end customer's demand, where the annual demand and the ordering cost were in the fuzzy environment. The buyer used a service level constraint instead of the stock-out cost term, so that the stock-out level per cycle was bounded. Then, the vendor produced and delivered products to the buyer. The vendor had a choice to commit an investment to reduce the setup cost. However, the vendor's production process was imperfect, thus the lot delivered contained some defective products. Moreover, the buyer's inspection process was not error-free since the inspector could be mistaken in categorizing the product's quality. The objective was to find the optimum value for the review period, the setup cost, and the number of deliveries in one production cycle which might minimize the joint total cost. Furthermore, the algorithm and numerical example were provided to illustrate the application of the model.