Stochastic machine breakdown and discrete delivery in an imperfect inventory-production system

Abstract

In this paper, we develop an integrated inventory model to determine the optimal lot size and production uptime while considering stochastic machine breakdown and multiple shipments for a single-buyer and single-vendor. Machine breakdown cannot be controlled by the production house. Thus, we assume it as stochastic, not constant. Moreover, we assume that the manufacturing process produces defective items. When a breakdown takes place, the production system follows a no resumption policy. Some defective products cannot be reworked and are discarded from the system. To prevent shortages, we consider safety stock. The model assumes that both batch quantity and the distance between two shipments are identical and that the transportation cost is paid by the buyer. We prove the convexity of the total cost function and derive the closed-form solutions for decision variables analytically. To obtain the optimal production uptime, we determine both the lower and upper bounds for the optimal production uptime using a bisection searching algorithm. To illustrate the applicability of the proposed model, we provided a numerical example and sensitivity analysis.