Incorporating outsourcing, stochastic failure, and scrap into batch fabrication planning

Abstract

In batch production planning, managers must consider the unforeseeable circumstances in the fabrication process and resources available to meet demand on time and determine the optimal replenishment policy. To address these concerns, this study examines a hybrid fabrication system incorporating outsourcing, stochastic machine failures, and random scraps. The objective is to decide the optimal uptime that minimizes the overall system expenses. Assumptions in this study include a partial outsourcing plan associated with a higher unit cost, random scrap, and stochastic breakdown under an abort/resume policy, wherein repair of a machine begins immediately after a breakdown, and the production of the interrupted batch resumes as soon as it is completed. A precise model is developed to explore this specific problem. Mathematical derivations, optimization methodology, and a recursive algorithm are used to derive the optimal replenishment policy. The applicability of the results is illustrated by a numerical example. To facilitate managerial decision making, it reveals the individual and/or combined impact of outsourcing, scrap, and machine failure on (i) the optimal policy; (ii) the system’s different cost contributors; (iii) total system expenses; (iv) machine utilization; and (v) other key parameters of the problem.