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.

在批量生产计划中，管理者必须考虑制造过程中不可预见的情况以及可用于满足准时需求的资源，并确定最佳的补货策略。为了解决这些问题，本研究研究了一种混合制造系统，其中包含外包，随机机器故障和随机报废。目的是确定最佳的正常运行时间，以最小化整个系统的费用。这项研究的假设包括部分外包计划，该计划涉及较高的单位成本，随机报废和在中止/恢复政策下的随机故障，其中机器在故障后立即进行维修，被中断的批次的生产将尽快恢复。完成后。开发了一个精确的模型来探索这个特定问题。数学推导 优化方法和递归算法用于得出最佳补货策略。数值示例说明了结果的适用性。为了促进管理决策，它揭示了外包，报废和机器故障对（i）最佳策略的个别和/或综合影响。（ii）系统的不同成本贡献者；（iii）系统总支出；（iv）机器利用率；（v）问题的其他关键参数。（iii）系统总支出；（iv）机器利用率；（v）问题的其他关键参数。（iii）系统总支出；（iv）机器利用率；（v）问题的其他关键参数。