This study considers a stochastic customer order scheduling and resource allocation problem in an unrelated parallel machine environment. Customer orders dynamically arrive at a machine station, and each consists of multiple product types with random workloads. Speeds of the machines are controllable through the allocation of limited resources such as overtime or dedicated manpower. The objective is to minimize the long run expected order cycle time by optimizing workload schedule and resource allocation. The impacts of workload variance, product similarity and machine speed are evaluated, and several optimal properties are explored. Three heuristic algorithms are proposed based on the theoretical results developed. The effectiveness of the proposed algorithms is demonstrated through extensive numerical experiments. This study brings new perspectives to resource allocation problems in stochastic environment, and provides insights into the relationship between resource allocation decisions and overall production efficiency.

本研究考虑了一个不相关的并行机环境中的随机客户订单调度和资源分配问题。客户订单动态地到达机器站，每个订单都包含具有随机工作负载的多种产品类型。机器的速度可以通过分配有限的资源（例如加班或专用人力）来控制。目标是通过优化工作负载计划和资源分配来最小化长期预期订单周期时间。评估了工作负载差异、产品相似性和机器速度的影响，并探索了几个最佳属性。基于所开发的理论结果提出了三种启发式算法。通过大量的数值实验证明了所提出算法的有效性。