In this paper, we address a scheduling problem belonging to a two-stage assembly system that can also be viewed as a mass customization system. The first stage of this system consists of a set of subassembly machines, each of which produces a component type. These components are then transferred in sublots to Stage 2, where they are assembled into finished products. Stage 2 consists of multiple parallel machines. Each of these machines represents an assembly facility devoted to a product type. We represent this configuration as a m+n system, where there are m parallel machines at Stage 1 and n parallel machines at Stage 2. Lot-attached and sublot-attached setups, and transfer times/costs are encountered on the machines at both the stages. We assume that the subassemblies are transferred in equal-sized sublots to Stage 2. Given a number of lots (jobs), the problem is to determine the number of sublots to use for each lot and the sequence in which to process the lots. We consider two different objective functions, namely, minimize makespan, and minimize the total cost incurred. In view of the fact that both of these problems are NP-hard, we develop two column generation-based heuristic methods and show their efficacy over direct solution of the mixed integer programming formulations of the underlying problems. In fact, the results of our computational investigation on the use of these methods on large-sized problems reveal attainment of almost optimal solutions within a few seconds of CPU time. We also present some managerial insights.

在本文中，我们解决了属于两阶段装配系统的调度问题，该系统也可以看作是大规模定制系统。该系统的第一阶段包括一组子装配机，每个子装配机都会产生一个零件类型。然后将这些组件在子批中转移到阶段2，在此将它们组装成成品。第2阶段由多个并行计算机组成。这些机器中的每一个都代表专门用于产品类型的组装设施。我们将此配置表示为m + n系统，在第1阶段有m台并行机，在第2阶段有n台并行机，在这两个阶段的机器上都存在批量连接和子批次连接的设置，以及转移时间/成本。我们假定子装配体在相等大小的子批中转移到阶段2。给定很多批次（工作），问题在于确定每个批使用的子批数量以及处理这些批的顺序。我们考虑两个不同的目标函数，即最小化制造时间和最小化总成本。鉴于这两个问题都是NP问题，因此，我们开发了两种基于列生成的启发式方法，并证明了它们在直接解决潜在问题的混合整数编程公式上的有效性。事实上，我们针对这些大型问题使用这些方法的计算研究结果表明，在几秒钟的CPU时间内即可获得几乎最佳的解决方案。我们还提出了一些管理上的见解。