Sequence Scheduling with Batching and Smoothing Considerations

现代生产计划的两个关键但又相互矛盾的概念是分组和平滑。当由于产品变化造成的设置损失不是微不足道的时候，对相同类型的产品进行分批以形成批次或批次对于有效的商店运营是必不可少的。平滑已被视为另一个关键概念，特别是在所谓的JIT环境中。这些概念都是单独研究的，但没有一起研究。这项研究集中在一条生产线上，其中一部分需要分批(如喷漆)，而另一部分需要光顺(如组合)。所考虑的系统是一个两阶段混合流水作业系统，其中第一阶段由两台平行机组成，要求对具有相同属性的产品进行分批，例如，颜色。另一方面，生产平滑是第二阶段的主要关注点。在描述了问题场景之后，给出了实现平滑的一般思想，并在“无库存同步生产”的假设下，确定了满足平滑“约束”的生产序列的性质。对数学规划进行四次模拟，以获得最终的序列，以最小化由于产品属性(例如，颜色)的变化而导致的第一阶段设置的数量。这项研究还讨论了一种方法，以做出适当的“颜色/产品类型分配”，从而减少颜色变化的次数。该问题也被表示为一个整数规划。文中还给出了一种基于拉格朗日的启发式算法和一种基于拉格朗日算法的启发式算法，该算法用于标准作业车间调度问题，其中工序优先约束被放松以产生每台机器的子问题。

Two critical, yet contradictory, concepts of modern production planning are grouping and smoothing. Batching of the same type of products to form batches or lots are essential for efficient shop operation when setup losses due to product changes are non-trivial. Smoothing has become viewed as an another key concept especially in the so-called JIT environment. These concepts have been studied individually but not together.This study focused on a production line a part of which calls for batching (such as painting), whereas the other calls for smoothing (such as assenbly). The system considered is a two-stage hybrid flowshop in which the first stage consists of two parallel machines and calls for batching of products having the same attribute, say, color. Production smoothing, on the other hand, is a major concern of the second stage. A production sequence which "compromises" both batching and smoothing considerations are sought.The study, after describing the problem scenario, presented a general idea to achieve smoothing and identified, under the assumpticn of "no-inventory synchronized production", properties of the production sequences to meet a smoothing "constraint". A mathematical program is fourmulated to obtain a final sequence to minimize the number of the first-stage setups due to changes of the product attribute (say, color). The study also discussed a method to make appropriate "color/product-type assignment" so that the number of color changes can be reduced. The problem is also formulated as an integer program. The proposed approach was evaluated computationally with real data.The study also presented 1) a Lagrangian-based heuristic for the standard job shop scheduling problem where operation precedence constraints are relaxed to yield subproblems for each machine, and 2) a colum-gen aration heuristic for a lot scheduling problem of single-stage parallel identical machines.