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Coordinated Capacitated Lot-Sizing Problem with Dynamic Demand: A Lagrangian Heuristic

机译：具有动态需求的协调式容量批量问题：拉格朗日启发式

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摘要

Coordinated replenishment problems are common in manufacturing and distribution when a family of items shares a common production line, supplier, or a mode of transportation. In these situations the coordination of shared, and often limited, resources across items is economically attractive. This paper describes a mixed-integer programming formulation and Lagrangian relaxation solution procedure for the single-family coordinated capacitated lot-sizing problem with dynamic demand. The problem extends both the multi-item capacitated dynamic demand lot-sizing problem and the uncapacitated coordinated dynamic demand lot-sizing problem. We provide the results of computational experiments investigating the mathematical properties of the formulation and the performance of the Lagrangian procedures. The results indicate the superiority of the dual-based heuristic over linear programming-based approaches to the problem. The quality of the Lagrangian heuristic solution improved in most instances with increases in problem size. Heuristic solutions averaged 2.52% above optimal. The procedures were applied to an industry test problem yielding a 22.5% reduction in total costs.
机译：当一类物品共享一条共同的生产线，供应商或运输方式时，协调补货问题在制造和分销中很常见。在这些情况下，跨项目共享（通常是有限的）资源的协调在经济上很有吸引力。针对具有动态需求的单户协调容量批量问题，本文描述了一种混合整数规划公式和拉格朗日松弛求解过程。该问题不仅扩展了多项目容量动态需求批量问题，而且还扩展了无容量协调动态需求批量问题。我们提供计算实验的结果，研究配方的数学性质和拉格朗日程序的性能。结果表明，基于双重启发式的方法比基于线性规划的方法的优越性。在大多数情况下，随着问题大小的增加，拉格朗日启发式解决方案的质量得到了提高。启发式解决方案平均比最佳解决方案高出2.52％。将该程序应用于行业测试问题，从而使总成本降低了22.5％。

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