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SOLVING THE CUTTING STOCK PROBLEM IN THE MANUFACTURING TO ORDER STEEL PRODUCTION

机译：解决订购钢铁生产中的切割库存问题

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摘要

For the manufacturing of steel products, all products are processed sequentially through three stages of processes, refining, continuous casting, and rolling, in which the cutting pattern planning will be directly related to the detail planning and scheduling among the processes. For a manufacturing to order steel factory including three stages of processes, the productions at theses processes are inter-related and should be coordinated rather than being treated as mutually independent. That is, rather than establishing high level of work-in-process between stages, the production coordination among the process stages is conducted through the cutting pattern planning to meet the summarized demands of customers in the perspective of product specification. In this paper we consider the one-dimension cutting stock problem with the objective to minimizing the total inventory, in which the demands of all product specifications should be satisfied. At the rolling mill, steel products of specific length are produced by cutting the milled steel, transformed from a beam billet or a bloom, corresponding to some specific pattern in the cutting plan. An integer programming model is firstly developed to solve the cutting problem optimally, and then a two-stage programming model is proposed to derive a solution of quality in a short time. To obtain an optimal solution for the considered problem, three categories of decision variables should be solved simultaneously, that is, the number of cutting patterns, the vector variables in a cutting pattern, and the repeated runs for a pattern, which implies the complexity of the problem and usually can not be solve optimally within accepted time. The two-phase model first finds a limited number of superior patterns, rather than lists all possible patterns, through grouping certain product length types depending on the magnitudes of customer orders, then determines the repeated runs of all patterns in the list to generate a quality solution quickly. A comparison on the performances of the proposed models basing on actual customer orders is also provided.
机译：对于钢铁产品，所有产品都通过精炼，连铸和轧制三个阶段的顺序进行加工，其中切割图案的计划将直接与各个过程中的详细计划和计划相关。对于包括三个过程阶段的按订单制造的钢铁厂，这些过程中的生产是相互关联的，应该进行协调，而不是相互独立对待。即，不是在阶段之间建立高水平的在制品，而是通过切割模式计划来进行过程阶段之间的生产协调，以从产品规格的角度满足客户的总结需求。在本文中，我们考虑一维切割库存问题，目的是最大程度地减少总库存，其中应满足所有产品规格的需求。在轧机上，通过切割由钢坯或大方坯转变而来的特定长度的钢材来生产特定长度的钢材，这些钢材对应于切割计划中的某些特定样式。首先建立一个整数规划模型来最优地解决切削问题，然后提出一个两阶段规划模型以在短时间内得出质量的解。为了获得针对所考虑问题的最佳解决方案，应同时解决三类决策变量，即切割模式的数量，切割模式中的矢量变量以及模式的重复运行，这意味着加工的复杂性。问题，通常无法在可接受的时间内最佳解决。两阶段模型首先根据客户订单的数量对某些产品长度类型进行分组，从而找到数量有限的上级模式，而不是列出所有可能的模式，然后确定列表中所有模式的重复运行以产生质量快速解决。还提供了根据实际客户订单对建议模型的性能进行的比较。

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