Abstract In this study, one-dimensional marble plane cutting problem is studied based on the cutting equipment productivity and effective use of marble blocks. Different types of marble planes should be cut from multiple stock sized marble blocks in parallel by using a stone block-cutting machine (gang saw). Marble blocks, which have different dimensions, and quality gradations are supplied by the marble processing factory’s own marble quarries. Different quality gradations of the marble blocks and cutting equipment productivity need to be taken into account in addition to minimize the total trim loss or cost in modelling the present cutting problem. The nature of the production process in the marble industry consists of large amount of waste. Minimizing the amount of waste can be controlled indirectly by establishing an appropriate cutting plan. Therefore, minimization of the total cost of transportation and overgrading (supplying higher quality material than specified by the customer) while determining a suitable cutting plan for the marble blocks is aimed. A mixed integer linear programming (MILP) model is developed for solving the present marble plane cutting problem for small-size instances. The salient feature of the developed model is not requiring a priori enumeration of all possible cutting patterns and to permit generation of retail to reuse. For larger size problem instances a Stochastic Diffusion Search (SDS) algorithm is developed. Extensive computational studies are performed by using test instances, which are collected from a marble processing company operating at Izmir. The computational results show that the developed models and SDS algorithm are very useful in providing effective cutting plans.

中文翻译：

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通过数学规划和随机扩散搜索方法建模和解决大理石行业的现实世界下料问题

摘要 本研究基于切割设备的生产率和大理石块的有效利用，对一维大理石平面切割问题进行了研究。应使用石块切割机（组锯）从多个库存大小的大理石块中平行切割不同类型的大理石平面。不同尺寸和质量等级的大理石块由大理石加工厂自己的大理石采石场供应。大理石块的不同质量等级和切割设备生产率，除了最小化总修剪损失或成本之外，还需要考虑对当前切割问题进行建模。大理石行业生产过程的性质包括大量废物。可以通过制定适当的切割计划来间接控制废物量的最小化。因此，在确定合适的大理石块切割计划的同时，最大限度地减少运输和分级（提供比客户指定的质量更高的材料）的总成本。混合整数线性规划 (MILP) 模型被开发用于解决目前针对小尺寸实例的大理石平面切割问题。开发模型的显着特点是不需要对所有可能的切割模式进行先验枚举，并允许生成零售以重复使用。对于较大的问题实例，开发了随机扩散搜索 (SDS) 算法。通过使用从伊兹密尔经营的大理石加工公司收集的测试实例进行广泛的计算研究。