The Optimization Problem of Batik Cloth Production with Fuzzy Multi-Objective Linear Programming and Application of Branch and Bound Method

Fevi Hanesti, Wardi Syafmen, Syamsyida Rozi
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Abstract

This study discussed fuzzy multi-objective linear programming (FMOLP) and its application. This research was conducted in Rumah Batik Mentari Jambi, which produces five batik motifs typical of the Jambi. In this research, the tolerance for additional raw material capacity is included in the model. This research aims to find out the number of tolerances needed, the maximum number of batik needed to be produced, and the minimum production time so that the producer can earn the maximum profit. The decision variables in FMOLP are the number of pieces of batik measuring in 2m2, which means the decision variables must be an integer. Therefore, after obtaining the optimal solution from FMOLP, then proceed with the branch and bound method to obtain the integer solution. The result of this research is that the addition of raw materials needed to earn optimal solutions is as much as 50% of the tolerance assumed in the model. Thus, owner can earn the optimal profit of Rp. 5,675,800.00/week by producing as many as 67 pieces of batik with the design of angso duo, 18 pieces with the design of gentala, and 50 pieces with the design of batang hari, and the minimum production time is 270 hours/week.
模糊多目标线性规划的蜡染生产优化问题及分支定界法的应用
研究了模糊多目标线性规划及其应用。这项研究是在Rumah Batik Mentari Jambi进行的,它生产了五种典型的Jambi蜡染图案。在本研究中,模型中包含了对额外原材料容量的容差。本研究旨在找出所需的公差数量,生产蜡染所需的最大数量,以及最短的生产时间,从而使生产商获得最大的利润。FMOLP中的决策变量为2m2的蜡染片数,即决策变量必须为整数。因此,在从FMOLP中得到最优解后,再用分支定界法得到整数解。本研究的结果是,获得最优解决方案所需的原材料的添加量高达模型中假设公差的50%。因此,业主可以通过生产最多67件angso duo设计的蜡染,18件gentala设计的蜡染,50件batang hari设计的蜡染,获得最优利润Rp. 5,675,800.00/周,最小生产时间为270小时/周。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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