arXiv:2507.15866cs.AI2025-07

优化肉类加工厂采购与生产,提升利润并解决实际约束难题。

Purchase and Production Optimization in a Meat Processing Plant

  • 基于整数线性规划设计迭代算法,处理多种加工路径和过期库存。
  • 考虑最小订单量和替代方案最低比例,显著提升方案可行性。
  • 算法快速求解真实案例,适配中小型企业生产决策需求。

食品生产行业,尤其是肉类生产领域,面临诸多挑战,尤其在欧盟能源危机后更加严峻。高效利用投入材料是影响企业利润的关键因素。本文针对一家肉类加工企业的采购与后续物料处理问题进行优化求解。不同于多数研究聚焦供应链管理,本工作专注于生产环节。问题包含物料加工的多种替代路径、不同保质期的库存,以及当前文献普遍忽略的两个关键约束:最小订单量和替代方案最低占比。我们证明这两个约束均使问题变为 $ ext{NP}$-难,因此设计了一种基于整数线性规划的简单迭代方法,可使用开源求解器解决实际规模问题。该方法还能缓解商业求解器中因数据值范围过大导致的数值问题。利用真实企业数据测试表明,本算法可在数秒内找到所有场景的最优解。

原文摘要 · Abstract (English)

The food production industry, especially the meat production sector, faces many challenges that have even escalated due to the recent outbreak of the energy crisis in the European Union. Therefore, efficient use of input materials is an essential aspect affecting the profit of such companies. This paper addresses an optimization problem concerning the purchase and subsequent material processing we solved for a meat processing company. Unlike the majority of existing papers, we do not concentrate on how this problem concerns supply chain management, but we focus purely on the production stage. The problem involves the concept of alternative ways of material processing, stock of material with different expiration dates, and extra constraints widely neglected in the current literature, namely, the minimum order quantity and the minimum percentage in alternatives. We prove that each of these two constraints makes the problem \mbox{$\mathcal{NP}$-hard}, and hence we design a simple iterative approach based on integer linear programming that allows us to solve real-life instances even using an open-source integer linear programming solver. Another advantage of this approach is that it mitigates numerical issues, caused by the extensive range of data values, we experienced with a commercial solver. The results obtained using real data from the meat processing company showed that our algorithm can find the optimum solution in a few seconds for all considered use cases.

生产优化整数规划肉类加工供应链

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