AI 中文总结
本文提出多目标企业绿色供应链网络设计问题，形式化建模并比较精确ILP、FPTAS和启发式算法，在八客户实例上验证了帕累托最优与近似保证。
AI 中文摘要
本文引入并研究了多目标企业绿色供应链网络设计问题（MOEDGSCND），它是著名的多目标供应链网络设计（MO-SCND）问题的一个扩展。在该问题中，这是一个三目标组合优化问题，需要在关于开设哪些配送中心以及如何将客户区域分配给已开设设施的二元决策上，同时最小化总成本f1、二氧化碳排放量f2和客户不满度f3。该问题推广了容量受限的设施选址问题，并且已知是NP难的。此外，本文给出了决策变量、目标函数和所有约束的形式化规范，然后使用一个数值实例研究并比较了三种求解方法：（A）通过PuLP求解的精确加权和整数线性规划，（B）三种完全多项式时间近似方案（FPTAS），提供ε:=0.15的(.94 + ε)保证近似，以及（C）两种用于比较的基线启发式算法。在一个拥有八个客户和五个候选配送中心的实例上，精确求解器在八个权重组合上验证了最优帕累托前沿，并且所有三种FPTAS变体都达到了其近似保证，在此规模下，它们在毫秒内完成，而使用PuLP求解器的精确ILP则需要百分之一秒。
英文摘要
This paper introduces and studies the Multi-Objective Enterprise Green Supply Chain Network Design problem (MOEDGSCND) an extension of the well known Multi-Objective Supply Chain Network Design (MO-SCND), in this case a three-objective combinatorial optimisation problem that simultaneously minimises total cost f1, carbon dioxide emissions f2, and customer dissatisfaction f3 over binary decisions on which distribution centres to open and how to assign customer zones to open facilities. The problem generalises capacitated facility location and is known to be NP-hard. Furthermore this paper lays out a formal specification of decision variables, objective functions, all constraints and then investigates and compares three solution approaches using a single numerical instance: (A) exact weighted-sum integer linear programming solved via PuLP, (B) three Fully Polynomial-Time Approximation Schemes (FPTAS) providing (.94 + $ε$)-guarantee approximations for $ε$ := 0.15, and (C) two baseline heuristics for comparison. On an eight-customer, five-candidate-DC instance the exact solver certifies the optimal Pareto front across eight weight combinations, and all three FPTAS variants achieve their approximation guarantees, finishing within milliseconds compared to centiseconds for the exact ILP using the PuLP solver on this scale.
Journal refCond. acc./R&R AJOR 16(4), 2026
