MOE − DGSCND: Multi-Objective Enterprise Green Supply Chain Network Design

This paper introduces and studies the Multi-Objective Enterprise Doubly-Green Sup-ply Chain Network Design (MOE-DGSCND) problem, an extension of Multi-ObjectiveSupply Chain Network Design. The problem studied here is a three-objective combi-natorial optimization problem that simultaneously minimizes total cost f1, carbondioxide emissions f2 and customer dissatisfaction f3 over binary decisions regard-ing which distribution centers to open and how to assign customer zones to openfacilities. The problem generalizes the capacitated facility location problem (CFLP)and is known to be NP-hard (Garey and Johnson, 1979). This paper formally speci-fies the decision variables, objective functions and constraints and investigates threesolution approaches using a single numerical instance: (A) an exact weighted-suminteger linear programming (ILP) formulation solved with Python combinatoriallyand via PuLP, (B) three Fully Polynomial-Time Approximation Schemes (FPTAS)providing (1 + ε)-approximate solutions for ε := 0.15 and (C) two baseline heuristicsfor comparison. On an instance with eight customers and five candidate distributioncenters, the exact solver certifies the optimal (sampled) supported solutions acrosseight weight combinations, while the FPTAS-based approaches complete withinmilliseconds, compared to centiseconds for the exact ILP on this tiny non-stochasticinstance.