The growing emphasis on environmental responsibility has compelled organisations to redesign conventional supplychain frameworks by incorporating sustainability-oriented objectives. In this context, the present work investigatesanoptimisation-based approach for green supply chain management by simultaneously addressing economic and environmentalperformance indicators. A multi-supplier, multi-customer supply chain network is formulated with the objective of minimisingoverall transportation cost and associated carbon emissions. Two widely used optimisation techniques, namely Linear Programming and Genetic Algorithm, are employed to solve theproposedproblem and their performances are comparatively analysed. Linear Programming is utilised due to its mathematical precisionandcomputational efficiency in handling structured optimisation problems, whereas the Genetic Algorithmis applied toexamineitsadaptability in dealing with complex and heuristic-based solution spaces. The evaluation is carried out by comparingsolutionquality in terms of total cost, emission levels, and computational behaviour. The results reveal that Linear Programming consistently delivers lower cost and emission values under the givenproblemformulation, demonstrating its suitability for deterministic and well-defined supply chain environments. Although the genetic algorithm provides feasible solutions and greater modelling flexibility, its effectiveness is strongly influenced by parameter selection and algorithm tuning. Keywords: Green Supply Chain, Linear Programming, Genetic Algorithm, Optimization, Sustainability, Cost Minimization