A multi-vendor multi-buyer integrated production-inventory model with greenhouse gas emissions

This paper presents an integrated production-inventory model for a two-level supply chain involving multiple vendors and buyers. The objective is to achieve a green and sustainable supply chain by considering greenhouse gas (GHG) emissions from production and transportation, along with a penalty scheme. The objective is to minimize the joint total cost of the supply chain and the GHG emissions by determining optimal delivery schedules and production lot sizes. To address this problem, the paper formulates it as an integer nonlinear programming model. Two metaheuristics, namely, the non-linear threshold algorithm and the simulated annealing method, are proposed to find pre-optimal solutions. Experimental comparisons are conducted with a non-commercial solver used for mixed integer nonlinear programming. The results demonstrate that the non-linear threshold algorithm outperforms simulated annealing significantly. Moreover, the findings highlight the significance of considering the cost of GHG emissions when optimizing the total cost in a scenario involving multiple vendors and buyers. Overall, this research emphasizes the importance of integrating environmental considerations into supply chain optimization and provides insights into the performance of different algorithms for addressing such challenging problems.