Sustainable two stage supply chain management: A quadratic optimization approach with a quadratic constraint

Abstract

Designing a supply chain to comply with environmental policy requires awareness of how work and/or production methods impact the environment and what needs to be done to reduce those environmental impacts and make the company more sustainable. This is a dynamic process that occurs at both the strategic and operational levels. However, being environmentally friendly does not necessarily mean improving the efficiency of the system at the same time. Therefore, when allocating a production budget in a supply chain that implements the green paradigm, it is necessary to figure out how to properly recover costs in order to improve both sustainability and routine operations, offsetting the negative environmental impact of logistics and production without compromising the efficiency of the processes to be executed. In this paper, we study the latter problem in detail, focusing on the CO 2 emissions generated by the transportation from suppliers to production sites, and by the production activities carried out in each plant. We do this using a novel mathematical model that has a quadratic objective function and all linear constraints except one, which is also quadratic, and models the constraint on the budget that can be used for green investments caused by the increasing internal complexity created by large production flows in the production nodes of the supply network. To solve this model, we propose a multistart algorithm based on successive linear approximations. Computational results show the effectiveness of our proposal. • We study the problem of minimizing the CO 2 emissions produced by transportation activities from suppliers to production facilities and by manufacturing activities carried out at each facility in a two-stage supply chain. • A novel mathematical model which has a quadratic objective function and all linear constraints but one is proposed. The nonlinear constraint is quadratic and models the restriction of the budget usable for green investments caused by the increasing inner complexity produced by large production flows in production nodes of the supply network. • To solve this model, we propose a multi-start algorithm based on successive linear approximations. • Computational results and a comparison with a commercial solver reveal the effectiveness of our proposal.