Sustainable multi-commodity capacitated facility location problem with complementarity demand functions

We investigate a multi-commodity capacitated facility location problem involving sustainability concerns (e.g., restrained carbon emission). In addition, this problem incorporates a complementarity demand function. We show that this incorporation can lead to superior decisions both analytically and computationally. The resultant formulation is a 0-1 mixed-integer non-concave quadratic program with equilibrium constraints. We adopt the piecewise-linear envelope method to transform the formulation into a 0-1 mixed-integer concave program. We then propose an efficient branch-and-refine algorithm with global convergence. Numerical examples demonstrate the effect of carbon emission limit and carbon trading on company decisions.

Automated summary

In this study, a multi-commodity capacitated facility location problem with sustainability concerns and a complementarity demand function is investigated. It is shown that incorporating this demand function can lead to superior decisions both analytically and computationally. The problem is transformed into a 0-1 mixed-integer concave program using the piecewise-linear envelope method, and an efficient branch-and-refine algorithm with global convergence is proposed. Numerical examples demonstrate the impact of carbon emission limit and carbon trading on company decisions.