Fuzzy bi-objective production-distribution planning problem under the carbon emission constraint

This study addresses the design of a four-stage production distribution system under a carbon emission constraint. The first stage contains a set of established retail outlets. The second stage consists of a set of possible distribution centers. The third stage is comprised of a set of manufacturing units. The final and fourth stage involves a set of suppliers. We propose a bi-objective optimization problem with a mixed-integer linear programming scheme for maximizing the total profits while minimizing the cumulative shortages in a multi-period planning horizon with inaccurate information on raw material resources. We also propose a two-phase approach to solve the proposed model and obtain a Pareto-optimal solution. The effectiveness of the solution method for obtaining the fuzzy efficient solution is demonstrated with computational experiments. Sensitivity analysis is used for examining the effect of the carbon emission constraint on the optimal decisions.