Fuzzy Bi-Objective Production-Distribution Planning Problem under the Carbon Emission Constraint

Abstract

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.

Multi-Objective Human Resource Allocation Approach for Sustainable Traffic Management

“…Consequently, the issue of selecting a particular method in a given context is still a subject of active research and largely depends on the decision makers. However, after the pioneering study by Zadeh [39], fuzzy set theory has become an efficient methodology for solving multi-objective programming problems (Zimmermann [40]; Sakawa et al [41]; Moghaddam [42]; Moon et al [43]; Chung et al [44]). Although the max-min approach [40] is frequently employed to solve multi-objective programming problems due to computational simplicity, the method does not always ensure a non-dominated fuzzy-efficient solution [45].…”

“…Consequently, we used two-phase method to find the allocation scheme. In addition, the method was used for solving production planning problem [43]; closed-loop supply chain network design problem [50]; and an optimal food preparation problem [51], etc.…”

Optimization and Analysis of a Manufacturing–Remanufacturing–Transport–Warehousing System within a Closed-Loop Supply Chain

“…Consequently, today, many managers are driving their supply chains through a sustainable supply chain management [1,2]. Several works have dealt with industrial sustainability.…”

Sustainable EOQ under Lead-Time Uncertainty and Multi-Modal Transport

“…Bouchery et al [10] reformulate the conventional EOQ model as a multi-objective problem because of the difficulty of developing a single objective problem that considers all aspects of sustainable issues. Moon et al [11] present a bi-objective mixed-integer linear programming model in a multi-period planning horizon with inaccurate information on raw material resources under a carbon emission constraint. However, the model does not consider combination of transport modes and the length of transportation routes, which are different from ours.…”