An Evolutionary Multi-objective Approach for Coordinating Supplier–Producer Conflict in Lot Sizing
Authors: Elarbi Maha , Elwadi Chaima , Bechikh Slim , Bahroun Zied , Said Lamjed Ben 
Published: October 2021

Context. This paper deals with bilateral joint decision making in supply chains, and more specifically focuses on coordinating the decisions taken by the supplier and the producer in lot sizing. Research gap. Previous existing works in lot sizing have modeled the coordination task as a bi-level optimization problem. Unfortunately, the bi-level model causes a hierarchy between the two actors by making the leader imposing the decisions that suits his/her interests to the follower. This induces a significant conflict of interest between the two stakeholders because the leaders benefit is always greater than the follower’s one. Objective. The main goal of this work is to attenuate the conflict of interest issue between both actors by proposing a multi-objective model that alleviates the hierarchy and creates a win–win situation. Method. We propose an effective multi-objective lot sizing model, called Supplier-Producer Multi-Objective Lot Sizing (SP-MOLS); that alleviates the hierarchy between the actors’ objectives by assigning them the same importance degree and hence optimizing them simultaneously. The resolution of our SP-MOLS model using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), as an effective meta-heuristic search engine, provides a set of trade-off solutions, each expressing a compromise degree between the two actors: the supplier and the producer. Results. To validate our approach, we use five test problems each containing 100 instances with a planning horizon of 10 periods and we analyze the obtained trade-off solutions using the compromise degree and the gap between costs as main consensus metrics. The obtained results reveal that a small sacrifice in the leader’s benefit could produce a significant improvement in the follower’s one. For instance, a 10% increase of the producer’s cost may generate a 42% decrease in the supplier’s one. Reciprocally, a 0.4% increase of the supplier’s cost may generate a 49% decrease in the producer’s cost. Method algorithmic improvement. As solutions of interests for both stakeholders are usually located within the extreme regions of the Pareto front, we propose NSGA-II with Focus on Extreme Regions (NSGA-II-FER) as a new variant of NSGA-II that focuses the search in the extreme regions of the Pareto front thanks to a modified crowding measure that is adaptively managed during the evolution process. This variant has shown its ability to eliminate dominance-resistant solutions and thus to come up with better extreme regions. Based on the experimental results, NSGA-II-FER is shown to have the ability to provide the decision makers with more convergent and more diversified extreme non-dominated solutions, expressing better trade-off degrees between both actors’ costs. Managerial implications. The promising results obtained by our proposal encourage decision makers’ to adopt a multi-objective approach rather than a bi-level one. From our personal perspective, we recommend running the three models (the multi-objective model and the two bi-levels ones); then analyzing the solutions of all models in terms of compromise degrees and logistic costs. This would allow both actors to observe how the hierarchy incurred by the bi-level models increases conflicts, while the multi-objective one generates solutions with much improved consensus degrees. Such observations will convince the supply chain stakeholders to adopt our multi-objective approach, while keeping an eye on the bi-level models’ solutions and the consensus degrees. Finally, we also recommend focusing on the extreme regions of the Pareto front since they contain rich solutions in terms of consensus. Such solutions are more convincing in the negotiation process and thus could lead to better win–win situations.