A note on bi-objective optimization for sustainable supply chain network design in omnichannel

PurposeThis paper aims to correct the existing mixed integer programming (MIP) model proposed by Yadav et al. (2019) [“Bi-objective optimization for sustainable supply chain network design in omnichannel.”, Journal of Manufacturing Technology Management, Vol. 30 No. 6, pp. 972–986].Design/methodology/approachThis paper first presents a counterexample to show that the existing MIP model is incorrect and then proposes an improved mixed integer linear programming (MILP) model for the considered problem. Last, a numerical experiment is conducted to test our improved MILP model.FindingsThis paper demonstrates that the formulations of the facility capacity constraints and the product flow balance constraints in the existing MIP model are incorrect and incomplete. Due to this reason, infeasible solutions could be identified as feasible ones by the existing MIP model. Hence, the optimal solution obtained with the existing MIP model could be infeasible. A counter-example is used to verify our observations. Computational results verify the effectiveness of our improved MILP model.Originality/valueThis paper gives a complete and correct formulation of the facility capacity constraints and the product flow balance constraints, and conducts other improvements on the existing MIP model. The improved MILP model can be easily implemented and would help companies to have more effective distribution networks under the omnichannel environment.