Solution of a pollution sensitive EOQ model under fuzzy lock leadership game approach

This paper considers pollution sensitive economic order quantity (EOQ) inventory model for items under several styles of managerial leadership via lock fuzzy game theoretic approach. The decision-maker (DM) controls several cost components by playing as Player 1 in one side and the consumers who may accept/reject those items (unwilling to buy those commodities) stand as Player 2 in the other side. At first, we develop a new pollution function through modeling, then we study a real case study in a brick factory. Based on this case study, we formulate a cost minimization EOQ model where the environmental pollution is incorporated. Because of the fuzzy flexibility of the model parameters, we also develop a fuzzy mathematical model by considering the demand and all cost parameters of the inventory system as triangular lock fuzzy numbers. Then, we develop a game problem by applying 5-stage leadership style employing several key vectors into the model itself. Also, we reformulate the proposed model into bi-objective game model with different strategies and solve it by an existing methodology. The problem has been solved for crisp, general fuzzy, bi-objective strategic fuzzy, and models of several leadership styles also. Numerical results show that for cooperative game, inventory cost function reaches its minimum rather than the non-cooperative game with the use of proper keys of the fuzzy locks. A comparative study between proposed method and existing method has been done for showing the superiority of the proposed methodology. Finally, in the sensitivity analysis, graphical illustrations are made to justify the new approach and a conclusive remark has been added followed by scope of future work of the proposed study.