Multi-objective multi-item fuzzy inventory and production management problem involving fuzzy decision variables

The pressure to conserve the environment as a result of global warming cannot be overstated. The necessity for operational managers to devise a sustainable green inventory stems from the fact that emissions from the production and inventory process contribute extremely to global warming. This study purposes a multi-objective multi-item fuzzy inventory and production management model with green investment in order to conserve the environment. The model is formulated in such a way that all of its ordering quantities (decision variables) and some of the input parameters are fuzzified. All the decision variables and some of the input parameters respectively are trapezoidal fuzzy decision variable and trapezoidal fuzzy number. The developed multi-objective model contains five objectives such as maximizing profit, minimizing total back-ordered quantity, minimizing the holding cost in the system, minimizing total waste produced by the inventory system per cycle and minimizing the total penalty cost due to green investment. Budget constraints, space restrictions, cost constraint on ordering each item, environmental waste disposal restrictions, pollution control costs, electricity consumption costs during production, and green house gas emission costs are among the restraints. To determine the crisp equivalent of this fuzzy model, an expected value method of defuzzification is used. The lexicographic method is applied on the resulting crisp mathematical model to find the compromise solutions. The methodology is demonstrated using a case study and the solution obtained provides a beneficial recommendation to industrial decision-makers.