Optimization techniques for crisp and fuzzy multi-objective static inventory model with Pareto front

Inventory management is an essential component of any business, but it can be difficult for businesses today to determine the ideal quantity level required to avoid shortages and to reduce waste. With the maximization of profit, if the backorder quantity is minimized, then this policy will be most preferred and economical. Likewise with the minimization of holding cost, the policy is such that the total order quantity is minimized. The model is formulated as a multi-objective linear programming problem with four objectives: maximizing profit, maximizing total ordering quantity, minimizing the holding cost in the system, minimizing total backorder quantity. The constraints are included with budget limitation, space restrictions and constraint on cost of ordering each item. When converting a fuzzy model to a crisp model, we employ the ranking function approach and graded mean integration method. In order to reduce stock out situations, the lowest optimal quantity level to place in the inventory is also determined using weighted sum and the \(\varepsilon\) $\epsilon$ -constraint method. To prevent shortages, the ordering quantity is increased. Minimizing holding costs and back order quantity together enhance the model's profit. Budgetary restrictions, space limitations, and a pricing restriction on ordering each item are all included in the constraints. In a fuzzy context, the proposed inventory model turns into a difficulty of many criteria decision-making. To transform the data from the fuzzy model to the crisp model, the ranking function approach using the triangular fuzzy number, trapezoidal fuzzy number and triangular intuitionistic fuzzy number and graded mean integration methods are used. The optimal solution is obtained using numerical demonstration. Pareto optimal solutions using genetic algorithm for different objective functions are included. Sensitivity analysis of the model is carried out to discuss the effectiveness of the model.