A numerical approach to a multi-objective optimal inventory control problem for deteriorating multi-items under fuzzy inflation and discounting

The optimal production and advertising policies for an inventory control system of deteriorating multi-items under a single management are formulated with resource constraints under inflation and discounting in fuzzy environment. Here, the deterioration of the items and depreciation of sales are at a constant rate. Deteriorated items are salvaged and the effect of inflation and time value of money are taken into consideration. The inflation and discount rates are assumed to be imprecise and represented by fuzzy numbers. These imprecise quantities are first transformed to corresponding intervals and then following interval mathematics, the related objective function is changed to respective multi-objective functions. Using Utility Function Method (UFM), the multi-objective problem is changed to a single objective problem. Here, the production and advertisement rates are unknown and considered as control(decision) variables. The production, advertisement and demand rates are functions of time tt. The total profit which consists of the sales proceeds, production cost, inventory holding cost and advertisement cost is formulated as an optimal control problem and evaluated numerically using UFM and generalized reduced gradient (GRG) technique. Finally numerical experiment, sensitivity analysis and graphical representation are provided to illustrate the system. For the present model, expressions and graphical results are presented when the rates of advertisement are constant.