A Multiobjective Multi-Item Inventory Control Problem in Fuzzy-Rough Environment Using Soft Computing Techniques

The optimal production and advertising policies for an inventory control system of multi-item multiobjective problem under a single management are formulated as an optimal control problem with resource constraints under inflation and discounting in fuzzy rough (Fu-Ro) environment. The objectives and constraints in Fu-Ro are made deterministic using fuzzy rough expected values method (EVM). Here, the production and advertisement rates are unknown and considered as control (decision) variables. The production, advertisement, and demand rates are functions of time t. Maximization of the total proceed from perfect and imperfect units and minimization of the total cost consisting of production, holding, and advertisement costs are formulated as optimal control problems and solved directly using multiobjective genetic algorithm (MOGA). In another method for solution, membership functions of the objectives are derived and the multi-objective problems are transformed to a single objective by the convex combination of the membership functions and then the problem is solved by generalized reduced gradient (GRG) method. Finally, numerical experiment and graphical representation are provided to illustrate the system.