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-itemmultiobjective problem under a single management are formulated as an optimal control problem with resourceconstraints under inflation and discounting in fuzzy rough (Fu-Ro) environment. The objectivesand 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. Theproduction, advertisement, and demand rates are functions of time t. Maximization of the total proceed fromperfect and imperfect units and minimization of the total cost consisting of production, holding, and advertisementcosts are formulated as optimal control problems and solved directly using multiobjective geneticalgorithm (MOGA). In another method for solution, membership functions of the objectives are derived andthe multi-objective problems are transformed to a single objective by the convex combination of the membershipfunctions and then the problem is solved by generalized reduced gradient (GRG) method. Finally, numerical experimentand graphical representation are provided to illustrate the system