Abstract
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.
Highlights
From financial standpoint, an inventory represents a capital investment and a lot of researchers’ works have been done since the Second World War
Most of the classical inventory models did not take into account the effects of inflation and time value of money
During last few decades, due to high inflation and consequent sharp decline in the purchasing power of money in the developing countries like Brazil, Argentina, India, Bangladesh, and so forth, the financial situation has been changed and so it is not possible to ignore the effect of inflation and time value of money any further
Summary
An inventory represents a capital investment and a lot of researchers’ works have been done since the Second World War. In 2008, Xu and Zhao [16] developed a class of fuzzy rough expected value multiobjective decision-making models and its application to inventory problems. No attempt has been made that includes all selling prices, production cost, holding cost, and advertisement cost as fuzzy rough variables It has been considered within the multiobjective inventory decisionmaking system with defective items. Based on the concept of fuzzy rough variables, we develop a fuzzy rough model applicable to multiobjective multi-item production inventory problems. Xu and Zhao [19] have developed a multiobjective decision-making model with fuzzy rough coefficients and made its application to the inventory problem. There is a strong motivation for the present research in the area, where we consider fuzzy rough constrained multi-item inventory problems.
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