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. 1. Introduction 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. This has happened mostly because of the belief that inflation and time value of money will not influence the cost and price components (i.e., the inventory policy) to any significant degree. But, 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. Following Buzacott [1], Misra [2] extended his approaches to different inventory models with finite replenishment, shortages, and so forth, by considering the time value of money, different inflation rates for the costs. Also Lo et al. [3] developed an integrated production-inventory model with a varying rate of deterioration under imperfect production process, partial backordering, and inflation. Again, some researchers (cf. Cho [4] and others) have assumed depreciation rate of sales as a function of time, . This assumption is supported by a general fact that,
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