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A production-repairing inventory model with fuzzy rough coefficients under inflation and time value of money
Authors:Madhab Mondal  Amit Kumar Maity  Manas Kumar Maiti  Manoranjan Maiti
Institution:1. Department of Mathematics, Mahishadal Girls’ College, Mahishadal, Purba-Medinipur 721628, West Bengal, India;2. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Paschim-Medinipur 721102, West Bengal, India;3. Department of Mathematics, Mahishadal Raj College, Mahishadal, Purba-Medinipur 721628, West Bengal, India
Abstract:In this paper, a production-repairing inventory model in fuzzy rough environment is proposed incorporating inflationary effects where a part of the produced defective units are repaired and sold as fresh units. Here, production and repairing rates are assumed as dynamic control variables. Due to complexity of environment, different costs and coefficients are considered as fuzzy rough type and these are reduced to crisp ones using fuzzy rough expectation. Here production cost is production rate dependent, repairing cost is repairing rate dependent and demand of the item is stock-dependent. Goal of the research work is to find decisions for the decision maker (DM) who likes to maximize the total profit from the above system for a finite time horizon. The model is formulated as an optimal control problem and solved using a gradient based non-linear optimization method. Some particular cases of the general model are derived. The results of the models are illustrated with some numerical examples.
Keywords:Dynamic production rate  Trust measure  Fuzzy rough variable  Fuzzy rough expectation
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