Control the preservation cost of a fuzzy production inventory model of assortment items by using the granular differentiability approach. (English) Zbl 1476.34008
Summary: This paper deals with a single period fuzzy production inventory model with the assortment items in a finite time horizon. Here, we tried to implement the preservation technology for decreasing the deterioration rate and control the preservation cost of the deteriorated products. In harmony with the real-life uncertain production inventory system, the decision variables and some of the parameters of the proposed model are assumed to be fuzzy variables. So a fuzzy dynamical system has been developed and solved for controlling the system. The optimality of the objective function in fuzzy optimal control has been derived and we have introduced a new approach, the granular differentiability for defuzzifying the system. Then the defuzzified optimal control problem is solved by using Pontryagin’s maximum principle. Here, we have used the Runge-Kutta forward-backward method of fourth-order through MATLAB software. The proposed model is illustrated through a numerical example to determine the optimality conditions and the results are shown both in tabular form and graphically.
MSC:
| 34A07 | Fuzzy ordinary differential equations |
| 93-10 | Mathematical modeling or simulation for problems pertaining to systems and control theory |
| 90-08 | Computational methods for problems pertaining to operations research and mathematical programming |
Keywords:
fuzzy dynamical system (FDS); granular differentiability (gr-differentiability); fuzzy preservation technology; fuzzy optimal control; assortment itemsSoftware:
MatlabReferences:
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