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arXiv · 2309.09027

Optimum Production through variational principle with the time quadratic demand, fuzzy time period and fuzzy integrand

J. N. Roul·K. Maity·S. Kar·M. Maiti
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Abstract

Here a real life optimal control problem under fuzzy time period using variational principle is formulated and Solved. The unit production cost is a function of production rate and also dependent on raw material cost, development cost due to durability and wear-tear cost. The holding cost is assumed to be non-linear, dependent on time. The profit function which consists of revenue, production cost and holding cost is formulated as a Fuzzy-Final Time and Fixed State System optimal control problem with fuzzy time period. Here production rate is unknown and considered as a control variable and stock level is taken as a state variable. It is formulated to optimize the production rate so that total profit is maximum. The non-linear optimization technique-Generalised Reduced Gradient Method (LINGO 11.0) is used. The optimum results are illustrated both numerically and graphically.

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J. N. Roul, K. Maity, S. Kar, M. Maiti. 2023-09-16. Optimum Production through variational principle with the time quadratic demand, fuzzy time period and fuzzy integrand. https://arxiv.org/abs/2309.09027

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