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

TL;DR

This paper formulates and solves a fuzzy optimal control problem for production scheduling using a variational principle, incorporating fuzzy time periods, non-linear costs, and a control variable for production rate to maximize profit.

Contribution

It introduces a novel fuzzy optimal control framework with a variational principle for production problems considering fuzzy time and costs, solved via a generalized reduced gradient method.

Findings

Optimal production rate maximizes profit under fuzzy conditions.

Numerical and graphical results demonstrate the effectiveness of the approach.

The model accounts for non-linear holding costs and fuzzy time periods.

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.