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ABSTRACTIn this paper, we present a general formulation for the production inventory optimal control problem to a class of fractional fuzzy differential systems with reliability-dependent imperfect production. we investigate this model under the uncertain environment of fuzzy numbers with the rate of change of stock level expressed by granular Caputo fractional fuzzy derivative of order . The demands depend on the selling price, product quality, and stock level of the product displayed in the store. The unit production cost depends on development cost due to reliability, raw material cost, and wear tear cost. Here state, co-state variables and parameters are taken as uncertain variables with triangular fuzzy numbers and using granular dierentiability the existence and uniqueness of solution to the fractional dierential system with fuzzy variables and parameters. The production inventory optimal control problem for the fractional system is proposed and a necessary condition for optimality is obtained. Finally, this optimal control problem was solved by using the Pontryagin Maximum principle and for numerical results and graphical representation.

The multicriteria optimization a shock and vibration isolation systems is considered. The concept of cooperative solution from game theory is used for trading of one criterion versus another. Results are obtained for a three degree-of-freedom system with an exponentially decaying type base disturbance. A single degree-of-freedom system is also considered to evaluate the relative worth of a multidegree-of-freedom system.

The design of an Euler-Bernoulli beam is considered with two performance measures where the first one depends solely on the values of the state variables and the second one concerns only the minimization of the control effort required. The object is to generate the Pareto optimal solutions of the problem and determine an optimal trade-off between the performance measures while satisfying the stated constraints.

The multicriteria optimization of function generating mechanisms is considered using game theory. Specifically the design of spherical four-revolute function generating mechanisms, with the objective of minimizing structural error, mechanical error and a measure of manufacturing cost, is considered. Both the side and behavior constraints are included in the formulation of the probabilistic model of the system. The solution concepts of game theory are translated in finding an optimal trade-off between the three objectives. A method of obtaining the desired Pareto-optimal solution, which maximizes a specified supercriterion, is discussed. The proposed method of synthesis is illustrated by considering the generation of the function y = sin x.

The problem of determining the optimum machining conditions for a job requiring multiple operations has been investigated. Three objectives, namely, the minimization of the cost of production per piece, the maximization of the production rate and, the maximization of the profit are considered in this work. In addition to the usual constraints that arise from the individual machine tools, some coupling constraints have been included in the formulation. The problems are formulated as standard mathematical programming problems, and nonlinear programming techniques are used to solve the problems.

The mathematical programing techniques are applied to determine the optimum cutting parameters of machining operations. Three objectives, the cost of production per piece, the production rate, and the profit, are considered for optimization. The different constraints that arise during the machining operation are also considered. As some parameters involved in the process may not be purely deterministic, a probabilistic model is set up for the cost of production per piece and the production rate. After converting the probabilistic model into an equivalent deterministic model, the mathematical programing techniques are applied and the results obtained are compared with those of the deterministic model. A sensitivity analysis with respect to the cost parameters is carried in the case of cost of production per piece.

The optimum design of an one-dimensional cooling fin is considered by including all modes of heat transfer in the problem formulation. The minimum principle of Pontryagin is applied to determine the optimum profile. A new technique is used to solve the reduced differential equations with split boundary conditions. The optimum profile found is compared with the one obtained by considering only conduction and convection.