| Summary: | 碩士 === 東海大學 === 數學系 === 88 === Different from applying the simulation modeling technique to a failure prone manufacturing system, the optimal production policy is constructed by using the mathematical model approach together with optimization technique. Firstly, parallel-machine systems with multistage production capability are modeled by a set of differential equations and the cost function for longterm operation serves to enforce desired system behavior which includes the manufacturing expenditure, inventory storage costs and lacklogged penalties. Through the minimization of the cost function, the location of optimal inventory can be decided and the control strategy is then stated.
The main difficulty arising from the optimization process is to solve the Hamilton-Jacobi-Bellman(HJB) equation for the value function. In the thesis, two boundary conditions for HJB equation are derived and a fourth-order Range-Kutta method is used to compute the approximation solution. Beside the study on the effect of different storage functions, failure rates and repair rates on the optimal inventory and value function, numerous examples show the optimal production policy is more practicable and effective than the intuitive production policy.
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