Optimal production control and marketing plan in two-machine unreliable flexible manufacturing systems

Abstract

In this paper, we have developed a production planning and marketing model in unreliable flexible manufacturing systems with inconstant demand rate that its rate depends on the level of advertisement on that product. The proposed model is more realistic and useful from a practical point of view. The flexible manufacturing system is composed of two machines that produce a single product. Markovian models frequently have been used in modeling a wide variety of real-world systems under uncertainties. Therefore, in this paper, the inventory balance equation is represented by a continuous-time model with Markov jump process to take into account machines breakdown. The objective is to minimize the expected total cost of the firm over an infinite time horizon. While the total cost consists of the cost of the product surplus, the cost of the production, and the cost of the advertisement. In the process of finding a solution to the problem, we first characterize an optimal control by a class of linear stochastic system where some parameter values are subject to random jump. By defining quadratic cost functions and characterizing the associated limiting optimal control problem, a discrete-time approximation model and an asymptotic optimal control model are developed. It is clear that such a solution exists and can be obtained as a limit of a monotonic sequence with solving the steady-state Riccati equation.