Computational method for optimal machine scheduling problem with maintenance and production

This paper considers an optimal scheduling problem of maintenance and production for a machine. Firstly, the problem is formulated as a stochastic switched impulsive optimal control problem. However, there exists the stochastic disturbance in this model. Thus, it is difficult to solve the problem by conventional optimisation techniques. To overcome this difficulty, the stochastic switched impulsive optimal control problem is transformed into a deterministic switched impulsive optimal control problem with continuous state inequality constraints. Then, by combining a time-scaling transformation, a second-order smoothing technique and a penalty function method, an improved Newton algorithm is developed for solving this problem. Convergence results indicate that the algorithm is globally convergent with quadratic rate. Finally, two numerical examples are provided to illustrate the effectiveness of the developed algorithm.