Production scheduling with hybrid dynamics and constraints

Production scheduling has significant economic impact for many industrial production systems. A new method is developed in this paper to solve a class of production scheduling problems with hybrid dynamics and constraints. It is based on a novel formulation of the discrete states so that the problem is decomposed into solving continuous and discrete problems separately. By employing the features of piecewise linear functions, break points of cost-to-go are mapped across time, and the production levels of a consecutive running span are determined efficiently by dynamic programming without discretization. Dynamic programming is also applied to determine the optimal discrete operating states across time. The new method can deal with non-convex continuous cost functions, often encountered in production scheduling problems. The numerical testing results show the new method is efficient and effective.