Optimization based scheduling for a class of production systems with integral constraints

Operation scheduling for a class of production systems with “instantly consumed” products is very important. It is challenging to satisfy the real time system demand and to consider the realizability of the production schedules. This paper formulates a new model for optimization based production scheduling problems with integral constraints. Based on the detailed analysis of the production rate constraints, it is proved that this type of optimization problems is equivalent to a smooth nonlinear programming problem. The reachable upper and lower bounds of the production amount in every period can be expressed as functions of two variables, i.e., the production rate at the start and end of that period. It is also proved that the gradients of these functions are monotonic, and their convexity or concavity is guaranteed. When the production cost function is convex, this type of optimization problems is equivalent to a convex programming problem. With the above analysis, a two-stage solution method is developed to solve the production scheduling problems with integral constraints, and in many applications the global optimal solution can be obtained efficiently. With the new model and solution method, the difficulties caused by the constraints on production rate can be overcome and the optimal schedule can be obtained with the real time system demand satisfied. Numerical testing for scheduling of electric power production systems is performed and the testing results are discussed. It is demonstrated that the new model and solution method are effective.