Optimal short-term scheduling of multiproduct single-stage batch plants with parallel lines

The short-term scheduling of multiproduct single-stage batch plants with parallel lines involves the constraints concerning the release times and due dates of orders, as well as the sequence-dependent setup times and forbidden subsequences of production orders and the ready times of units. Taking the above constraints into consideration, this paper develops a short-term scheduling model for the multiproduct single-stage batch plants with parallel lines using the continuous-time domain representation and the notation of time slot. When the model is developed, the allocation of orders and units to time slots is represented by two sets of binary variables. The model is formulated as a mixed-integer linear programming (MILP) problem. It not only involves fewer binary variables than any other model based on the notation of time slot (Pinto, J. M.; Grossman, I. E. Ann. Oper. Res. 1998, 81, 433) but also can be used to optimize several types of objective functions. Based on the characteristics of the model and multiproduct single-stage batch plants, some heuristic rules are introduced. The rational employment of these heuristic rules can cut down the size of the model and has no effect on the optimality of the scheduling problem. A number of computational examples show that the optimal scheduling can be obtained by solving the MILP model in reasonable CPU time, especially when the scheduling problem involving several identical orders is considered.