A Strengthened Continuous Time Formulation for the Cyclic Scheduling of a Plant

We study in this paper a continuous time formulation for the cyclic scheduling of mixed pro-duction lines, i.e. composed of batch and continuous processes. The objective is to maximize productivity. We base our formulation on the resource task network representation proposed by Pantelides [5]. The initial continuous time mixed integer linear programming (MILP) formulation proposed is similar to the one introduced by Schilling and Pantelides [6]. Other continuous time formulations were proposed by Castro et al. [2] and Wu and Ierapetritou [9]. The main characteristic of this continuous time formulation is that the size of the time interval between two events (i.e points in time when the system state changes) and the duration of the cycle are variables of the model. Moreover, this continuous time formulation is very compact in the sense that the number of events is much smaller than the number of time periods needed for the corresponding discrete time formulation. The latter formulation is usually quite tight but the size of the time period is fixed and has to be smaller than the greatest common divisor of all the processing times of the batch processes. Therefore, the number of time periods needed in discrete time formulations is typically very large, see Shah et al. [7]. Although much more compact, the drawback of continuous time formulations is that they are very weak, i.e. duality gaps are large