Enhanced Discrete Time Formulation for a Short-Term Batch Process Scheduling Problem with Utility Constraints

For a short-term production scheduling problem with utility constraints, the discrete-time modeling approach has its inherent advantages compared with the continuous-time approach. Even so, there are still some limitations to the discrete-time approach in calculating utility consumption. This paper aims to enhance the capability of the discrete-time model to calculate utility consumption more accurately. In this paper, a four-dimensional binary variable is introduced on the basis of a basic three-dimensional discrete-time model framework. Constraints crucial to utility consumption calculation, including allocation, batch size, and material balance, are modified significantly. Moreover, production rate fluctuation and safe inventory interval constraints are considered in the proposed model, which can increase the stability and robustness of production and operation. Finally, two cases demonstrate that the proposed four-dimensional discrete-time model is more accurate than the basic three-dimensional model in terms of calculating utility consumption. In addition, when the disturbance of utility supply amount appears, the proposed model can also respond to the disturbance.