A novel precedence-based and heuristic approach for short-term scheduling of multipurpose batch plants

Many continuous-time formulations have been proposed during the last decades for short-term scheduling of multipurpose batch plants. Although these models establish advantages over discrete-time representations, they are still inefficient in solving moderate-size problems, such as maximization of profit in long horizon, and minimization of makespan. Unlike existing literature, this paper presents a new precedence-based mixed integer linear programming (MILP) formulation for short-term scheduling of multipurpose batch plants. In the new model, multipurpose batch plants are described with a modified state-task network (STN) approach, and binary variables express the assignments and sequences of batch processing and storing. To eliminate the drawback of precedence-based formulations which commonly include large numbers of batches, an iterative procedure is developed to determine the appropriate number of batch that leads to global optimal solution. Moreover, four heuristic rules are proposed to selectively prefix some binary variables to 0 or 1, thereby reducing the overall number of binary variables significantly. To evaluate model performance, our model and the best models reported in the literature (S&K model and I&F model) are utilized to solve several benchmark examples. The result comparison shows that our model is more effective to find better solution for complex problems when using heuristic rules. Note that our approach not only can handle unlimited intermediate storage efficiently as well as the I&F model, but also can solve scheduling problems in limited intermediate storage more quickly than the S&K model.