An analysis of some unit-specific event-based models for the short-term scheduling of noncontinuous processes

Several event-based formulations for scheduling noncontinuous processes have been reported in the past decade. In fact, some unit-specific event-based models have proved more efficient than other models on several literature problems. Recently, Janak and Floudas [Comput. Chem. Eng. 2008, 32 (4-5), 913-955] and Shaik and Floudas [Ind. Eng. Chem. Res. 2009, 48 (6), 2947 -2964] have shown that, without allowing tasks to occur over multiple events, some unit-specific event-based models may lead to suboptimal solutions. In this work, we present five examples, involving batch and semicontinuous processes, to study the performance of some recent variants of unit-specific event-based models. The first two examples involve batch plants with finite storage as a shared resource for which a recent unit-specific event-based model [Shaik, M. A.; Floudas, C. A. Comput. Chem. Eng. 2008, 32 (1-2), 260-274] gives trivial or suboptimal solutions, depending on the example and data. Our analysis confirms that assuming a single event point for each task is one cause for the observed performance. When the tasks are allowed to span multiple events using the recent unified model of Shaik and Floudas [Ind. Eng. Chem. Res. 2009, 48 (6), 2947 -2964], the issue is resolved. Three more examples involving semicontinuous processes are considered, the solutions of which explore the limitations of a recent unit-specific event-based model [Shaik, M. A.; Floudas, C. A. Ind. Eng. Chem. Res. 2007, 46 (6), 1764-1779]. In addition, the task sequencing constraints in the later model may require further study to ensure generality. The five examples presented in this work can serve as test problems for future scheduling models.