Scheduling of multipurpose batch plants is challenging and has received considerable attention so far. Several formulations for this problem exist in the literature. The early attempts using Mixed Integer Linear Programming (MILP) formulations were with discrete-time representations (Kondili et al., 1993; Shah et al., 1993; Mockus and Reklaitis, 1994; Lee et al., 2001). However, recent focus has been on continuous-time representation (Maravelias and Grossmann, 2003a; Janak et al., 2004; Sundaramoorthy and Karimi, 2005; Shaik et al., 2006; Mendez et al., 2006) using slot-based, event-based, and sequence-based modeling techniques. For problem/process representation, these models employ various approaches such as State Task Network (STN), Resource-task network (RTN), and Generalized Recipe Diagram (GRD). Sundaramoorthy & Karimi (2005) used process slots (Liu & Karimi, 2007) in their work, but no model has so far used the concept of unit slots (Liu & Karimi, 2007) for scheduling multipurpose plants.

In this work, we use the GRD approach to focus on the generic problem of short-term scheduling in batch processes. For this, we present a novel continuous-time mixed integer linear programming (MILP) model that uses unit slots (Liu & Karimi, 2007). As expected, this leads to a significant reduction in the numbers of slots and binary variables in the formulation. Our model allows variable batch sizes and processing times, various storage configurations (Classes: UIS, LIS, and FIS with policies: UW, LW, and NW), different scheduling objectives (such as profit maximization and makespan minimization), and limited resources and utilities. To demonstrate the effectiveness of our model, we evaluate its performance with some recent models from the literature. Through our extensive numerical evaluation, we further shed light on various considerations that affect solution time. Our comparisons show that our model outperforms the best formulations existing in the literature, and it also uses fewer binary variables, continuous variables, and constraints.

References:

1. Kondili, E., Pantelides, C.C., Sargent, R.W.H., 1993. A general algorithm for short-term scheduling of batch operations-I. MILP formulation. Computer and Chemical Engineering 17, 211-227.

2. Mockus, L., Reklaitis, G.V., 1994. Mathematical programming formulation for scheduling of batch operations based on non-uniform time discretization. Computers and Chemical Engineering 21, 1147.

3. Maravelias, C.T., Grossmann, I.E., 2003a. New general continuous time state-task network formulation for short-term scheduling of multipurpose batch plants. Industrial and Engineering Chemistry Research 42, 3056-3074.

4. Karimi, I.A., McDonald, C.M., 1997. Planning and scheduling of parallel semi continuous processes. 2. Short-term scheduling. Industrial and Engineering Chemistry Research 36, 2701-2714.

5. Ierapetritou, M.G., Floudas, C.A., 1998. Effective continuous time formulation for short term scheduling. 1. Multipurpose batch processes. Industrial and Engineering Chemistry Research 37, 4341-4359.

6. Arul, S., Karimi, I.A., 2005. A simpler better slot-based continuous-time formulation for short term scheduling in multipurpose batch plants. Chemical Engineering Science 60, 2679-2702.

7. Janak, S. L., Lin, X., & Floudas, C. A. (2004). Enhanced continuous-time unit-specific event-based formulation for short-term scheduling of multipurpose batch processes: Resource constraints and mixed storage policies. Industrial and Engineering Chemistry Research, 43, 2516-2533.

8. Pantelides, C. C. Unified frameworks for optimal process planning and scheduling. In Proceedings of the Second International Conference on Foundations of Conputer-Aided Process operations, Crested Butte, CO, 1993; Rippin, D. W. T., Hale, J. C., Davis, J., Eds.; CACHE: Austin, TX, 1993; pp 253-274.

9. Shaik, M. A., Janak, S. L., Floudas, C. A., 2006. Continuous-time models for short-term scheduling of multipurpose batch plants: A comparative study. Industrial and Engineering Chemistry Research, 45, 6190.

10. Mendez, C. A., Jaime C., Grosmann, I. E., Harjunkoski, I., Fahl, M., 2006. State-of-the-art review of optimization methods for short-term scheduling of batch processes. Computers and Chemical Engineering, 30, 913-946.

11. Liu Yu, Karimi, I. A., 2007. Novel continuous-time formulations for scheduling multi-stage batch plants with identical parallel units. Computers and Chemical Engineering, 31, 1671-1693.