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A New Network-Based Representation for Process Scheduling

Diego M. Giménez1, Gabriela P. Henning1, and Christos T. Maravelias2. (1) Universidad Nacional del Litoral, CONICET, Santa Fe, Argentina, (2) University of Wisconsin - Madison, 1415 Engineering Drive, Madison, WI 53706

In this paper we present a new mixed-integer programming (MIP) formulation for the scheduling of general (multi-purpose) process networks. Current models are based on the state-task network (STN) or the resource-task network (RTN) representation (Kondili et al., 1994; Pantelides, 1994). In most existing formulations, it is implicitly assumed that:

a) material transfer between units is always possible, i.e. all process units are connected to all the vessels that are used for the storage of the corresponding input and output states;

b) all input (output) states of a task are transferred simultaneously to (from) the process unit when the task starts (ends);

c) stable output states can be temporarily stored in a process unit after a task is completed, but input states cannot be temporarily stored before a task starts, i.e. in continuous time representations, the beginning of a task must coincide with a time point and at such point all the materials should be available.

However, these assumptions do not always hold. For example, if an intermediate chemical is produced in multiple processes, then several vessels may be used for its storage and each vessel may not be connected to all downstream units. Also, in many processes, input (output) states are not transferred simultaneously to (from) the processing unit. For example, in recovery and purification processes the solvent can be drained earlier. Similarly, in certain chemical reactions reactants are fed before the beginning of the task which actually occurs when the catalyst is added. It is interesting to note here that although the scheduling of multipurpose facilities has received considerable attention, most approaches focus on the development of alternative MIP formulations for the existing STN and RTN representations, but there are very few attempts to address the above limitations. The issue of unit connectivity was tackled by Barbosa-Póvoa and Macchietto (1994). However, to our knowledge none of the existing approaches deals with the shortcomings due to assumptions (b) and (c).

The goal of this paper is the development of a MIP formulation that overcomes these limitations. In achieving this, we develop four key new ideas. First, we use a time representation that does not require tasks to start exactly at a time point, thus probably reducing the number of time points necessary to represent a solution. Second, we allow input (output) states to be transferred to (from) a process unit before (after) a task begins (ends) via the introduction of a “storage” state for each unit. Third, we explicitly model material transfer via “flow” variables, thus explicitly taking into account forbidden connections between units. Fourth, we introduce new variables to denote the idle and storage time in a process unit, as well as the time elapsed before (after) a task starts (finishes). These new variables allow us to enforce matching between tasks and time points without using big-M constraints.

The proposed representation introduces several novel modeling concepts that turn it into a powerful tool. The advantages are considerable in comparison with previous approaches. In spite of its generality, the resulting model complexity is not greater than in many other continuous-time formulations. Also, the proposed approach can be extended to model utility consumption, changeovers and continuous processes. We present several examples where the proposed approach yields solutions that cannot be represented by existing models.

Kondili, E., Pantelides, C.C., Sargent, R. (1993). Comput. Chem. Eng., 17, 211-227.

Pantelides, C.C. (1994). Proceedings on the 2nd FOCAPO Conference, 253–274.

Barbosa-Póvoa, A.P., Macchietto, S. (1994). Comput. Chem. Eng., 18, 1013-1042.