(472e) A General Network-Based Representation for Process Scheduling

In most existing scheduling approaches it is implicitly assumed that: a) material transfer between units is always possible, i.e. all processing units are connected to all the vessels that are used for the storage of the corresponding input and output materials, as well as connected to all upstream/downstream processing units; b) all input (output) materials consumed (produced) by a task are transferred simultaneously to (from) the processing unit when the task starts (ends); c) stable input materials cannot be temporarily stored before a task actually starts, i.e. in continuous-time representations the beginning of a task must coincide with a time point; d) the storage of stable output materials is always bounded by the time point representing the end of the task; and e) transfer tasks are instantaneous and do not require any type of resources.

However, these assumptions do not always hold in practice. For example, if an intermediate chemical is produced in multiple tasks, then several storage vessels may be used for its storage and each of these vessels may not be connected to all downstream processing units. Also, in many processes, input (output) materials associated with a task are not forced to be transferred simultaneously to (from) the corresponding processing unit. For instance, in certain chemical reactions reactants can be fed before the beginning of the task, which actually occurs when the catalyst is added. In this way, the reactor can also be used as a temporary storage tank. On the other hand, a certain input (output) material may be fed (discharged) into (from) a processing unit by resorting to multiple transfers of the same material (?partial? transfer), instead of making a unique one. The goal of this work is to develop a general network-based scheduling framework that addresses the aforementioned limitations of existing approaches.

First, we present five novel modeling concepts that lead to more flexible continuous-time MILP formulations (Giménez et al., 2009a):

1) Our approach employs a new continuous-time representation that does not require tasks to start (end) exactly at a time point; thus reducing the number of time points needed to represent a solution.

2) Processing units are modeled as being in different activity states to allow storage of input/output materials.

3) Time variables for "idle" and "storage" periods of a unit are introduced to enable the matching between tasks and time points without big-M constraints.

4) Material transfer variables are introduced to explicitly account for unit connectivity.

5) Inventory variables for storage in processing units are incorporated to model non-simultaneous and partial material transfers.

Second, we discuss how the proposed framework is extended to address features such as (Giménez et al., 2009b):

1) Preventive maintenance activities on unary resources (e.g. processing and storage units) that were planned ahead of time.

2) Resource-constrained changeover activities on processing and shared storage units.

3) Non-instantaneous resource-constrained material transfer activities.

4) Intermediate deliveries of raw materials and shipments of finished products at predefined times.

5) Situations where part of the schedule is fixed because it has been programmed in the previous scheduling horizon.

The generality of our representation leads to MILP formulations which can tackle situations that cannot be modeled by existing methods; thus, obtaining solutions that otherwise could not be achieved.

Third, we discuss a number of methods for the reduction of the computational effort required to address medium-size instances. Thus, in spite of its generality, the computational complexity of the resulting MILP models is not greater than in many other continuous-time formulations.

Finally, we close our presentation with a number of example problems that illustrate how the proposed integrated framework can be used to address a wide variety of process scheduling problems, many of which are intractable with existing tools.

References:

Giménez, D. M.; Henning, G. P.; Maravelias, C. T. (2009a). A novel network-based continuous-time representation for process scheduling: Part I. Main concepts and mathematical formulation. Computers and Chemical Engineering, in press, (DOI: 10.1016/j.compchemeng.2009.03.007).

Giménez, D. M.; Henning, G. P.; Maravelias, C. T. (2009b). A novel network-based continuous-time representation for process scheduling: Part II. Integrated framework. Computers and Chemical Engineering, in press, (DOI: 10.1016/j.compchemeng.2009.04.013).