Mixed Integer Linear Programming in Process Scheduling: Modeling ...

132 FLOUDAS AND LIN
single-unit multiproduct processes to the most general multipurpose processes. These
process scheduling problems are inherently combinatorial in nature because of the many
discrete decisions involved, such as equipment assignment and task allocation over time.
They belong to the set of NP-complete problems (Garey and Johnson, 1979), which
means that the solution time scales exponentially as the problem size increases in the
worst case. This has important implications for the solution of scheduling problems.
There has been a number of reviews related to process scheduling in the chemical
engineering and the operations research literature. Reklaitis (1992) reviewed the
scheduling and planning of batch process operations, focusing on the basic components
of chemical process scheduling problems and the available solution methods. Rippin
(1993) summarized the development of batch process systems engineering with particular
reference to the areas of design, planning, scheduling and uncertainty. Grossmann et al.
(1996) provided an overview of mixed-integer optimization techniques for the design and
scheduling of batch chemical processes. They concentrated on basic solution methods
and recent developments for mixed-integer linear and nonlinear programming problems
and also discussed issues in modeling and reformulation. Bassett et al. (1996a) reviewed
existing strategies for implementing integrated applications based on mathematical programming
models and examined four classes of integration including scheduling, control,
planning and scheduling across single and multiple sites, and design under uncertainty.
Applequist et al. (1997) discussed the formulation and solution of process scheduling and
planning problems, as well as issues associated with the development and use of scheduling
software. Shah (1998) examined first different techniques for optimizing production
schedules at individual sites, with an emphasis on formal mathematical methods, and
then focused on progress in the overall planning of production and distribution in multisite
flexible manufacturing systems. Pekny and Reklaitis (1998) discussed the nature
and characteristics of the scheduling/planning problems and pointed out the key implications
for the solution methodology for these problems. They reviewed the available
scheduling technologies, including randomized search, rule-based methods, constraint
guided search, simulation-based strategies, as well as mathematical programming formulation
based approaches using conventional and engineered solution algorithms. Pinto
and Grossmann (1998) presented an overview of assignment and sequencing models used
in process scheduling with mathematical programming techniques. They identified two
major categories of scheduling models—one for single-unit assignment and the other for
multiple-unit assignment—and discussed the critical issues of time representation and
network structure.
Given the computational complexity of combinatorial problems arising from process
scheduling, it is of crucial importance to develop effective mathematical formulations
to model the manufacturing processes and to explore efficient solution approaches
for such problems. The objective of this paper is to present an overview of advances in
MILP based approaches for process scheduling problems. We focus on the short-term
scheduling of general network represented processes. The rest of this paper is organized
as follows. First, the mathematical models that have been proposed in the literature are
classified and presented along with their strengths and limitations. Then, a variety of