A Study of Time Representation in a Class of Short Term Scheduling Problems
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Date
2016-08-17
Authors
Lagzi, Saman
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
The problem of scheduling operations has received significant attention from academia
and industrial practitioners in the past few decades. A key decision in various scheduling
operations problems is when to perform an operation and thus the quality of the final
schedule can be seriously affected by the choice of how to model the times at which such
a decision may take place. The two most commonly used approaches for modeling these
times are: Discrete time approaches, which pre-specify a finite set of time points when any
decision may be taken, and continuous time approaches, in which the optimization model
determines, through the use of continuous decision variables, at which point in time the
operation will be performed.
The focus of this thesis will be to study the benefits and limitations of each of these
approaches within the context of an analytical services facility. Such a facility receives a
large number of samples that need to be analyzed/processed through a specific sequence of
limited resources/machines before its analysis is completed. The results of these analyses
form a basis for many of the decisions made in their client industries (e.g. oil and mining),
which in turn indicates the economic importance of the analytical services sector. The
operations of such facilities have several particular conditions that need to be modeled and
a particularly important one is called multitasking. If analyzing each type of samples is
regarded as a task, then the machines in such facilities have the ability to perform multiple
tasks at the same time as they are able to analyze different types of samples together at
the same (as long as their capacity is not overloaded). The above mentioned study will
be performed through an empirical comparison of the discrete and continuous approaches
that take into account all the conditions in such facilities, including multitasking.
While discrete and continuous approaches have often been independently employed,
few studies have considered a comparison between them [37, 28, 39]. In addition, none of
these studies consider the operational conditions that are present in short-term scheduling
of operations in an analytical services facility.
Since the continuous time formulations in the literature are not capable of accounting
for multitasking, this thesis presents a novel continuous time mixed-integer linear programming
(MILP) formulation that is capable of accommodating such feature and several other
operational constraints present at analytical services facilities. The performance of the presented
formulation is studied in comparison with a singletasking formulation. The results
show that, while the multitasking formulation is not more costly in terms of solution time,
it is capable of producing significantly better solutions. Furthermore, this thesis extends
the idea of flexible time discretization for discrete time formulations, previously proposed
by Velez and Maravelias [40], to be able to account for the operational constraints of an
analytical services facility.
Description
Keywords
Scheduling, Continuous Time Formulations, Non-Uniform Time Discretization