Generating robust and stable machine schedules from a proactive standpoint
Author(s)
Advisor
Sabuncuoğlu, İhsanDate
2009Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
In practice, scheduling systems are subject to considerable uncertainty in highly
dynamic operating environments. The ability to cope with uncertainty in the
scheduling process is becoming an increasingly important issue. In this thesis we take
a proactive approach to generate robust and stable schedules for the environments
with two sources of uncertainty: processing time variability and machine breakdowns.
The information about the uncertainty is modeled using cumulative distribution
functions and probability theory is utilized to derive inferences.
We first focus on the single machine environment. We define two robustness
(expected total flow time and expected total tardiness) and three stability (the sum of
the squared and absolute differences of the job completion times and the sum of the
variances of the realized completion times) measures. We identify special cases for
which the measures can be optimized without much difficulty. We develop a
dominance rule and two lower bounds for one of the robustness measures, which are
employed in a branch-and-bound algorithm to solve the problem exactly. We also
propose a beam-search heuristic to solve large problems for all five measures. We
provide extensive discussion of our numerical results.
Next, we study the problem of optimizing both robustness and stability
simultaneously. We generate the set of all Pareto optimal points via -constraint
method. We formulate the sub-problems required by the method and establish their
computational complexity status. Two variants of the method that works with only a
single type of sub-problem are also considered. A dominance rule and alternative ways to enforce the rule to strengthen one of these versions are discussed. The
performance of the proposed technique is evaluated with an experimental study. An
approach to limit the total number of generated points while keeping their spread
uniform is also proposed.
Finally, we consider the problem of generating stable schedules in a job shop
environment with processing time variability and random machine breakdowns. The
stability measure under consideration is the sum of the variances of the realized
completion times. We show that the problem is not in the class NP. Hence, a
surrogate stability measure is developed to manage the problem. This version of the
problem is proven to be NP-hard even without machine breakdowns. Two branchand-bound
algorithms are developed for this case. A beam-search and a tabu-search
based two heuristic algorithms are developed to handle realistic size problems with
machine breakdowns. The results of extensive computational experiments are also
provided.
Keywords
Single machine schedulingjob shop scheduling
robustness
stability
proactive scheduling
branch-and-bound
beam search
tabu search
-constraint method