Single machine scheduling problems: early-tardy penalties
Author
Oguz, Ceyda
Advisor
Dinçer, Cemal
Date
1993Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
The primary concern of this dissertation is to analyze single machine total earliness
and tardiness scheduling problems with different due dates and to develop
both a dynamic programming formulation for its exact solution and heuristic
algorithms for its approximate solution within acceptable limits. The analyses of
previous works on the single machine earliness and tardiness scheduling problems
reveal that the research mainly focused on a restricted problem type in which
no idle time insertion is allowed in the schedule. This study deals with the
general case where idle time insertion is allowed whenever necessary. Even
though this problem is known to be A'P-hard in the ordinary sense, there is
still a need to develop an optimizing algorithm through dynamic programming
formulation. Development of such an algorithm is necessary for further identifying
an approximation scheme for the problem which is an untouched issue in the
earliness and tardiness scheduling theory. Furthermore, the developed dynamic
programming formulation is extended to an incomplete dynamic programming
which forms the core of one of the heuristic procedure proposed.A second aspect of this study is to investigate two special structures for the
different due dates, namely Equal-Slack and Total-Work-Content rules, and to
discuss computational complexity of the problem with these special structures.
Consequently, solution procedures which bear on the characteristics of the special
due date structures are proposed. This research shows that the total earliness
and tardiness scheduling problem with Equal-Slack rule is A/’P-hard but can be
solvable in polynomial time in certain cases. Moreover, a very efficient heuristic
algorithm is proposed for the problem with the other due date structure and the
results of this part leads to another heuristic algorithm for the general due date
structure.
Finally, a lower bound procedure is presented which is motivated from the
structure of the optimal solution of the problem. This lower bound is compared
with another lower bound from the literature and it is shown that it performs
well on randomly generated problems.
Keywords
Deterministic Single Machine SchedulingLower Bounds
Heuristic Algorithms
Dynamic Programming
Computational Complexity Theory
Minimizing Total Earliness and Tardiness