Browsing by Subject "Lower Bounds"

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    A new dominance rule to minimize total weighted tardiness on a single machine
    (1996) Yıldırım, Mehmet Bayram
    We present a new dominance rule for the single machine total weighted tardiness problem with job dependent penalties. The proposed dominance rule provides a sufficient condition for local optimality, i.e. if any sequence violates the dominance rule, switching a violating job either lowers the total weighted tardiness or leaves it unchanged. We introduce an algorithm based on the dominance rule, which is compared to a number of competing heuristics for a set of randomly generated problems. Our computational results over •30000 problems indicate that the proposed algorithm dominates the competing heuristics in all runs. Furthermore, the new dominance rules can be used in reducing the number of alternatives for finding the optimal solution in complete enumeration techniques. We show that the proposed dominance rule increases the number of global dominance relationships generated by the Emmons’ Rule which is used heavily in literature to restrict the search space. We also show that having a better upper bound value usually improves the lower bound value which is obtained from the linear lower bound.
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    Single machine scheduling problems: early-tardy penalties
    (1993) Oguz, Ceyda
    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.