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This book is mainly concerned with single machine bicriteria scheduling problems . Following a theoretic framework and a literature survey, four single machine b icriteria scheduling problems are studied. ?
The first one is a single machine scheduling problem to minimize the total weigh ted earliness subject to minimal number of tardy jobs. First, several properties of the problem are discussed in analyzing the problem. Then, a heuristic algori thm of time complexity O(n2) and an efficient branch and bound algorit hm a re proposed. The computational experiments show that the heuristic algorithm is ?effective? in terms of quality of the solutions in most instances while the b ranch and bound algorithm is efficient for medium sized problems. ?
The second one is a single machine scheduling problem with distinct due windows to minimize total weighted earliness and tardiness. A mathematical formulation i s presented and several important properties of the problem are studied. Then an optimal timing algorithm to decide job completion times for a given job sequenc e is proposed. The Tabu search scheme is employed together with the optimal timi ng algorithm to generate job sequences and final schedules. Several experiments were designed and carried out to demonstrate the performance of the proposed app roach.?
The third one is a single machine common due window scheduling problem in which job processing times are controllable with linear costs. The objective of the pr oblem is to find a job sequence, a processing time for each job, and a position of the common due window to minimize the total cost of weighted earliness/tardin ess and processing time compression. Several properties of the problem are studi ed and a polynomial time algorithm of time complexity ?O(n3) is developed f or solving the problem. ?
The last one is concerned with the computational complexity of a single machine scheduling problem to minimize total processing plus weighted flow cost. The com putational complexity of the problem has been open for some twenty years. A posi tive answer to a conjecture for this problem is presented, showing that it is NP hard at least in the ordinary sense.?
Finally, some concluding remarks and future research directions relevant to the studies are given, providing a guideline for further research.
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