Author:  Liu, Lili 
Title:  Batch scheduling problems 
Degree:  Ph.D. 
Year:  2007 
Subject:  Hong Kong Polytechnic University  Dissertations. Production scheduling. Production planning  Mathematical models. 
Department:  Dept. of Logistics 
Pages:  ix, 104 leaves : ill. ; 30 cm. 
Language:  English 
InnoPac Record:  http://library.polyu.edu.hk/record=b2116779 
URI:  http://theses.lib.polyu.edu.hk/handle/200/439 
Abstract:  Batch scheduling is motivated by the burnin operation of the final testing stage in the manufacturing of very largescale integrated circuits, in which a machine can process several jobs simultaneously. The processing time of a batch is equal to the longest processing time of the jobs in the batch. Some other practical applications of this model include heat treatment in the metalworking industry, diffusion or oxidation processing in wafer fabrication of semiconductor manufacturing, etc. This thesis examines several batch scheduling problems on a single batch processing machine and parallel batch processing machines. The organization of the thesis is as follows: Chapters 1 and 2 introduce the problem and present a literature review of the class of scheduling problems under study in this thesis. In Chapter 3 we consider bicriterion scheduling on a single batch processing machine, in which two criteria are considered at the same time. Most of the bicriterion scheduling problems on a single batch processing machine are strongly NPhard. We mainly focus on the bicriterion scheduling problem with makespan as the primary criterion. We propose an optimal algorithm for the problem with total completion time as the secondary criterion, which runs in polynomial time when the machine capacity is fixed. We then prove that the problem with number of tardy jobs as the secondary criterion is binary NPhard, and the problem with total weighted number of tardy jobs as the secondary criterion is strongly NPhard. Our results also shed light on the computational complexity issues of two open problems of scheduling incompatible families of jobs on a single batch processing machine. From the NPhardness proof of the problem with number of tardy jobs as the secondary criterion, we deduce that the problem of minimizing number of tardy jobs with incompatible job families is binary NPhard. From the strong NPhardness proof of the problem with weighted number of tardy jobs as the secondary criterion, we deduce that the problem of minimizing the weighted number of tardy jobs with incompatible job families is strongly NPhard. In Chapter 4 we study the problems of scheduling jobs with agreeable processing times and due dates on a single batch processing machine to minimize total tardiness and weighted number of tardy jobs, respectively. Polynomial time algorithms for the problems of minimizing maximum tardiness and number of tardy jobs have been presented in the literature. We prove that the problem of minimizing total tardiness is binary NPhard even if the machine capacity is two, and we propose a pseudopolynomial time algorithm for an NPhard special case of this problem. We also develop a pseudopolynomial time algorithm for the NPhard problem of minimizing weighted number of tardy jobs, which indicates that this problem cannot be strongly NPhard unless P=NP. Most of the results appearing in batch scheduling deal with scheduling problems on a single batch processing machine. In Chapter 5 we explore the scheduling problems with release dates on parallel unbounded batch processing machines. We prove that the problem of minimizing any due date related objective is strongly NPhard. Since the maximum lateness could be zero or even negative, it is meaningless to develop an approximation algorithm for it. We obtain a polynomial time approximation scheme (PTAS) for the problem of minimizing maximum delivery completion time, which is equivalent to minimizing maximum lateness from an optimization perspective. We show that the problem of minimizing total weighted completion time is strongly NPhard, too. We provide a PTAS for this problem. In Chapter 6, the last chapter, we conclude the major findings of the study and suggest some directions for future research. 
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