Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name



SQC and OR Unit (Chennai)


Prasad, Rajendra, V. (SQCOR-Chennai; ISI)

Abstract (Summary of the Work)

Scheduling problens are quite common in real life. They arise whenever there is a need to plan execution of various tasks over time and therefore they play very important roles in commercial set-ups concerning manufacturing or service in the optimal use of resources and/or customers satisfaction. The theory of scheduling deals with the construction of suitable models and their analyses. Researchersattention was drawn to the study of scheduling problems using mathematical modeling, probably for the first time when Johnson (1954] published his famous work on flowshop problem. Since then, the study of scheduling problem and its context has gradually attracted the researchers from various other fields. At present, a vast collection of research work on this area is available in the literature. For a comprehensive study of the subject, one may refer to Conway, Maxwell and Miller [1967), Baker [1974), Lawler, Lenstra, Rinnooy Kan and Shmoys (1990), Rinnooy Kan (1976], French (1982j etc. The formulation and analysis of mathematical models representing schedul- ing problems involve the operations research techniques such as combinatorial analysis, dynamic programming, integer programming, network analysis etc. Depending upon the nature of the problem, the scheduling problems are clas- sified into several groups, namely, single machine, Flowshop, Jobshop, Parallel machines etc.Currently, the single machine scheduling problem has been of keen interest to many researchers. Each of the above classes of problems is further treated in two different ways, viz, using (a) deterministic model and (b) non- deterministic (stochastic) model. A large number of deterministic models are designed to represent scheduling problems. The essential feature of these models is that they are combinatorial in nature, and unfortunately, the available mathematical tools are not adequate enough to cope with such problem efficiently. As a matter of fact, the majority of these problems are recognized as difficult ones. The very recent trend has been to develop pseudopolynomial procedures for the complex scheduling problems. An extensive literature is available on the single machine scheduling starting from the work of Smith (1956]. (For reference, see the review papers of Sen and Gupta (1984], Emmons (1987), Gupta and Kyparisis (1987), Raghavachari (1988]. Cheng and Gupta (1989], Baker and Scudder (1990] etc.) A major part of the literature deals with the natural early-tardy problem with various cost structures as objective functions where the due dates of the jobs are either fixed or treated as decision variables.The above objective (4) has drawn great interest from the researchers due to the current emphasis on Just-in-time (JIT) production philosophy which espouses the notion that earliness as well as tardiness should be discouraged. (See for reference Bagchi, Sullivan and Chang (1989), Hall, Kubiak and Sethi (1991], Kahlbacher (1989], Panwalker, Smith and Siedmann (1982] etc..) An important special case of this objective is the variance of job completion times which is not a regular measure of performance.In this thesis, we study the problem of scheduling jobs on a single machine so as to minimize the variance of job completion times.


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