#### Date of Submission

2-22-1974

#### Date of Award

2-22-1975

#### Institute Name (Publisher)

Indian Statistical Institute

#### Document Type

Doctoral Thesis

#### Degree Name

Doctor of Philosophy

#### Subject Name

Mathematics

#### Department

Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)

#### Supervisor

Rao, A. R. (TSMU-Kolkata; ISI)

#### Abstract (Summary of the Work)

The problems of sequencing arise in almost all walks of life. Theory of scheduling deals with such problems. Usually, these probl ems are stated in the literature in terms of jobs, machines, operations, penalties, due dates et cetera, that is, in the language of machine shops. The real life problems of In machine - shop job sequencing are of a complex nature. general, we consider processing n items on a certain group of machines, so as to optimize certain objective, subject to various cons traints on precedence, machine availability, due date and so on. The job sequencing problems are includ ed in a general class of problems known as resource cons trained network probloms. These are the well known CPM/PERT type network problems wi th constraints on available resources.Johnsons (1954) paper initiated work in developing and analysing mathema tical models representing machine - shops which was continued by Wagner (1959), Bowman (1959), Manne (1960), Dantzig (1960), Held and Karp (1962), Brown and Lomnicki (1966), to name a fow, In the past nineteen years many rosearchers have contributed to the growth of the sequencing theory. A review of the work done up to 1968 is available in Elmaghraby (1968). Another review has beon done by Day and Hottens tein (1970). A survey of the methods proposed for the sequencing OF compreion, OCR, wb optimon uing a wetemad ovalaton copy of CVISION PD problems with the objec tive of minimising total elapsod time is given in Bakshi and Arora (1969).In the recent past several papers have appeared on the general machine shop problems. Balas (1969) has given a dis junctive graph approach to sequencing problems, in which several critical path subproblems are salved to find an optimal solution to the problem using an implicit onumeration method. Death and Charlton (1970), Nabashima (1971), Florian and others (1971), Schrage (1970) have also given procedures for solving general scheduling problems.. Fisher (1973) gives a Lagrangian approach, to the resource-cons trained scheduling problem, in which he uses Lagrangian multipliers to find bounds and uses the bounds in a Branch and Bound algorithm.Even though the general problem has many algorithms, it is of interest to consider some particular cas es with certain assumptions, as efficient algorithms are then possible exploiting the simplicity arising out of these as sumptions. The Flow-shop problems under some usual assumptions have been considered by many authors with various objectives (see Elmaghraby (1968), Szwerc (1971), Maxwell and others (1967)). Inspite of the fact the probl ems studied are very much restrictive under such assumptions, the study of such problems is no less important because the method of attack for simplified sys tems may be useful in solving more complex ones and thes e simplified BP8BI aS are thems elves interes ting research problems.In this work we consider mainly the flow-shop situation under the following assumptions.A.1 A set N of jobs must be processed.A.2 All the machines and jobs are available for processing at time 0.A.3 At any given ins tant of time, on any machine, processing can go on for one and only one job.

#### Control Number

ISILib-TH20

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

#### DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

#### Recommended Citation

Arthanari, T. S. Dr., "On Some Problems of Sequenting and Grouping." (1975). *Doctoral Theses*. 250.

https://digitalcommons.isical.ac.in/doctoral-theses/250

## Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843028