#### Date of Submission

3-22-1980

#### Date of Award

3-22-1981

#### Institute Name (Publisher)

Indian Statistical Institute

#### Document Type

Doctoral Thesis

#### Degree Name

Doctor of Philosophy

#### Subject Name

Computer Science

#### Department

Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)

#### Supervisor

Mukhopadhyay, Anis Chandra (TSMU-Kolkata; ISI)

#### Abstract (Summary of the Work)

Researchers attention was drawn to the study of schodulirg problems through mathemtical modelling, probably for the first time, when Johnson (1954) publishod his famous paper in mval research logistic quarterly. Thercafter, mny authors have contimued to contribute to the growth of the theory of scheduling. A vast colloctim of papers related to this area is rogularly published by journals like mamgement science, operations research, operational research quarterly, naval research logistic quarterly, opsearch etc.. A good grasp of the litermture in this arca can be had from the books by Conway et al. (1967), Baker (1974) and Rinnooy Kan (1976).This thesis restricts its attention to the well known determi- nistic flow-shop scheduling problems which include the two machine flow-shop probl em handlod by Johnson (1954). The min feature of the flow-shop schoduling problem is : Thore are machinos and n jobs. Ea ch job consists of m tasks such that ihe task canbo performed only on the ith machine named Mi. Purther, the task of a job can start on th machine Mi only after the completion of (i-1)th task of that job on machine M. i-1 â€¢ 2â‰¤iâ‰¤m. In the following we briefly outline the contents of this thesis chap terwise.Chapter I denls with the basic definitions and notation used in this thesis. Under sections 1.0 and 1.1 we provide the definitions of the scheduling problem and the common objective functions used. In sections 1.2 and 1.3 we state clearly the flow-shop assumptions and define most of the symbols and concepts used in the later chapters of this thesis. In section 1.4 we introduce the lower bound classifi- cation and no ta tion due to Iageweg et al. (1978). Under section 1.5 we provide a lucid introduction to NP-completeness following the presentation of Horowitz et al. (1978).Chapter II denls with the (n/3/F/Fmax) problem which is proved max to be NP-complete by Garey et al. (1976). Under section 2.1 (based on Achuthan (1978)) we discuss the known special cases of this problem with polynomial time complex algorithms and subsequently discuss four new special cases and give polynomial time complex algorithms for them. To des cribe the new special cases we define q to be the smallest integer such that the sum of any q processing times on machine Mi. is greater than or equal to sum of any a processing times on mchine Mk. This condition is denoted by Mi qâ‰¥Mk. The four new special cases of this section are : (1) M2 qâ‰¥M1. (2) M2 qâ‰¥M3. (3, M2 qâ‰¥M3 and and (4) the processing times of all the jobs on second 2 2. ma chine are equal and either M32â‰¥M2 or M1 2â‰¥M2 holds. In section 2.2 we discuss the heuristics proposed in the literature for the (n/3/F/Fmaxproblem and conduct an experimental investigation max wi th the aim of comparing the polynomial time complex heuristics for their performnces. The experimental study includes six new basic heuristics and two new imment procedures. On the basis of restrictions on processing times the problems are classified into three disjoint groups.

#### Control Number

ISILib-TH34

#### 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

Achuthan, N. R. Dr., "Flow-Shop Scheduling Problems." (1981). *Doctoral Theses*. 176.

https://digitalcommons.isical.ac.in/doctoral-theses/176

## 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:28842953