Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


SQC and OR Unit (Bangalore)


Ramamurthy, K. G. (SQCOR-Bangalore; ISI)

Abstract (Summary of the Work)

Scheduling problems are quite common in nature. They arise whenever there is a need to plan the execution of various operations over time. Like many ot her real life problems such as inventories, networks, queues etc. almost all the scheduling problems car be rapresented by appropriate mathematical models. The theory of scheduling is a disciplina which doals with the construction of suitable mathematical models for sche duling problems and their analysis. Scheduling theory came into prominance after Johnson (1954) had published his work on a fiow shop sche duling problem.The current reseu rch work in scheduling thoory can ba classified into two types: (1) un doterministic modols and (2) cn non-deteministic ( stochastic) models. A largo numbur of aterninistic modols that havo beun disigned to rapresent various scheduling probloms are combinatorial in nature. Unfortunatoly, the available mat homatical tools are not sufficient to deal with such combinatorial models officiantly. For this Ieasci, wo prusently depend upon branch and bound and heuristic methods, which are not efficient, to sclve these models. Scmo of the scheduling problems can be fomulated as standard mo dels like integer progranıming but the magnitud of such fomulations will be quite large.Recently, rosoarchors like Gittins, Glazebrock, Nash, Pine do, Webur, Weiss otc. heve been formulating the schoduling probloms with random processing times as stochastic models. The tools and techniques required for analysing these stochastic models are different from those of dterministic mo dels. Quite ofton, the theory of scmi-Markov decision procusses is found usaful in analysing the stochastic modbls which represent the schoduling preblams.In this thesis, we main manily daal with the methematical nspects of deterministic as well as atochastic schoduling problems. We give below a brief account of the work that is prosentod in this thusis.Choptor II sals with dotoministic flow.ahop schaduling problems. In suction 2.2 of Chepter II wo consi dor a moru genəral kind of flaw shop sche duling problcins callui hybria flow-shop scheduling problums in which Bome of the machines can process simultaneously all the jobs that are to bo procussod, that is, 6ach eno of thum can process all the jobs simultaniously. Jackson (1956) has considered a 3-machine, n-jab problem of this kind in which the first and the third (last) machines can procosa only one job at a time wrorees the mi ddlo ono can proceus all then jobs simultaneously and ho hea e hown thet this problem is oquivalent to either of Jotnscn's (1954) special catoa of the (n/3/F/Fmex) problom. Tho flow-shope with preparatory max ope rationa (on the floor) of jcbs which do not require any proconning machine can be categorised as hybrid flow shops. We coneider threo types of spucial Cases of the hybrid flow stop scheduling problom with the objective of minimising tho total elepeed timo (makuapan). Wo decuce a mejority of flow atap upecial cases consi dered in the litorature from thcse threo typos of apecial cases. For hybrid flow shop probloms wo dorive cominanca criteria and lower bounca (cn makospan) similar to those of (n/m/F/Fmax) probloms.


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