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BRANCHING TECHNIQUE FOR A BI-OBJECTIVE TWO-STAGE ASSIGNMENT PROBLEM

Published online by Cambridge University Press:  15 August 2022

EKTA JAIN Open the ORCID record for EKTA JAIN [Opens in a new window] ,
KALPANA DAHIYA Open the ORCID record for KALPANA DAHIYA [Opens in a new window]  and
VANITA VERMA Open the ORCID record for VANITA VERMA [Opens in a new window]
EKTA JAIN
Affiliation:
MCM DAV College for Women, Chandigarh, India; e-mail: ekta_jain30@yahoo.com
KALPANA DAHIYA*
Affiliation:
University Institute of Engineering and Technology, Panjab University, Chandigarh, India
VANITA VERMA
Affiliation:
Department of Mathematics, Panjab University, Chandigarh, India; e-mail: v_verma1@yahoo.com
*
e-mail: kalpanas@pu.ac.in
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Abstract

We discuss a bi-objective two-stage assignment problem (BiTSAP) that aims at minimizing two objective functions: one comprising a nonlinear cost function defined explicitly in terms of assignment variables and the other a total completion time. A two-stage assignment problem deals with the optimal allocation of n jobs to n agents in two stages, where $n_1$ out of n jobs are primary jobs which constitute Stage-1 and the rest of the jobs are secondary jobs constituting Stage-2. The paper proposes an algorithm that seeks an optimal solution for a BiTSAP in terms of various efficient time-cost pairs. An algorithm for ranking all feasible assignments of a two-stage assignment problem in order of increasing total completion time is also presented. Theoretical justification and numerical illustrations are included to support the proposed algorithms.

Keywords

Bi-objectiveassignmentefficient pairtime minimizationrankingscanning

MSC classification

Primary: 90C27: Combinatorial optimization
Type
Research Article
Information
The ANZIAM Journal , Volume 64 , Issue 2 , April 2022 , pp. 183 - 204
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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