Branching technique for a bi-objective two-stage assignment problem




bi-objective, assignment, efficient pair, time minimization, ranking, scanning


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.


Author Biographies

Ekta Jain, Panjab University

MCM DAV College for Women, Chandigarh, INDIA.


Kalpana Dahiya, University Institute of Engineering and Technology,Panjab University

Dr. Kalpana Dahiya Associate Professor (Mathematics), Department of Applied Science, UIET, Panjab University, Chandigarh, INDIA.

Vanita Verma, Panjab University

Professor, Department of Mathematics, Panjab University, Chandigarh, India





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