## On-line version ISSN 2224-7890Print version ISSN 1012-277X

### S. Afr. J. Ind. Eng. vol.21 n.2 Pretoria  2010

GENERAL ARTICLE

Pareto optimal solutions for multi-objective generalized assignment problem

S. PrakashI; M.K. SharmaII; A. SinghIII

IDepartment of Applied Sciences, Amity School of Engineering & Technology, New Delhi, India sprakash@aset.amity.edu
IISchool of Mathematics & Computer Applications, Thapar University, Patiala, India mksharma@thapar.edu
IIIDepartment of Applied Sciences, Baba Banda Singh Bahadur Engineering College, Fatehgarh Sahib, India amarinder77@gmail.com

ABSTRACT

The Multi-Objective Generalized Assignment Problem (MGAP) with two objectives, where one objective is linear and the other one is non-linear, has been considered, with the constraints that a job is assigned to only one worker - though he may be assigned more than one job, depending upon the time available to him. An algorithm is proposed to find the set of Pareto optimal solutions of the problem, determining assignments of jobs to workers with two objectives without setting priorities for them. The two objectives are to minimise the total cost of the assignment and to reduce the time taken to complete all the jobs.

OPSOMMING

'n Multi-doelwit veralgemeende toekenningsprobleem ("multi-objective generalised assignment problem - MGAP") met twee doelwitte, waar die een lineêr en die ander nielineêr is nie, word bestudeer, met die randvoorwaarde dat 'n taak slegs toegedeel word aan een werker - alhoewel meer as een taak aan hom toegedeel kan word sou die tyd beskikbaar wees. 'n Algoritme word voorgestel om die stel Pareto-optimale oplossings te vind wat die taaktoedelings aan werkers onderhewig aan die twee doelwitte doen sonder dat prioriteite toegeken word. Die twee doelwitte is om die totale koste van die opdrag te minimiseer en om die tyd te verminder om al die take te voltooi.

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