International Journal of Operations Research and Information Systems, 6(1), 19-29, January-March 2015 19 Copyright © 2015, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. ABSTRACT A heuristic algorithm that uses iteratively LPT and MF approaches on different job and machine sets con- structed by using the current solution is developed to solve a classical multiprocessor scheduling problem with the objective of minimizing the makespan. Computational results indicate that the proposed algorithm is very competitive with respect to well-known constructive algorithms for a large number of benchmark instances. Minimizing Makespan on Identical Parallel Machines Abey Kuruvilla, Department of Business, University of Wisconsin-Parkside, Kenosha, WI, USA Giuseppe Paletta, Dipartimento di Economia e Statistica, Università della Calabria, Cosenza, Italy Keywords: Different Job and Machine Sets, Empirical Results, Heuristic Algorithm, Identical Parallel Machines, Minimizing Makespan INTRODUCTION The scheduling problem of independent jobs on parallel machines is one of the most studied problem in combinatorial optimization both for its theoretical interest and for its practical aspect in many real world applications (see Lee, Lei & Pinedo, 1997). Still it continues to interest many researchers (Huang, Zhang, & Alexan- der, 2012; Montoya-Torres, Gómez-Vizcaíno, Solano-Charris, & Paternina-Arboleda, 2010; Mungan, Yu, Sarker, & Rahman, 2012; Wang, Moraga, & Ghrayeb, 2011). In this paper we address the classical problem of scheduling a set J={1,...,j,...,n} of n independent jobs, with positive processing times p j >0, j∈J and simul- taneously available, on a set M={1,...,i,...,m} of m identical parallel machines. Each machine can process at the most one job at a time, and each job must be processed without interruption by exactly one of the m machines. The paper considers the problem of finding the schedule that minimizes the maximum job completion time (makespan). This problem is denoted in the literature as P||C max , see Graham, Lawler, Lenstra, & Rinnooy Kan, 1979. A feasible solution (schedule) for P||C max is represented by an m-partition S={S 1 ,..., S i ,...,S m } of the set J, where each S i represents the subset of jobs assigned to the machine i, i∈M. For each feasible solution S, the work-loads of the machines are represented by the m-set C(S) ={C(S 1 ),...,C(S i ),...,C(S m )}, where C(S i )=∑ j∈Si p j is the work-load of machine i∈M. In other DOI: 10.4018/ijoris.2015010102