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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 6591632, 11 pages
Research Article

Heuristic and Exact Algorithms for the Two-Machine Just in Time Job Shop Scheduling Problem

1Qatar University, Doha, Qatar
2Colorado State University-Pueblo, Pueblo, CO, USA
3Old Dominion University, Norfolk, VA, USA

Received 23 April 2016; Revised 26 September 2016; Accepted 18 October 2016

Academic Editor: Thomas Hanne

Copyright © 2016 Mohammed Al-Salem et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problem addressed in this paper is the two-machine job shop scheduling problem when the objective is to minimize the total earliness and tardiness from a common due date (CDD) for a set of jobs when their weights equal 1 (unweighted problem). This objective became very significant after the introduction of the Just in Time manufacturing approach. A procedure to determine whether the CDD is restricted or unrestricted is developed and a semirestricted CDD is defined. Algorithms are introduced to find the optimal solution when the CDD is unrestricted and semirestricted. When the CDD is restricted, which is a much harder problem, a heuristic algorithm is proposed to find approximate solutions. Through computational experiments, the heuristic algorithms’ performance is evaluated with problems up to 500 jobs.