* Corresponding author. Tel:+98 21 88021067
E-mail address: h.kazemipoor@piau.ac.ir (H. Kazemipoor)
© 2012 Growing Science Ltd. All rights reserved.
doi: 10.5267/j.msl.2011.10.010
Management Science Letters 2 (2012) 681–688
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Management Science Letters
homepage: www.GrowingScience.com/msl
Solving a mixed-integer linear programming model for a multi-skilled project scheduling
problem by simulated annealing
H. Kazemipoor
*a
, R. Tavakkoli-Moghaddam
b
and P. Shahnazari-Shahrezaei
c
a
Department of Industrial Engineering, Islamic Azad University-Science and Research Branch, Tehran, Iran
b
Department of Industrial Engineering, College of engineering, University of Tehran, Tehran, Iran
c
Department of Industrial Engineering, Islamic Azad University- Firoozkooh Branch, Firoozkooh, Iran
A R T I C L E I N F O A B S T R A C T
Article history:
Received July 20, 2011
Received in Revised form
October, 12, 2011
Accepted 15 October 2011
Available online
20 October 2011
A multi-skilled project scheduling problem (MSPSP) has been generally presented to schedule
a project with staff members as resources. Each activity in project network requires different
skills and also staff members have different skills, too. This causes the MSPSP becomes a
special type of a multi-mode resource-constrained project scheduling problem (MM-RCPSP)
with a huge number of modes. Given the importance of this issue, in this paper, a mixed integer
linear programming for the MSPSP is presented. Due to the complexity of the problem, a meta-
heuristic algorithm is proposed in order to find near optimal solutions. To validate performance
of the algorithm, results are compared against exact solutions solved by the LINGO solver. The
results are promising and show that optimal or near-optimal solutions are derived for small
instances and good solutions for larger instances in reasonable time.
© 2012 Growing Science Ltd. All rights reserved.
Keywords:
Project scheduling
Simulated annealing
Mixed integer linear programming
1. Introduction
Project scheduling, which involves the planning of project activities over time by taking some
constraints into account in order to minimize or maximize some objectives, is a crucial task in project
management. For this reason, the project scheduling problem has been a popular research area over
the years. The resource-constrained project scheduling problem (RCPSP) is one of the most
complicated project scheduling problems. For the first time Blazewicz et al. (1983) showed that the
RCPSP is a generalization of the classical job shop scheduling problem, belonging to NP-hard
optimization problems. For the first time, the multi-skilled project scheduling problem (MSPSP),
which is an expansion of RCPSP, has been presented by Neron and Boptista (2002). As a general
rule, this problem is an extended model of the multi-mode RCPSP (MM-RCPSP) (Bellenguez-
Morineau & Neron, 2005).
The main differences between the MSPSP and classical project scheduling problems are in the
resources and the requirement type of each resource. In the MSPSP, the resources are staff members