new approaches for solving the resource-constrained project scheduling problem
TRANSCRIPT
4OR-Q J Oper Res (2012) 10:105–106DOI 10.1007/s10288-011-0156-x
PHD THESIS
New approaches for solving the resource-constrainedproject scheduling problem
Oumar Koné
Received: 1 April 2010 / Revised: 30 January 2011 / Published online: 18 February 2011© Springer-Verlag 2011
This is a summary of the author’s PhD thesis supervised by Pierre Lopez (LAAS-CNRS, France) and Marcel Mongeau (Institut de mathématiques de Toulouse, France),with the participation of Christian Artigues (LAAS-CNRS, France), and defended inDecember 2009 at the University of Toulouse. The thesis is written in French and wasfinancially supported both by the laboratory LAAS-CNRS in France and the govern-ment of Ivory Cost. It is available from the author upon request. This work deals withthe resource-constrained project scheduling problem (RCPSP), which is one of thebest-known cumulative scheduling problems due to the interest from the operationalresearch community, and to its many industrial applications.
RCPSP is a combinatorial optimization problem, NP-hard in the strong sense, wherea set of activities must be scheduled on a set of available renewable resources availablein limited quantity. It consists in finding a non-preemptive (with no interrupted activi-ties) schedule of minimum makespan (its end date) subject to precedence constraintsand resource constraints. An extension of this problem dealing with specific resources,called the RCPSP with consumption and production of resources is also treated.
From models using mixed integer linear programming, instead of relying on thetraditional discretization of the time horizon, we propose MILP formulations for theRCPSP based on the concept of event: the Start/End formulation and the On/Off for-mulation.
In 2008, Zapata et al. propose such an event-based formulation for a multimodeRCPSP. Their formulation considers that an event occurs when an activity starts or
O. KonéLAAS-CNRS, Toulouse, France
Present Address:O. Koné (B)CIRRELT, Montréal, QC, Canadae-mail: [email protected]
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ends. Transposed to the RCPSP, this model involves three types of binary variablesper activity.
In our first formulation (Start/End), we need only two types of binary variables peractivity. The first one is used to mark the beginning of the processing of each activ-ity, and the second binary variable is used to indicate its end. In our second proposal(On/Off), only one type of binary variable is required. It identifies events at whichthe activity starts or continues its processing. Since, in these formulations the numberof variables is not function of the scheduling horizon, these two new formulationsinvolve fewer variables than the traditional formulations indexed by time. Moreover,they perform better on instances with very large scheduling horizon.
The RCPSP with consumption and production of resources consists in taking more-over into account specific resources that can be consumed during the processing ofeach activity, but also produced (in another quantity) at the end of the processingof each activity. We propose an adaptation of our event-based formulations, of thediscrete-time formulations of Pritsker and Christofides, and of the flow-based con-tinuous-time formulation proposed by Artigues et al. (2008) on basis of the work ofBalas.
Compared to other models in the literature, our MILP proposals perform very wellon instances with long scheduling horizons containing activities with disparate dura-tions. In particular, on highly cumulative instances (basic characteristics of RCPSP),they are the most efficient. Thus, our contribution brings a major improvement tothe MILP formulation class, which could in turn has a positive impact on targetedapplications in the process industry, where we can find these kinds of instances.
References
Artigues C, Demassey S, Néron E (eds) (2008) Resource-constrained project scheduling: models, algo-rithms, extensions and applications. ISTE-WILEY, London
Zapata JC, Hodge BM, Reklaitis GV (2008) The multimode resource constrained multiproject schedulingproblem: alternative formulations. AIChE J 54(8):2101–2119
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