Branch-and-price approach for the multi-skill project scheduling problem

Abstract

International audienceThis work introduces a procedure to solve the multi-skill project scheduling problem (MSPSP) (Néron and Baptista, International symposium on combinatorial, optimization (CO'2002), 2002). The MSPSP mixes both the classical resource constrained project scheduling problem and the multi-purpose machine model. The aim is to find a schedule that minimizes the completion time (makespan) of a project, composed of a set of activities. In addition, precedence relations and resources constraints are considered. In this problem, resources are staff members that master several skills. Thus, a given number of workers must be assigned to perform each skill required by an activity. Practical applications include the construction of buildings, as well as production and software development planning. We present a column generation approach embedded within a branch-and-price (B&P) procedure that considers a given activity and time-based decomposition approach. Obtained results show that the proposed B&P procedure is able to reach optimal solutions for several small and medium sized instances in an acceptable computational time. Furthermore, some previously open instances were optimally solved

An Evolutionary Hyper-heuristic for the Software Project Scheduling Problem

“…It is impractical to use exact methods to solve medium or large SPSP instances. Evolutionary algorithms have been employed to solve the SPSP [1], [5], [12], [14], [16], [17]. Other metaheuristics have also been used, such as ant colony optimization and its variants [4], [6], [15].…”

“…Other metaheuristics have also been used, such as ant colony optimization and its variants [4], [6], [15]. A column generation approach was presented in [12], embedded within a branch-andprice procedure.…”

Lower bounds for a multi-skill project scheduling problem

“…Indeed firms hold an increasing share of their activities in project mode and wish that this part of their activities could be linked to other ERP modules, eg, billing passed time. Therefore, we aim at providing a generic model which can integrate an open source platform, but also closely match the needs of the customers of Nereide (a service company specialized in open source software, at the initiative of this project 1 ). The model selected may be seen as a multi-skill project scheduling problem with preemption [6,7].…”

A note on “branch-and-price approach for the multi-skill project scheduling problem”

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In a recent paper published in Optimization Letters, Montoya et al (Optim Lett 8:1721-1734, 2014 proposed a branch-and-price approach for a multi-skill project scheduling problem. In that paper, an integer linear programming formulation was first introduced which, unfortunately, has a number of inconsistences.

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“…It should be noted that in our opinion, the issues found in the second section of the above mentioned paper do not influence the technical contents of Sections 3-7. In fact, in order to develop their branch-and-price approach, the authors started by developing a column generation formulation which is independent from the aspects we discuss in this note.The relevance of this note arises from the fact that models like the one proposed by Montoya et al [2] are important for practitioners because, often, they do not have the necessary skills to make full use of integer and combinatorial optimization tools, thus I. Correia (B) …”