Modeling frameworks for the multi‐skill resource‐constrained project scheduling problem: a theoretical and empirical comparison

Abstract

In this paper, we study and compare several integer and mixed‐integer linear programming formulations for the multi‐skill resource‐constrained project scheduling problem. This is a problem characterized by a set of activities to be executed that in addition to the usual precedence constraints require several resources for each skill needed for their execution. A set of multi‐skill resources is assumed. The objective is to minimize the project's makespan. We revisit two existing models for the problem and propose two new ones. Additionally, we perform a theoretical comparison between the lower bounds provided by the linear programming relaxations of the models. Furthermore, a numerical experiment is performed on a set of instances from the literature to evaluate the suitability of an off‐the‐shelf solver to compute optimal solutions and lower bounds to the studied problem, using the aforementioned models.

A multi-mode multi-skill project scheduling reformulation for reconnaissance mission planning

“…Problem formulation. Following the model presented in [4] for the multi-skill project scheduling problem, the formulation of the reconnaissance mission planning problem can be obtained by adding (1) to calculate the mode infor-mation and (2) to consider the transfer time between tasks:…”

Mixed-integer/linear and constraint programming approaches for activity scheduling in a nuclear research facility

“…A MILP formulation, having similarities with the model proposed by Correia et al (2012), was priorly proposed by Li and Womer (2009) for the MSPSP with minimal and maximal time lags. Discrete-time based formulations have been proposed by Bellenguez-Morineau (2006), Montoya et al (2014) (Correia and Saldanha-da Gama (2015) proposed minor corrections to this model) and Almeida et al (2019), all of them using binary timeindexed step variables. For a given activity i, the binary step variables Z i,t with t lower than the starting time of the activity are all equal to 0, whereas the variables with t equal to or greater than the starting time are all equal to 1.…”

Heuristic and metaheuristic methods for the multi‐skill project scheduling problem with partial preemption

“…In some industrial environments, such as nuclear research facilities described in Polo-Mejía et al (2020) that inspired our study, scheduling activities need to take into account a set of skills and clearances required to execute the activities and to match them with those that some technicians master. In this context, where regulations require the presence of a group of technicians having a set of well-defined skills for the execution of an activity, the multi-skill project scheduling problem (MSPSP) is important, see for example Bellenguez-Morineau and Néron (2007); Bellenguez-Morineau (2008); Montoya et al (2014); Correia and Saldanha-da Gama (2015); Almeida et al (2016); Young et al (2017); Almeida (2018); Almeida et al (2019). The MSPSP, initially proposed to schedule IT development projects (Néron, 2002), turns out to be more challenging than traditional scheduling problems, due to additional decisions to be made: it is needed to decide not only which resources will be allocated to each activity, but also the skills with which they will contribute.…”