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

Bernardo F. Almeida · Isabel Correia · Francisco Saldanha‐da‐Gama

44 citations0/0 files storedInternational Transactions in Operational Research

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Resource-Constrained Project Scheduling Scheduling and Optimization Algorithms Scheduling and Timetabling Solutions

Abstract

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.

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References

1999Resource-constrained project scheduling: Notation, classification, models, and methods 2009A survey of variants and extensions of the resource-constrained project scheduling problem 1969Multiproject Scheduling with Limited Resources: A Zero-One Programming Approach 2002Project Scheduling: A Research Handbook 1987Project scheduling with resource constraints: A branch and bound approach 1998An Exact Algorithm for the Resource-Constrained Project Scheduling Problem Based on a New Mathematical Formulation 2003Insertion techniques for static and dynamic resource-constrained project scheduling 2010Project scheduling with finite or infinite number of activity processing modes – A survey

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