Project scheduling with flexible resources: formulation and inequalities

In this paper, we study a variant of the resource-constrained project scheduling problem in which resources are flexible, i.e., each resource has several skills. Each activity in the project may need several resources for each required skill. We present a mixed-integer linear programming formulation for this problem. Several sets of additional inequalities are also proposed. Due to the fact that some of the above-mentioned inequalities require a valid upper bound to the problem, a heuristic procedure is proposed. Computational experience is reported based on randomly generated data, showing that for instances of reasonable size the proposed model enlarged with the additional inequalities can be solved efficiently.

[1]  Willy Herroelen,et al.  Project scheduling under uncertainty: Survey and research potentials , 2005, Eur. J. Oper. Res..

[2]  Gang Yu,et al.  A Branch-and-Cut Procedure for the Multimode Resource-Constrained Project-Scheduling Problem , 2006, INFORMS J. Comput..

[3]  Ramón Alvarez-Valdés,et al.  GRASP and path relinking for project scheduling under partially renewable resources , 2008, Eur. J. Oper. Res..

[4]  Rema Padman,et al.  An integrated survey of deterministic project scheduling , 2001 .

[5]  Jan Karel Lenstra,et al.  Scheduling subject to resource constraints: classification and complexity , 1983, Discret. Appl. Math..

[6]  Odile Bellenguez-Morineau,et al.  Lower Bounds for the Multi-skill Project Scheduling Problem with Hierarchical Levels of Skills , 2004, PATAT.

[7]  Erik Demeulemeester,et al.  Resource-constrained project scheduling: A survey of recent developments , 1998, Comput. Oper. Res..

[8]  Jan Węglarz,et al.  Project scheduling : recent models, algorithms, and applications , 1999 .

[9]  Odile Bellenguez-Morineau,et al.  Multi-skill Project Scheduling Problem and Total Productive Maintenance , 2007 .

[10]  Stéphane Dauzère-Pérès,et al.  Multi-resource shop scheduling with resource flexibility , 1998, Eur. J. Oper. Res..

[11]  Sönke Hartmann,et al.  A survey of variants and extensions of the resource-constrained project scheduling problem , 2010, Eur. J. Oper. Res..

[12]  Marcel Mongeau,et al.  Event-based MILP models for resource-constrained project scheduling problems , 2011, Comput. Oper. Res..

[13]  Sophie Demassey.  Mathematical Programming Formulations and Lower Bounds , 2010 .

[14]  Odile Bellenguez-Morineau,et al.  A Branch-and-Bound method for solving Multi-Skill Project Scheduling Problem , 2007, RAIRO Oper. Res..

[15]  V. Maniezzo,et al.  An Exact Algorithm for the Resource-Constrained Project Scheduling Problem Based on a New Mathematical Formulation , 1998 .

[16]  Norbert Trautmann,et al.  Scheduling the factory pick-up of new cars , 2004, OR Spectr..

[17]  William J. Cook,et al.  A Computational Study of the Job-Shop Scheduling Problem , 1991, INFORMS Journal on Computing.

[18]  Philippe Baptiste,et al.  Tight LP bounds for resource constrained project scheduling , 2004, OR Spectr..

[19]  J. Carlier,et al.  An algorithm for solving the job-shop problem , 1989 .

[20]  Rainer Kolisch,et al.  Project Scheduling Under Partially Renewable Resource Constraints , 1999 .

[21]  Erwin Pesch,et al.  A branch-and-bound algorithm for the resource-constrained project scheduling problem , 2000, Math. Methods Oper. Res..

[22]  Rainer Kolisch.  Serial and parallel resource-constrained project scheduling methods revisited: Theory and computation , 1994 .

[23]  Armin Scholl,et al.  Computing lower bounds by destructive improvement: An application to resource-constrained project scheduling , 1999, Eur. J. Oper. Res..

[24]  Rainer Kolisch,et al.  PSPLIB - A project scheduling problem library: OR Software - ORSEP Operations Research Software Exchange Program , 1997 .

[25]  Rolf H. Möhring,et al.  Resource-constrained project scheduling: Notation, classification, models, and methods , 1999, Eur. J. Oper. Res..

[26]  J. M. Tamarit,et al.  Project scheduling with resource constraints: A branch and bound approach , 1987 .

[27]  Jacques Carlier,et al.  On linear lower bounds for the resource constrained project scheduling problem , 2003, Eur. J. Oper. Res..

[28]  Ramón Alvarez-Valdés Olaguíbel,et al.  The project scheduling polyhedron: Dimension, facets and lifting theorems , 1993 .

[29]  Rainer Kolisch,et al.  Characterization and generation of a general class of resource-constrained project scheduling problems , 1995 .

[30]  Rainer Kolisch,et al.  PSPLIB - a project scheduling problem library , 1996 .

[31]  Peter Brucker,et al.  A branch and bound algorithm for the resource-constrained project scheduling problem , 1998, Eur. J. Oper. Res..

[32]  Thomas Hanne,et al.  A multiobjective evolutionary algorithm for scheduling and inspection planning in software development projects , 2005, Eur. J. Oper. Res..

[33]  Ramón Alvarez-Valdés,et al.  A scatter search algorithm for project scheduling under partially renewable resources , 2006, J. Heuristics.

[34]  Rainer Kolisch,et al.  Scheduling and staffing multiple projects with a multi-skilled workforce , 2010, OR Spectr..

[35]  R. Kolisch,et al.  Heuristic algorithms for the resource-constrained project scheduling problem: classification and computational analysis , 1999 .

[36]  Dimitri P. Bertsekas,et al.  RELAX-IV : a faster version of the RELAX code for solving minimum cost flow problems , 1994 .

[37]  Odile Bellenguez-Morineau,et al.  Methods to solve multi-skill project scheduling problem , 2008, 4OR.

[38]  Odile Bellenguez-Morineau,et al.  Genetic algorithms for the Multi-Skill Project Scheduling Problem , 2006 .