Scheduling projects with multi-skilled personnel by a hybrid MILP/CP benders decomposition algorithm

We study an assignment type resource-con- strained project scheduling problem with resources being multi-skilled personnel to minimize the total staffing costs. We develop a hybrid Benders decomposition (HBD) algorithm that combines the complimentary strengths of both mixed-integer linear programming (MILP) and constraint programming (CP) to solve this NP-hard optimization problem. An effective cut-generating scheme based on temporal analysis in project scheduling is devised for resolving resource conflicts. The computational study shows that our hybrid MILP/CP algorithm is both effective and efficient compared to the pure MILP or CP method alone.

[1]  Haitao Li,et al.  Modeling the supply chain configuration problem with resource constraints , 2008 .

[2]  Christoph Schwindt,et al.  Generation of Resource-Constrained Project Scheduling Problems with Minimal and Maximal Time Lags , 1998 .

[3]  Alexander Bockmayr,et al.  Branch and Infer: A Unifying Framework for Integer and Finite Domain Constraint Programming , 1998, INFORMS J. Comput..

[4]  A. Thesen,et al.  Measures of the restrictiveness of project networks , 1977, Networks.

[5]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

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

[7]  Edward P. K. Tsang,et al.  Foundations of constraint satisfaction , 1993, Computation in cognitive science.

[8]  Klaus Jansen.  An Approximation Scheme for Bin Packing with Conflicts , 1999, J. Comb. Optim..

[9]  Edward P. K. Tsang,et al.  Constraint Based Scheduling: Applying Constraint Programming to Scheduling Problems , 2003, J. Sched..

[10]  George L. Nemhauser,et al.  CP Based Branch-and-Price , 2004 .

[11]  J. F. Benders.  Partitioning procedures for solving mixed-variables programming problems , 1962 .

[12]  David Joslin,et al.  "Squeaky Wheel" Optimization , 1998, AAAI/IAAI.

[13]  Erlendur S. Thorsteinsson.  Branch-and-Check: A Hybrid Framework Integrating Mixed Integer Programming and Constraint Logic Programming , 2001, CP.

[14]  Peter Brucker,et al.  Lower bounds for resource-constrained project scheduling problems , 2003, Eur. J. Oper. Res..

[15]  Meinolf Sellmann,et al.  Constraint Programming Based Lagrangian Relaxation for the Automatic Recording Problem , 2003, Ann. Oper. Res..

[16]  Thierry Benoist,et al.  Constraint Programming Contribution to Benders Decomposition: A Case Study , 2002, CP.

[17]  Jeremy Frank,et al.  Mixed Discrete and Continuous Algorithms for Scheduling Airborne Astronomy Observations , 2005, CPAIOR.

[18]  Mark Wallace,et al.  Hybrid Benders Decomposition Algorithms in Constraint Logic Programming , 2001, CP.

[19]  Philippe Baptiste,et al.  Constraint - based scheduling : applying constraint programming to scheduling problems , 2001 .

[20]  Klaus Jansen,et al.  An Approximation Scheme for Bin Packing with Conflicts , 1998, J. Comb. Optim..

[21]  Alf Kimms,et al.  Optimization guided lower and upper bounds for the resource investment problem , 2001, J. Oper. Res. Soc..

[22]  Michela Milano,et al.  Constraint and Integer Programming: Toward a Unified Methodology (Operations Research/Computer Science Interfaces, 27) , 2003 .

[23]  Yixin Chen,et al.  An Efficient Hybrid Strategy for Temporal Planning , 2006, CPAIOR.

[24]  Yixin Chen,et al.  Constraint partitioning in penalty formulations for solving temporal planning problems , 2006, Artif. Intell..

[25]  Vipul Jain,et al.  Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems , 2001, INFORMS J. Comput..

[26]  María Auxilio Osorio Lama,et al.  Mixed Logical-linear Programming , 1999, Discret. Appl. Math..

[27]  Wim Nuijten,et al.  Solving Scheduling Problems with Setup Times and Alternative Resources , 2000, AIPS.

[28]  Rolf H. Möhring,et al.  Scheduling project networks with resource constraints and time windows , 1988 .

[29]  T. Benoist,et al.  Lagrange Relaxation and Constraint Programming Collaborative schemes for Traveling Tournament Problems , 2001 .

[30]  Peter Brucker,et al.  A linear programming and constraint propagation-based lower bound for the RCPSP , 2000, Eur. J. Oper. Res..

[31]  O. Zeynep Akşin,et al.  A REVIEW OF WORKFORCE CROSS-TRAINING IN CALL CENTERS FROM AN OPERATIONS MANAGEMENT PERSPECTIVE , 2007 .

[32]  Rina Dechter,et al.  Temporal Constraint Networks , 1989, Artif. Intell..

[33]  Pascal Van Hentenryck.  The OPL optimization programming language , 1999 .

[34]  Matthew L. Ginsberg,et al.  Limited Discrepancy Search , 1995, IJCAI.

[35]  J. Hooker,et al.  Logic-Based Methods for Optimization: Combining Optimization and Constraint Satisfaction , 2000 .

[36]  Jacques F. Benders,et al.  Partitioning procedures for solving mixed-variables programming problems , 2005, Comput. Manag. Sci..

[37]  D. Atkin.  OR scheduling algorithms. , 2000, Anesthesiology.

[38]  Professor Dr. Klaus Neumann,et al.  Project Scheduling with Time Windows and Scarce Resources , 2003, Springer Berlin Heidelberg.

[39]  Maria Fox,et al.  PDDL2.1: An Extension to PDDL for Expressing Temporal Planning Domains , 2003, J. Artif. Intell. Res..

[40]  Peter Brucker,et al.  Scheduling and constraint propagation , 2002, Discret. Appl. Math..

[41]  Maria Fox,et al.  Hybrid STAN: Identifying and Managing Combinatorial Optimisation Sub- problems in Planning , 2001, IJCAI.

[42]  Maria Fox.  Planning for Mixed Discrete Continuous Domains , 2006, CPAIOR.

[43]  Peter Brucker,et al.  2 Solving Large-Sized Resource-Constrained Project Scheduling Problems , 1999 .

[44]  Leon S. Lasdon,et al.  Optimization Theory of Large Systems , 1970 .

[45]  John N. Hooker,et al.  Logic, Optimization, and Constraint Programming , 2002, INFORMS J. Comput..

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

[47]  Joachim Schimpf,et al.  ECLiPSe: A Platform for Constraint Logic Programming , 1997 .

[48]  Michela Milano,et al.  Constraint and Integer Programming , 2004, Operations Research/Computer Science Interfaces Series.

[49]  Pascal Van Hentenryck,et al.  The Constraint Logic Programming Language CHIP , 1988, FGCS.