A Lagrangian Relaxation Based Forward-Backward Improvement Heuristic for Maximising the Net Present Value of Resource-Constrained Projects

In this paper we propose a forward-backward improvement heuristic for the variant of resource-constrained project scheduling problem aiming to maximise the net present value of a project. It relies on the Lagrangian relaxation method to generate an initial set of schedules which are then improved by the iterative forward/backward scheduling technique. It greatly improves the performance of the Lagrangian relaxation based heuristics in the literature and is a strong competitor to the best meta-heuristics. We also embed this heuristic into a state-of-the-art CP solver. Experimentation carried out on a comprehensive set of test data indicates we compare favorably with the state of the art.

[1]  Peter J. Stuckey,et al.  Maximising the Net Present Value of Large Resource-Constrained Projects , 2012, CP.

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

[3]  Alf Kimms,et al.  Maximizing the Net Present Value of a Project Under Resource Constraints Using a Lagrangian Relaxation Based Heuristic with Tight Upper Bounds , 2001, Ann. Oper. Res..

[4]  Rema Padman,et al.  A metaheuristic scheduling procedure for resource‐constrained projects with cash flows , 1999 .

[5]  Rainer Kolisch,et al.  Semi-active, active, and non-delay schedules for the resource-constrained project scheduling problem , 1995 .

[6]  David Zuckerman,et al.  Optimal speedup of Las Vegas algorithms , 1993, [1993] The 2nd Israel Symposium on Theory and Computing Systems.

[7]  Peter J. Stuckey,et al.  Explaining Time-Table-Edge-Finding Propagation for the Cumulative Resource Constraint , 2012, CPAIOR.

[8]  Hanyu Gu,et al.  Computation of approximate alpha-points for large scale single machine scheduling problem , 2008, Comput. Oper. Res..

[9]  Nicolas Beldiceanu,et al.  Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimzation Problems , 2012, Lecture Notes in Computer Science.

[10]  Martin W. P. Savelsbergh,et al.  An experimental study of LP-based approximation algorithms for scheduling problems , 1998, SODA '98.

[11]  S. Selcuk Erenguc,et al.  A Branch and Bound Procedure for the Resource Constrained Project Scheduling Problem with Discounted Cash Flows , 1996 .

[12]  Yugeng Xi,et al.  Randomized Lagrangian heuristic based on Nash equilibrium for large scale single machine scheduling problem , 2007, 2007 IEEE 22nd International Symposium on Intelligent Control.

[13]  Erik Demeulemeester,et al.  A classification scheme for project scheduling , 1999 .

[14]  Rainer Kolisch,et al.  Experimental evaluation of state-of-the-art heuristics for the resource-constrained project scheduling problem , 2000, Eur. J. Oper. Res..

[15]  Erik Demeulemeester,et al.  On Maximizing the Net Present Value of a Project Under Renewable Resource Constraints , 2001, Manag. Sci..

[16]  Mario Vanhoucke,et al.  A scatter search heuristic for maximising the net present value of a resource-constrained project with fixed activity cash flows , 2010 .

[17]  Rainer Kolisch,et al.  Experimental investigation of heuristics for resource-constrained project scheduling: An update , 2006, Eur. J. Oper. Res..

[18]  Peter J. Stuckey,et al.  Propagation via lazy clause generation , 2009, Constraints.

[19]  Robert J Willis,et al.  An iterative scheduling technique for resource-constrained project scheduling , 1992 .

[20]  Rolf H. Möhring,et al.  Solving Project Scheduling Problems by Minimum Cut Computations , 2002, Manag. Sci..

[21]  Jürgen Zimmermann,et al.  Project Scheduling with Discounted Cash Flows and General Temporal Constraints , 2000 .

[22]  Nicolas Beldiceanu,et al.  9th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR'12) , 2012 .

[23]  Mario Vanhoucke,et al.  A Decomposition-Based Genetic Algorithm for the Resource-Constrained Project-Scheduling Problem , 2007, Oper. Res..

[24]  A. H. Russell.  Cash Flows in Networks , 1970 .

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

[26]  Peter J. Stuckey,et al.  Maximising the Net Present Value for Resource-Constrained Project Scheduling , 2012, CPAIOR.

[27]  Peter J. Stuckey,et al.  Explaining the cumulative propagator , 2010, Constraints.