A New Multi-resource cumulatives Constraint with Negative Heights

This paper presents a newcumulatives constraint, which generalizes the original cumulative constraint in different ways. The two most important aspects consist in permitting multiple cumulative resources as well as negative heights for the resource consumption of the tasks. This allows modeling in an easy way workload covering, producer-consumer, and scheduling problems. The introduction of negative heights has forced us to come up with new filtering algorithms and to revisit existing ones. The first filtering algorithm is derived from an idea called sweep, which is extensively used in computational geometry; the second algorithm is based on a combination of sweep and constructive disjunction; while the last is a generalization of task intervals to this new context. A real-life crew scheduling problem originally motivated this constraint which was implemented within the SICStus finite domain solver and evaluated against different problem patterns.

[1]  Mats Carlsson,et al.  An Open-Ended Finite Domain Constraint Solver , 1997, PLILP.

[2]  Nicolas Beldiceanu.  Sweep as a generic pruning technique , 2000 .

[3]  Jörg Würtz.  Oz Scheduler: A Workbench for Scheduling Problems , 1996, ICTAI.

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

[5]  Helmut Simonis,et al.  Modelling Producer/Consumer Constraints , 1995, CP.

[6]  Nicolas Beldiceanu,et al.  Extending CHIP in order to solve complex scheduling and placement problems , 1993, JFPL.

[7]  Nicolas Beldiceanu.  Pruning for the Minimum Constraint Family and for the Number of Distinct Values Constraint Family , 2001, CP.

[8]  Mats Carlsson,et al.  Sweep as a Generic Pruning Technique Applied to the Non-overlapping Rectangles Constraint , 2001, CP.

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

[10]  Christian Artigues,et al.  A polynomial activity insertion algorithm in a multi-resource schedule with cumulative constraints and multiple modes , 2000, Eur. J. Oper. Res..

[11]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[12]  Philippe Baptiste,et al.  Constraint-based scheduling , 2001 .

[13]  Pieter H. Hartel,et al.  Programming Languages: Implementations, Logics, and Programs , 1996, Lecture Notes in Computer Science.

[14]  J. Christopher Beck,et al.  Constraint-directed techniques for scheduling alternative activities , 2000, Artif. Intell..

[15]  Pascal Van Hentenryck,et al.  Design, Implementation, and Evaluation of the Constraint Language cc(FD) , 1994, Constraint Programming.

[16]  Henri Beringer,et al.  A CLP Language Handling Disjunctions of Linear Constraints , 1993, ICLP.

[17]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[18]  Erik Demeulemeester,et al.  A classification scheme for project scheduling problems , 1998 .

[19]  Philippe Baptiste,et al.  Satisfiability tests and time‐bound adjustmentsfor cumulative scheduling problems , 1999, Ann. Oper. Res..

[20]  François Laburthe,et al.  Improved CLP Scheduling with Task Intervals , 1994, ICLP.

[21]  Roman Barták.  Dynamic Constraint Models for Planning and Scheduling Problems , 1999, New Trends in Constraints.

[22]  François Laburthe,et al.  Cumulative Scheduling with Task Intervals , 1996, JICSLP.