The project scheduling problem with production and consumption of resources: A list-scheduling based algorithm

The paper deals with algorithms for applying classical list scheduling to a project scheduling problem where the units of resources are produced or consumed at the occurrence of precedence-related events. It is shown that the feasibility variant of the project scheduling problem is NP-complete. Moreover, polynomial-time scheduling algorithms are devised for the three cases where the occurrence time sequence of all events or the consuming events or the producing events is given in advance. By enumerating these sequences (called linear orders), one obtains a list-scheduling based algorithm for minimizing the makespan of a project scheduling problem with production and consumption of resources.

[1]  Ravindra K. Ahuja,et al.  Network Flows , 2011 .

[2]  Amihood Amir,et al.  A fast feasibility test for relocation problems , 1988 .

[3]  Bertrand M. T. Lin,et al.  Minimizing the weighted number of tardy jobs and maximum tardiness in relocation problem with due date constraints , 1999, Eur. J. Oper. Res..

[4]  J. Christopher Beck.  Heuristics for scheduling with inventory: dynamic focus via constraint criticality , 2002 .

[5]  Klaus Neumann,et al.  Heuristics for the minimum project-duration problem with minimal and maximal time lags under fixed resource constraints , 1995, J. Intell. Manuf..

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

[7]  Ravi Sethi,et al.  Complete register allocation problems , 1973, SIAM J. Comput..

[8]  Francis Sourd,et al.  Continuous filling and emptying of storage systems in constraint-based scheduling , 2005, Eur. J. Oper. Res..

[9]  Berit Johannes,et al.  On the complexity of scheduling unit-time jobs with OR-precedence constraints , 2005, Oper. Res. Lett..

[10]  Philippe Laborie,et al.  Algorithms for propagating resource constraints in AI planning and scheduling: Existing approaches and new results , 2003, Artif. Intell..

[11]  Klaus Neumann,et al.  Scheduling of continuous and discontinuous material flows with intermediate storage restrictions , 2005, Eur. J. Oper. Res..

[12]  Ravindra K. Ahuja,et al.  Chapter IV Network flows , 1989 .

[13]  Hussein M. Abdel-Wahab,et al.  Scheduling to Minimize Maximum Cumulative Cost Subject to Series-Parallel Precedence Constraints , 1978, Oper. Res..

[14]  J. Christopher Beck.  Heuristics for Constraint-Directed Scheduling with Inventory , 2000, AIPS.

[15]  Aziz Moukrim,et al.  Solving RCPSP with resources production possibility by tasks , 2005 .

[16]  Joanna Józefowska,et al.  Perspectives in modern project scheduling , 2006 .

[17]  Eugene L. Lawler,et al.  The recognition of Series Parallel digraphs , 1979, SIAM J. Comput..

[18]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

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

[20]  Stephen F. Smith,et al.  A Constraint-Based Method for Project Scheduling with Time Windows , 2002, J. Heuristics.

[21]  George L. Nemhauser,et al.  Handbooks in operations research and management science , 1989 .

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

[23]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

[24]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

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

[26]  Klaus Neumann,et al.  Resource-Constrained Project Scheduling with Time Windows , 2006 .

[27]  Klaus Neumann,et al.  Project scheduling with inventory constraints , 2003, Math. Methods Oper. Res..