Packing problems and project scheduling models: an integrating perspective

This paper considers two problem classes, namely packing and project scheduling problems that are important to researchers as well as practitioners. The two problem categories are described, and a classification is given for the different kinds of packing problems and project scheduling concepts. While both problem classes are different with respect to their fields of application, similarities of their mathematical structures are examined. It is shown that all packing problems considered here are special cases of models for project scheduling. The aim is to indicate which project scheduling models can be used to capture the different types of packing problems. Finally, some implications for research on optimisation algorithms for these two problem classes are discussed, and the applicability of the results of this work in practice are pointed out.

[1]  Armin Scholl,et al.  Bison: A fast hybrid procedure for exactly solving the one-dimensional bin packing problem , 1997, Comput. Oper. Res..

[2]  F. Brian Talbot,et al.  Resource-Constrained Project Scheduling with Time-Resource Tradeoffs: The Nonpreemptive Case , 1982 .

[3]  Arno Sprecher,et al.  An exact algorithm for project scheduling with multiple modes , 1997 .

[4]  Gündüz Ulusoy,et al.  A survey on the resource-constrained project scheduling problem , 1995 .

[5]  Andrew Chi-Chih Yao,et al.  Resource Constrained Scheduling as Generalized Bin Packing , 1976, J. Comb. Theory A.

[6]  Willy Herroelen,et al.  Assembly line balancing by resource-constrained project scheduling : a critical appraisal , 1997 .

[7]  Nicos Christofides,et al.  An exact algorithm for general, orthogonal, two-dimensional knapsack problems , 1995 .

[8]  A. Sprecher.  A competitive branch-and-bound algorithm for the simple assembly line balancing problem , 1999 .

[9]  John E. Beasley,et al.  A Genetic Algorithm for the Multidimensional Knapsack Problem , 1998, J. Heuristics.

[10]  Erik Demeulemeester,et al.  New Benchmark Results for the Resource-Constrained Project Scheduling Problem , 1997 .

[11]  Roman Słowiński,et al.  Two Approaches to Problems of Resource Allocation Among Project Activities — A Comparative Study , 1980 .

[12]  Sándor P. Fekete,et al.  A New Exact Algorithm for General Orthogonal D-Dimensional Knapsack Problems , 1997, ESA.

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

[14]  Arno Sprecher,et al.  A competitive exact algorithm for assembly line balancing , 1997 .

[15]  Arno Sprecher,et al.  Multi-mode resource-constrained project scheduling by a simple, general and powerful sequencing algorithm , 1998, Eur. J. Oper. Res..

[16]  Arno Sprecher,et al.  Resource-Constrained Project Scheduling: Exact Methods for the Multi-Mode Case , 1994 .

[17]  Philip M. Wolfe,et al.  Multiproject Scheduling with Limited Resources: A Zero-One Programming Approach , 1969 .

[18]  Andreas Drexl,et al.  Distribution requirements and compactness constraints in school timetabling , 1997 .

[19]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

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

[21]  Reinaldo Morabito,et al.  A simple and effective recursive procedure for the manufacturer's pallet loading problem , 1998, J. Oper. Res. Soc..

[22]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[23]  Heinrich Exeler,et al.  Das homogene Packproblem in der betriebswirtschaftlichen Logistik , 1988 .

[24]  J. We¸Glarz,et al.  ON CERTAIN MODELS OF RESOURCE ALLOCATION PROBLEMS , 1980 .

[25]  Harald Dyckhoff,et al.  A typology of cutting and packing problems , 1990 .

[26]  Sönke Hartmann,et al.  Project Scheduling with Multiple Modes: A Genetic Algorithm , 2001, Ann. Oper. Res..

[27]  Salah E. Elmaghraby,et al.  Activity networks: Project planning and control by network models , 1977 .

[28]  John E. Beasley,et al.  An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure , 1985, Oper. Res..

[29]  Erik Demeulemeester,et al.  Modelling setup times, process batches and transfer batches using activity network logic , 1996 .

[30]  Linus Schrage,et al.  Solving Resource-Constrained Network Problems by Implicit Enumeration - Nonpreemptive Case , 1970, Oper. Res..

[31]  Fuh-Hwa F. Liu,et al.  A three-dimensional pallet loading method for single-size boxes , 1997 .