Constructing a course schedule by solving a series of assignment type problems

We propose in this paper a new approach for tackling constrained course scheduling problems. The main idea is to decompose the problem into a series of easier subproblems. Each subproblem is an assignment type problem in which items have to be assigned to resources subject to some constraints. By solving a first series of assignment type subproblems, we build an initial solution which takes into account the constraints imposing a structure on the schedule. The total number of overlapping situations is reduced in a second phase by means of another series of assignment type problems. The proposed approach was implemented in practice and has proven to be satisfactory.

[1]  L. V. Wassenhove,et al.  A survey of algorithms for the generalized assignment problem , 1992 .

[2]  A. Hertz Tabu search for large scale timetabling problems , 1991 .

[3]  Alain Hertz,et al.  Tabaris: An exact algorithm based on tabu search for finding a maximum independent set in a graph , 1990, Comput. Oper. Res..

[4]  Richard M. Soland,et al.  A branch and bound algorithm for the generalized assignment problem , 1975, Math. Program..

[5]  D. Werra,et al.  Tabu search: a tutorial and an application to neural networks , 1989 .

[6]  Egon Balas,et al.  Addendum: Minimum Weighted Coloring of Triangulated Graphs, with Application to Maximum Weight Vertex Packing and Clique Finding in Arbitrary Graphs , 1992, SIAM J. Comput..

[7]  Onno B. de Gans,et al.  A computer timetabling system for secondary schools in the Netherlands , 1981 .

[8]  Richard M. Karp,et al.  Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems , 1972, Combinatorial Optimization.

[9]  John M. Mulvey A classroom/time assignment model , 1982 .

[10]  David S. Johnson,et al.  Computers and Inrracrobiliry: A Guide ro the Theory of NP-Completeness , 1979 .

[11]  Egon Balas,et al.  Minimum Weighted Coloring of Triangulated Graphs, with Application to Maximum Weight Vertex Packing and Clique Finding in Arbitrary Graphs , 1991, SIAM J. Comput..

[12]  Alain Hertz,et al.  Finding a feasible course schedule using Tabu search , 1992, Discret. Appl. Math..

[13]  D. Costa,et al.  A tabu search algorithm for computing an operational timetable , 1994 .

[14]  D. de Werra,et al.  An introduction to timetabling , 1985 .

[15]  Jacques A. Ferland,et al.  Exchanges procedures for timetabling problems , 1992, Discret. Appl. Math..

[16]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

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

[18]  Michel Gendreau,et al.  Solving the maximum clique problem using a tabu search approach , 1993, Ann. Oper. Res..

[19]  George L. Nemhauser,et al.  Scheduling to Minimize Interaction Cost , 1966, Oper. Res..

[20]  Alain Hertz,et al.  An Object-Oriented Methodology for Solving Assignment-Type Problems with Neighborhood Search Techniques , 1996, Oper. Res..

[21]  Arabinda Tripathy A Lagrangean Relaxation Approach to Course Timetabling , 1980 .