On project scheduling problem

Consideration was given to the resource-constrained project scheduling problem and its special cases. The existing lower estimates of the objective function—minimization of the project time—were compared. It was hypothesized that the optimal value of the objective function of the nonpreemptive resource-constrained project scheduling problem is at most twice as great as that of the objective function with preemption. The hypothesis was proved for the cases of parallel machines and no precedence relation.

[1]  A. Lazarev.  Graphic approach to combinatorial optimization , 2007 .

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

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

[4]  V. Maniezzo,et al.  An Exact Algorithm for the Resource-Constrained Project Scheduling Problem Based on a New Mathematical Formulation , 1998 .

[5]  Rainer Kolisch,et al.  PSPLIB - a project scheduling problem library , 1996 .

[6]  Hans Kellerer,et al.  Knapsack problems , 2004 .

[7]  R. Kolisch,et al.  Heuristic algorithms for solving the resource-constrained project scheduling problem: Classification and computational analysis , 1998 .

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

[9]  Peter Brucker,et al.  Complex Scheduling , 2006 .

[10]  Eugene L. Lawler,et al.  Sequencing and scheduling: algorithms and complexity , 1989 .

[11]  Erik Demeulemeester,et al.  An efficient optimal solution procedure for the preemptive resource-constrained project scheduling problem , 1996 .

[12]  Hartmut Schmeck,et al.  Ant colony optimization for resource-constrained project scheduling , 2000, IEEE Trans. Evol. Comput..

[13]  Peter Brucker,et al.  Complex Scheduling (GOR-Publications) , 2006 .

[14]  Rainer Kolisch,et al.  PSPLIB - A project scheduling problem library: OR Software - ORSEP Operations Research Software Exchange Program , 1997 .

[15]  Ronald L. Graham,et al.  Bounds for certain multiprocessing anomalies , 1966 .

[16]  Rema Padman,et al.  An integrated survey of project scheduling , 1997 .