Abstract
This paper develops a mathematical model for project time compression problems in CPM/PERT type networks. It is noted this formulation of the problem will be an adequate approximation for solving the time compression problem with any continuous and non-increasing time-cost curve. The kind of this model is Mixed Integer Linear Program (MILP) with zero-one variables, and the Benders' decomposition procedure for analyzing this model has been developed. Then this paper proposes a new approach based on the surrogating method for solving these problems. In addition, the required computer programs have been prepared by the author to execute the algorithm. An illustrative example solved by the new algorithm, and two methods are compared by several numerical examples. Computational experience with these data shows the superiority of the new approach.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Benders, J.F. (1962). ‘Partitioning Procedures for Solving Mixed Variables Programming Problems.’ Numerische Mathematik 4, 238–252.
Cote, G. and M.A. Laughton. (1984). ‘Large-Scale Mixed Integer Programming: Benders-type Heuristics.’ European Journal of Operational Research 16, 327–333.
Diaby, M. (1993). ‘Implicit Enumeration for the Pure Integer 0/1 Minimax Programming Problem.’ Operations Research 41, 1172–1176.
Elmaghraby, S.E., and P.S. Pulat. (1979). ‘Optimal Project Compression with Due-Dated Events.’ Naval Research Logistics Quarterly 25, 331–348.
Falk, J.E., and J.L. Horowitz. (1972). ‘ Critical Path Problems with Concave Cost-Time Curves.’ Management Science 19, 446–455.
Fulkerson, D.R. (1961). ‘A Network Flow Computation For Project Cost Curves.’ Management Science 7, 167–178.
Glover, F. (1975). ‘Surrogate Constraint Duality in Mathematical Programming.’ Operations Research 23, 434–451.
Goyal, S.K. (1975). ‘A Note on A Simple CPM Time Cost Trade-off Algorithm.’ Management Science 21, 718–722.
Holmberg, K. (1994). ‘On Using Approximations of the Benders Master Problem.’ European Journal of Operational Research 77, 111–125.
Holmberg, K. (1999). ‘Exact Solution Methods for Uncapacitated Location Problems with Convex Transportation Costs.’ European Journal of Operational Research 114, 127–140.
Kuyumcu, A., and A. Garcia-Diaz. (1994). ‘A Decomposition Approach to Project Compression with Concave Activity Cost Functions.’ IIE Transactions 26, 63–73.
Panagiotakopoulos, D. (1977). ‘A CPM Time Cost Computational Algorithm for Arbitrary Activity Cost Functions.’ Infor 15, 183–195.
Paula, J.R. and N. Maculan. (1988). ‘A P-median Location Algorithm based on the Convex Lagrangean Relaxation of the Benders Master Problem.’ Presented at the 13 th International Symposium on Mathematical Programming, Tokyo, Japan.
Philips, S., Jr., and M.I. Dessouky. (1977). ‘Solving the Project Time–Cost Trade-Off Problem Using the Minimal Cut Concept.’ Management Science 24, 393–400.
Rana, K., and R.G. Vickson. (1988). ‘A Model and Solution Algorithm for Optimal routing of a Time-chartered Container Ship.’ Transportation Science 22, 83–95.
Siemens, N. (1971). ‘A Simple CPM Time Cost Trade-off Algorithm.’ Management Science 17, 354–363.
Tufekci, S. (1982). ‘A Flow-Preserving Algorithm for the Time-Cost Trade-off Problem.’ IIE Transactions 14, 109–113.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bidhandi, H.M. A new approach based on the surrogating method in the project time compression problems. Ann Oper Res 143, 237–250 (2006). https://doi.org/10.1007/s10479-006-7385-y
Issue Date:
DOI: https://doi.org/10.1007/s10479-006-7385-y