Approximation algorithms for the discrete time-cost tradeoff problem
- Technische Universitaet, Berlin (Germany)
Due to its obvious practical relevance, the Time-Cost Tradeoff Problem has achieved the attention of many researchers over the last thirty years. Within this context, we consider projects given by a set of single activities and precedence constraints on these activities. The duration of each activity is variable. However, the shorter the chosen duration is, the higher is the cost caused by executing the activity. This defines the proper time-cost tradeoff: short project durations correspond to high cost and vice versa. If the cost of a single activity depends linearly on the chosen duration, the Time-Cost Tradeoff Problem can exactly be solved in polynomial time. However, its discrete variant is known to be NP-hard. Hence, in the past there have been several heuristic attempts to find {open_quotes}good{close_quotes} algorithms to solve this problem. In this paper we present the first polynomial-time approximation algorithms for the Discrete Time-Cost Tradeoff Problem with constant performance guarantee on various special classes of instances. Specifically, we consider the problem of finding an optimal schedule for a project with a given budget that must not be overspent. We give a polynomial time approximation algorithm with a performance ratio of 3 for projects with alternatives 0/1 or 0/2 for the duration of each activity. Moreover, we can show that this is the best approximation that can be found, unless P = NP. Finally, we kind of generalize our result to arbitrary projects by giving an approximation algorithm with a performance guarantee 3/2 log{sub 2}{ell} + 7/2. Here, {ell} is the ratio of the maximum allowed duration of any activity to the minimum allowed non-zero duration of any activity.
- OSTI ID:
- 471707
- Report Number(s):
- CONF-970142-; TRN: 97:001377-0056
- Resource Relation:
- Conference: 8. annual Association for Computing Machinery (ACM)-Society for Industrial and Applied Mathematics (SIAM) symposium on discrete algorithms, New Orleans, LA (United States), 5-7 Jan 1997; Other Information: PBD: 1997; Related Information: Is Part Of Proceedings of the eighth annual ACM-SIAM symposium on discrete algorithms; PB: 798 p.
- Country of Publication:
- United States
- Language:
- English
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