Approximation Algorithms for the Discrete Time-Cost Tradeoff Problem

Due to its obvious practical relevance, the Time-Cost Tradeoff Problem has attracted the attention of many researchers over the last forty years. While the Linear Time-Cost Tradeoff Problem can be solved in polynomial time, its discrete variant is known to be NP-hard. We present the first approximation algorithms for the Discrete Time-Cost Tradeoff Problem. Specifically, given a fixed budget we consider the problem of finding a shortest schedule for a project. We give an approximation algorithm with performance ratio 3 / 2 for the class of projects where all feasible durations of activities are either 0, 1, or 2. We extend our result by giving approximation algorithms with performance guarantee O( log l ) , where l is the ratio of the maximum duration of any activity to the minimum nonzero duration of any activity. Finally, we discuss bicriteria approximation algorithms which compute schedules for a given deadline or budget such that both project duration and cost are within a constant factor of the duration and cost of an optimum schedule for the given deadline or budget. 1. Introduction. An instance P of the Time-Cost Tradeoff Problem is a project given by a finite set of activities J P A J together with a partial order ( J, ‡ ) on the set of activities. In order to carry out a project, the activities have to be executed in accordance with the precedence constraints given by the partial order: if j‡ k, activity k may not be started before activity j is completed. The activities are indivisible tasks, hence their