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The budget constrained discrete time/cost trade-off problem in project networks

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2008
Değirmenci, Güvenç
The time/cost trade-off models in project management aim to compress the project completion time by accelerating the activity durations at an expense of additional resources. The budget problem in discrete time/cost trade-off scheduling selects the time/cost mode -among the discrete set of specified modes- for each activity so as to minimize the project completion time without exceeding the available budget. There may be alternative modes that solve the budget problem optimally, however each solution may have a different total cost value. In this study we aim to find the minimum cost solution among the optimal solutions of the budget problem. We analyze the structure of the problem together with its linear programming relaxation and derive some mechanisms for reducing the problem size. We solve the reduced problem by linear programming relaxation and branch and bound based approximation and optimization algorithms. We find that our branch and bound algorithm finds optimal solutions for medium-sized problem instances in reasonable times and the approximation algorithms produce high quality solutions. We also discuss the way our algorithms could be used to construct the time/cost trade-off curve.