A note on time/cost tradeoff curve generation for project scheduling with multi-mode resource availability costs

In this note we combine two known algorithms and show how they can be used in order to generate tradeoff curves between time and cost for deterministic project scheduling problems with multiple modes and resource availability costs. The approach can handle linear and non-linear non-decreasing cost functions and it is based on the exact algorithm presented in Demeulemeester (1995) for the resource availability cost problem without multiple modes. As the problem is NP-hard, the method is computationally viable to solve only problems of a moderate size. The performance of the combined algorithm is compared to solutions generated by GAMS/CPLEX.