Effective meta-heuristics for scheduling on uniform machines with resource-dependent release dates

This paper considers a uniform machine scheduling problem in which the release date of a job can be compressed by additional resources. The objective is to minimise the total resource usage, subject to the constraint that the makespan does not exceed a given deadline. The problem is known to be strongly NP-hard. We define two types of job moves - the right move and the left move - and analyse their effect on the resource usage. We discuss the calculation of total resource usage for two types of neighbourhood generation methods - the insertion method and exchange method. A variable neighbourhood search algorithm and a simulated annealing algorithm are developed as heuristics. To evaluate the performance of the heuristics, we develop a lower bound by relaxing the original problem to an assignment problem, which can be solved in O(n3)$ O(n^3) $ time. Finally, we generate a large number of random data, and test the performance and efficiency of the proposed heuristics. Our results indicate that the heuristics are reasonably efficient and perform very well compared with the lower bound.