A heuristic approach to allocating the continuous resource in discrete--continuous scheduling problems to minimize the makespan (Q1860373)

The jobs of a given set have to be processed on a number of parallel identical machines. One renewable continuous resource is available, its amount is limited. No pre-emption is allowed. The processing rate of a job depends on the amount of the resource allocated to that processing and is governed by a differential equation. The objective is to minimize the makespan. A two-phase approach is presented which first involves finding a sequence of jobs and then the continuous resource distribution. Several heuristic algorithms, including a tabu search algorithm are described and the results of a series of computational experiments are reported.