We consider the Continuous Energy-Constrained Scheduling Problem (CECSP). A
set of jobs has to be processed on a continuous, shared resource. A schedule
for a job consists of a start time, completion time, and a resource consumption
profile. We want to find a schedule such that: each job does not start before
its release time, is completed before its deadline, satisfies its full resource
requirement, and respects its lower and upper bounds on resource consumption
during processing. Our objective is to minimize the total weighted completion
time. We present a hybrid local search approach, using simulated annealing and
linear programming, and compare it to a mixed-integer linear programming (MILP)
formulation. We show that the hybrid local search approach matches the MILP
formulation in solution quality for small instances, and is able to find a
feasible solution for larger instances in reasonable time.Comment: 19 pages, 2 figures, submitted for review at Journal of Schedulin