Discrete–continuous scheduling to minimize the makespan for power processing rates of jobs

A class of discrete–continuous scheduling problems is considered when each nonpreemptable, independent job simultaneously requires for its processing a machine from a set of m identical, parallel machines and an amount, arbitrary within interval [0,1], of a continuously divisible, renewable resource available in amount 1. Job processing rates are described by power functions of the resource amount allotted at a time. Some properties of optimal schedules are proved which allow us to find such schedules analytically in some cases and to construct efficient heuristics in the general case. Results of a computational experiment are described.