Scheduling with job dependent machine speed

The power consumption rate of computing devices has seen an enormous increase over the last decades. Therefore computer systems must make a trade-off between performance and energy usage. This observation has led to speed scaling, a technique that adapts the speed of the system to balance energy and performance. Fundamentally, when implementing speed scaling, an algorithm must make two decisions at each time: (i) a scheduling policy decides which jobs to serve, and (ii) a speed scaler decides how fast to run. In this thesis we introduce a preemptive single machine scheduling problem where the machine speed is externally given and depends on the number of jobs that is available for processing. A job is available for processing when it is released but not yet completed. The objective is to minimize the sum of weighted completion times. We will look at some variations of this problem by adding release dates or restricting ourselves to unit weights, unit processing times or by looking at the non-preemptive case. When the machine speed is constant over time, it is well known that the Smith’s rule yields an optimal schedule for both the preemptive and non-preemptive case. Unfortunately this rule gives arbitrary bad results for the problem under consideration. We introduce a greedy algorithm that solves the problem to optimality when all weights are equal. With only small changes we can alter this algorithm to work when weights are arbitrary and we have unit processing times. For arbitrary weights and processing times our algorithm finds an optimal schedule when we restrict ourselves to a certain order of job completions. However, we do not know which is an optimal order of job completions. The WSPT-order, which is optimal when machine speed is fixed, can even give arbitrary bad results.