In this work we consider a problem from the field of power- and energy-aware scheduling, in which a set of batteries have to be charged in a minimum time. The formulated problem is to schedule independent and nonpreemptable jobs to minimize the schedule length, where each job requires some amount of power and consumes a certain amount of energy during its processing. We assume that the power demand of each job linearly decreases with time, as it is the case when Li-ion batteries are being charged. For the assumed job model we prove that each next job should be started as soon as the required amount of power is available. Basing on the proven theorem we formulate a procedure generating a minimum-length schedule for an assumed order of jobs. We also analyze the case of identical jobs, and show some interesting properties of this case.

This paper explores selected heuristics methods, namely CDS, Palmer’s slope index, Gupta’s

algorithm, and concurrent heuristic algorithm for minimizing the makespan in permutation

flow shop scheduling problem. Its main scope is to explore how different instances sizes

impact on performance variability. The computational experiment includes 12 of available

benchmark data sets of 10 problems proposed by Taillard. The results are computed and

presented in the form of relative percentage deviation, while outputs of the NEH algorithm

were used as reference solutions for comparison purposes. Finally, pertinent findings are

commented.

The presented method is constructed for optimum scheduling in production lines with parallel

machines and without intermediate buffers. The production system simultaneously

performs operations on various types of products. Multi-option products were taken into

account – products of a given type may differ in terms of details. This allows providing for

individual requirements of the customers. The one-level approach to scheduling for multioption

products is presented. The integer programming is used in the method – optimum

solutions are determined: the shortest schedules for multi-option products. Due to the lack

of the intermediate buffers, two possibilities are taken into account: no-wait scheduling,

possibility of the machines being blocked by products awaiting further operations. These two

types of organizing the flow through the production line were compared using computational

experiments, the results of which are presented in the paper.