Jacob Jan Paulus

Time-constrained project scheduling

We propose a new approach for scheduling with strict deadlines and apply this approach to the Time-Constrained Project Scheduling Problem (TCPSP). To be able to meet these deadlines, it is possible to work in overtime or hire additional capacity in regular time or overtime. For this problem, we develop a two stage heuristic. The key of the approach lies in the first stage in which we construct partial schedules. In these partial schedules, jobs may be scheduled for a shorter duration than required. The second stage uses an ILP formulation of the problem to turn a partial schedule into a feasible schedule, and to perform a neighborhood search. The developed heuristic is quite flexible and, therefore, suitable for practice. We present experimental results on modified RCPSP benchmark instances. The two stage heuristic solves many instances to optimality, and if we substantially decrease the deadline, the rise in cost is only small.

A tight analysis of Brown-Baker-Katseff sequences for online strip packing

We study certain adversary sequences for online strip packing which were first designed and investigated by Brown, Baker and Katseff (Acta Inform. 18:207–225) and determine the optimal competitive ratio for packing such Brown-Baker-Katseff sequences online. As a byproduct of our result, we get a new lower bound of

Online scheduling & project scheduling

\rho \ge 3/2+\sqrt{33}/6 \approx 2.457

Online Algorithms for Parallel Job Scheduling and Strip Packing

for the competitive ratio of online strip packing.

Online algorithm for parallel job scheduling and strip packing

This thesis presents new and improved scheduling algorithms for a number of scheduling problems. The first part of the thesis deals with two online-list scheduling problems, both with the objective to minimize the makespan. In these problems, the jobs arrive one by one and the decision maker has to irrevocably schedule the arriving job before the next job becomes known. In the second part, a new solution methodology for the time-constrained project scheduling problem is developed, and a decomposition method for the time-constrained project scheduling problem with adjacent resources is presented. The first online problem considered, is online-list scheduling of parallel jobs with the objective to minimize the makespan, and some of its special cases. In these problems there is a set of identical machines to process a set of parallel jobs. In contrast to the jobs in classical machine scheduling problems, parallel jobs require a number of machines simultaneously for their processing. For this problem, a 6.6623-competitive online algorithm and a lower bound of 2.43 on the competitive ratio of any online algorithm are presented. Both results are also applicable to the online orthogonal strip packing problem. Besides the tight lower bound of 2 on the competitive ratio of the problem with exactly two machines, also improved online algorithms for the case with exactly three machines and the semi-online case where jobs appear in non-increasing order of machine requirement are given. The second online problem covered, is the online-list batch scheduling problem with the objective to minimize the makespan. In this problem, there is one machine with a given batch capacity that processes the jobs in a parallel batching manner. Parallel batching means that all jobs in one batch receive processing at the same time. A complete classification of the tractability of this online problem is given; with respect to the competitive ratio an optimal online algorithm for any capacity of the batching machine is presented. The second part of this thesis presents a new scheduling approach for scheduling with strict deadlines on the jobs. This approach is applied to the time-constrained project scheduling problem. In this problem there is a set of resources, each with its own capacity, and a set of jobs requiring a specific amount of each of the resources during its processing. Additionally, there are precedence relations between the jobs and each job has a deadline. To be able to meet the deadlines in this problem, it is possible to work in overtime or hire additional capacity in regular time or overtime. In the developed two stage heuristic, the key step lies in the first stage where partial schedules are constructed. In these partial schedules, jobs may be scheduled for a shorter duration than required. The goal is to create a schedule in which the usage of overtime and extra hiring is low. The proposed method tries to prevent a pile up of costs toward the deadlines by including all jobs partially before addressing the bottlenecks. Computational tests are preformed on modified resource-constrained project scheduling benchmark instances. Many instances are solved to optimality, and lead only to a small increase of costs if the deadline is substantially decreased. Finally, the time-constrained project scheduling problem is considered under the addition of a new type of constraint, namely an adjacent resource constraint. An adjacent resource constraint requires that the units of the resource assigned to a job have to be adjacent. On top of that, adjacent resources are not required by single jobs, but by job groups. The additional complexity introduced by adding adjacent resources to the project scheduling problem, plays an important role both for the computational tractability and the algorithm design when solving the problem. The developed decomposition method separates the adjacent resource assignment from the rest of the scheduling problem. Once the job groups are assigned to the adjacent resource, the scheduling of the jobs can be done without considering the adjacent resource. The presented decomposition method forms a first promising approach for the time-constrained project scheduling problem with adjacent resources and may form a good basis to develop more elaborated methods.