Hi Nick, 90 competitions is quite a lot. I would advise to try the greedy heuristic. It should not be that difficult to get first results... Good luck! Talentink

Dear Nick, It seems that your problem belongs to the class of machine scheduling problems, a well-known area of Operations Research. Suppose each competition has to take place at one stage and cannot be intterupted by another competition (non-preemptive scheduling). Moreover, I assume that the number of competitions is not very large (say max 10 or 15). If one of these assumptions is wrong, please let me know. Let's introduce some notation: * you have s stages, * there are m different competitions, * n competitors want to take part. In terms of machine scheduling, the stages are the machines and the jobs are the competitions (using the first assumption). Your objective is to minimize the overall completion time (which is the maximum completion time of the stages). Now, you can aggregate the n competitors resulting in m jobs, each competion gets the number of competitors in this competition as duration. The problem breaks down to scheduling m jobs with different durations on s machines. This could be done by a greedy heuristic: schedule the largest unscheduled competition at the stage with the earliest (current) completion time and repeat until all competitions are scheduled. Enumerating the schedules is also an option because the number of jobs is relatively small (using the second assumption). Of course, there is a trade-off between the number of stages and the completion time. Moreover, different durations of competitors in different competitions can be incorporated easily. In that case, the duration of each competition becomes a weighted sum. With a bit more effort, you could be able to incorporate precedence constraints if you like (schedule competiton i before competition j). In case you would like to schedule all competitors individually, the problem becomes intractable and I would advise to see if the greedy heuristic described above can be of any help. I hope this helps. By searching "machine scheduling" in Google, you will probably find a wealth of information. Kind regards, Talentink