The weights may be heuristic measures defined by the managers - in an optimal schedule when using such a criterion, the higher the weight the earlier a job will be completed. It is of course difficult to select these weights, as there is a priori no known selection rule.

There are also other objectives in real production, such as the minimum tardiness criterion - in this case there is a measure of how long we are willing to wait, and the tardiness objective penalizes being late in comparison with that measure - all jobs that are finished on time or even earlier have the same value in such an objective function. This is of course related to a constraint on the completion time, and one realizes that it is not an easy task to define the "right" tardiness weight, but perhaps it can be related to penalties according to contracts.

Whatever one uses - it has to be made clear what context the problem is formulated in, so the actual case studied utilizes an objective - or indeed multiple objectives - that the management find reasonable.

I agree with Michael Patriksson.

I sugest you read this paper "A dynamic neighborhood based tabu search algorithm for real-world flight instructor scheduling problems"

Thanks for your answers, have you another suggestions of the interest of minimizing the weighted sum completion time ? I find that this criterion is used in application to instruction scheduling in VLIW processors, but I didn't understand enough

What I need to know for instance is the interest of minimizing ∑WiCi, what is the benefit in real word problems when we consider the optimise this criterion in academic scheduling problems

Hi,

As mentionned in Pinedo's famous book "Scheduling: Theory and applications" (Springer 2008), The sum of the weighted completion times of the n jobs gives an indication of the total holding or inventory costs incurred by the schedule. In the weighted version of the mean flow time, the higher the weight of a job, the earlier the latter has to be completed.

I hope this helps,

Kind regards,

Imène.

Dear Himanshu

which Fuzzy method? there are many. can you describe it briefly or send me interesting link?

Best regard