The payoff of a scheduling model within time delay considerations

It is a common practice in the scheduling literature to focus on a given model and then, from there, a study is carried out. In this paper, we consider the problem of measuring the payoff one may expect from choosing one model instead of another one. In other words, given the same instance, we measure the distance between the optimal solution produced in one model and the optimal solution produced in another model. This question is motivated by the fact that in some applications the model within which problems might arise are not fixed a priori. Thus, scheduling the jobs within a given model may only be justified by the practical facilities offered by that model at a given time, but not before hand. In this study, we consider the open, flow and permutation shops environments with time delays incurred by the transfer of jobs from one machine to another. The criterion we are addressing is the overall schedule length or the makespan.