Scheduling equal-length jobs with delivery times on identical processors

The problem of scheduling n jobs of equal duration p with release and delivery times on m identical processors with the objective to minimize the maximal job completion time is considered. An algorithm is proposed that has the time complexity O(mn log n) if the maximal job delivery time q(max) is bounded by some constant. This is better than the earlier known best bound of O(mn(2)log(np/m)) for the version of the problem with non-restricted q(max). The algorithm has the time complexity O(q(max)(2) n log n max {m, q(max) }) without the restriction on q(max). As the presented computational experiments show, practical behavior of the algorithm remains good without restriction on q(max), i.e., for arbitrarily long delivery times, the running time of the algorithm, in practice, does not depend on q(max).