Single-machine minmax common due-window assignment and scheduling problems with convex resource allocation

In this article, the common due-window (CON DW) assignment and scheduling problem on a single machine is studied. The minmax CON DW problem is extended by considering convex resource allocation. In extended problems, the scheduler needs to find, in addition to the optimal job sequence, the start time and size of the due window, as well as the actual processing time of each job that optimizes a cost function. First, the focus is on minimizing the maximum scheduling criteria subject to maximal resource consumption. Next, the complementary problem of minimizing resource consumption subject to an upper bound on the scheduling measure is solved. For these problems, a closed form solution is provided, with computational complexity of O(n), where n is the number of jobs. An extension to the first problem is offered by assuming general position-dependent workloads, proving that the problem remains polynomially solvable.