Abstract:

This paper mainly addresses a two-stage supply chain scheduling problem in which jobs have an assignable common due window. The due window need to be determined, because the start and completion time of the window is a variable instead of a constant. A job which is processed completely by the machine need to be dispatched with batch to customer by many vehicles, and a job will incur a holding cost if its completion time is earlier than its dispatch date. Each job will incur an early (tardy) penalty if it is early (tardy) with respect to the common due window under a given schedule. The objective is to find the optimal size and location of the window, the optimal dispatch date for each job, as well as an optimal job sequence to minimize a cost function based on earliness, tardiness, holding time, window location, window size, and batch delivery. We consider the case where the unit cost of tardiness is not more than the unit cost of holding time, and the unit cost of holding time is not more than the unit cost of earliness. We provide an O(n^{8}) dynamic programming algorithm for this case.

Key words: due window, batch delivery, supply chain scheduling, dynamic programming algorithm