This paper considers the coordinated production and delivery scheduling problem. We have a planning horizon consisting of
delivery times each with a unique delivery capacity. Suppose we have a set of jobs each with a committed delivery time, processing time, production window, and profit. The company can earn the profit if the job is produced in its production window and delivered before its committed delivery time. From the company point of view, we are interested in picking a subset of jobs to process and deliver so as to maximize the total profit subject to the delivery capacity constraint. We consider both the single delivery time case and the multiple delivery times case.
Suppose the given set of jobs are
-disjoint, that is, the jobs can be partitioned into
lists of jobs such that the jobs in each list have disjoint production windows. When
is a constant, we developed a PTAS for the single delivery case. For multiple delivery times case, we also develop a PTAS when the number of delivery times is a constant as well.