Two-agent integrated scheduling of production and distribution operations with fixed departure times

We consider integrated scheduling of production and distribution operations associated with two customers (agents). Each customer has a set of orders to be processed on the single production line at a supplier on a competitive basis. The finished orders of the same customer are then packed and delivered to the customer by a third-party logistics (3PL) provider with a limited number of delivery transporters. The number of orders carried in a delivery transporter cannot exceed its delivery capacity. Each transporter incurs a fixed delivery cost regardless of the number of orders it carries, and departs from the 3PL provider to a customer at fixed times. Each customer desires to minimise a certain optimality criterion involving simultaneously the customer service level and the total delivery cost for its orders only. The customer service level for a customer is related to the times when its orders are delivered to it. The problem is to determine a joint schedule of production and distribution to minimise the objective of one customer, while keeping the objective of the other customer at or below a predefined level. Using several optimality criteria to measure the customer service level, we obtain different scenarios that depend on optimality criterion of each customer. For each scenario, we either devise an efficient solution procedure to solve it or demonstrate that such a solution procedure is impossible to exist.