The bi-level programming model between the manufacture and the supplier

We consider a serial supply chain consisting of a supplier and a manufacturer, where production, inventory, transportation, backlogging and subcontracting decisions are integrated. A sequence of deterministic but non-stationary demands of the manufacturer for single good needs to be satisfied by the supplier over a finite horizon. In each period, the supplier can produce items by himself; also can use the subcontracting option if he can not satisfy the manufacturer´s need, or due to the cost consideration. Generally, manufacturer´s order decisions can influence the supplier´s profits straightly, and on the contrary, supplier´s plan of production also can influence the cost of manufacturer. Hence, it is not appropriate to take them as one group with public benefit sometimes. We establish a bi-level programming model in which the manufacturer is the leader, the supplier is the follower and the production and subcontracting capacities are stationary. The manufacturer as the leader, first gives the decisions of ordering, aiming to reduce the cost of himself, then the follower-supplier, decides his plan of production or subcontracting according to the manufacture´s order to minimize his own cost. By solving the model, we can get the relative optimal schemes satisfied by both of the manufacturer and the supplier.