Time-dependent order and distribution policies in supply networks S. G¨ ottlich 1 , M. Herty 2 , and Ch. Ringhofer 3 1 Department of Mathematics, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany 2 Department of Mathematics, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany 3 Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA Summary. The dynamic of a production networks is modeled by a coupled system of ordinary differential delay equations. Distribution and order policies are deter- mined by an optimization problem for maximizing the profit of the production line. 1 Introduction We consider a network of suppliers which order goods from each other and process a product according to orders, and receive payments according to a pricing policy. The dynamics of supply chains has been investigated in re- cent years (see c.f. [1, 2, 3, 5, 7]) and extended to include money flows and bankrupctcy, e.g. [2]. We extend existing results in the following ways: We con- sider general networks, represented by an arbitrarily connected graph. Each node in the network has a finite production or cycle time and a finite produc- tion capacity, as well as a front-end and back-end inventory. It is therefore possible that a supplier orders more than can be produced and stockpiles supplies. It is also possible that a supplier produces more than is ordered and stockpiles the output. Each supplier receives payments according to a dynam- ically determined pricing policy. Bankruptcy occurs if payments made exceed payments received beyond a certain available credit limit. Distribution and or- der policies are chosen in order to maximize the total profit. Mathematically, this problem is formulated as a mixed–integer programming problem. 2 The model The supply chain is modeled as a network of S 1 ,..,S J nodes (suppliers) which order and deliver goods according to given (dynamic or static) policies, and