22 March - 26 March 2010

Isaac Newton Institute for Mathematical Sciences, Cambridge, UK

**Workshop Organisers:** Takis Konstantopoulos (*Heriot-Watt*) and Kavita Ramanan (*Brown University*).

**Workshop Programme Committee:** Vivek Borkar (*Tata Institute of Fundamental Research*), Serguei Foss (*Heriot-Watt University*), Peter Glynn (*Stanford*),

Bruce Hajek (*University of Illinois*), Frank Kelly (*Cambridge*), P.R. Kumar (*University of Illinois*), Tom Kurtz (*University of Wisconsin-Madison*), Jean Mairesse (*LIAFA*), Philippe Robert (*INRIA*), John Tsitsiklis (*MIT*) and Ruth Williams (*University of California, San Diego*)

in association with the Newton Institute programme

Stochastic Processes in Communication Sciences (11 January to 2 July 2010) Participants | Application | Accommodation and Cost**Assemble-to-Order Inventory Systems as Newsvendor Networks**

The assemble-to-order system is a classical model in inventory theory, where multiple components are used to produce multiple products. All components are obtained from an uncapacitated supplier after a deterministic lead time, while demand for the products is random. The optimal control for this system (where the goal is to minimize the long run average inventory + backlog cost) is not known except for very special cases. I will describe an approach to solving this problem using a two-stage stochastic linear program, known as the newsvendor network, which provides a lower bound on achievable cost in the inventory system. I will also describe how to translate the solution of this stochastic program into a control policy for the inventory system in some special cases and introduce our conjecture that these policies are asymptotically optimal as the lead time grows. I will finally describe how state-space collapse and related ideas from heavy traffic theory can be applied to these systems, despite the fact that there are no capacitated resources.

The talk is based on joint work with Mustafa Dogru and Qiong Wang.

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