In many inventory systems, lost sales or backorders are not allowed. When
demand overshoots on-hand inventory, an emergency order has to be placed to
bring just enough stock to satisfy the extra demand. The resulting inventory
dynamics is similar to that of lost sale systems, but with one significant
difference, that there is a fixed emergency order cost. Unlike the regular
fixed order cost, the emergency order cost is a result of uncontrolled random
events not directly associated to one's ordering decision. In this talk, we
demonstrate that the properties (shape) of the one-stage cost depend on the
properties (shape) of the demand distribution, and as a result, the
replenishment policy structure depends on the demand distribution.

Specifically, we derive conditions under which the one-stage cost is unimodal
or is what we call DXING-convex. We further show that when the one-stage cost
is unimodal or DXING-convex, the optimal one-stage or multi-stage decision
policy has a modified (s, S) structure under which it is possible to have no
regular order at all. To demonstrate the importance of demand distribution, we
illustrate some cases in which one has two order-up-to levels and two reorder
ranges. We find that our models and results are highly relevant both
theoretically and practically.

Biography:

Xiaolan Xie (Ecole Nationale Superieure des Mines de Saint Etienne, France),
received the Ph.D. degree from University of Nancy I, Nancy, France, in 1989,
and the Habilitation a Diriger des Recherches degree from University of Metz,
Metz, France, in 1995.

Dr. Xie is a professor of industrial engineering in Ecole Nationale Superieure
des Mines de Saint Etienne, a 190-year old top-10 French graduate engineering
school, since April 2005. He was a research director at the Institut National
de Recherche en Informatique et en Automatique (INRIA) from September 2002 to
March 2005, a full professor at the Ecole Nationale d'Ingenieurs de Metz (ENIM,
a French engineering school from 1999 to 2002, a senior research scientist at
INRIA from 1990 to 1999.

Prof. Xie's areas of expertise include: discrete event dynamic systems,
performance evaluation and optimisation, supervisory control, Petri nets,
production planning and scheduling, manufacturing systems, health care systems,
preventive maintenance of manufacturing systems, supply chain design and
optimisation. He is co-author of four books on Petri nets and has authored/co-
authored over 60 journal papers in related fields.

Prof. Xie has rich industrial application experiences with European industries.
He was the INRIA-leader for the European Project GROWTH-ONE for the strategic
design of supply chain networks, for the GRWOTH thematic network TNEE on
extended enterprises and for I*PROMS NoE on intelligent machines and
intelligent production systems.

Prof. Xie is an Associate Editor of IEEE Transactions on Automation Science and
Engineering and IEEE Transactions on Automatic Control and was an Associate
Editor of IEEE Transactions on Robotics & Automation (2001-2004). He has served
as a Guest Editor of a 2001 special issue of IEEE Transactions on Robotics and
Automation on semiconductor manufacturing systems, a 2001 special issue of
International Journal of Production Research on modelling, specification and
analysis of manufacturing systems, a 2004 special issue of International
Journal of Production Research on Modelling of Reactive Systems, and a 2005
special issue of IJCIM on Discrete Event System Techniques for CIM. He has been
served on International Program Committees for many conferences such as:
WODES'06 '04 '02 '00, ESM2005, IEEE-CASE05, MSR'05 '03, PENTOM'2005 '2003,
IEEE-SMC'04 '03 '02 '01, IMS2004, MOSIM'06 '04 '03 '01, etc.