Warehouses for a Stochastic Network by Christian Klaus

Christian Klaus is currently a Ph.D. student in the Operatoins Research Department at the Naval Postgraduate School.  His thesis topic is on designs for network reliability.  He delivered versions of this talk at ISMP 2012 and INFORMS 2012.  This part of his thesis has to do with increasing the reliability of a stochastic logistics network by introducing warehouses.

Abstract

Humanitarian assistance cargo is shipped by the Department of Defense using uncertain space-available on regularly scheduled transportation routes, i.e. by ship and aircraft. The uncertainty of available space suggests a stochastic directed network model, where arcs, representing transportation routes, can randomly fail. Currently, cargo cannot be stored in transshipment nodes.  If the cargo's origin and destination are disconnected in the stochastic network, shipment has to be delayed. The expected shipping time is the average time cargo has to wait until shipped.

The research objective is to minimize the expected shipping time by adding storage capacity, warehouses, to some of the transshipment nodes. We provide a method to find the optimal location for one or two warehouses.  Our method uses novel necessary inequalities to eliminate many possible solutions from consideration, saving on computational eff ort. Furthermore, we give a bound on the shipping time based on an unlimited number of warehouses.  For a real-world network between the US and Europe that bound shows that adding extra warehouses beyond two provides little additional benfi t.

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