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Recent Applications of Linear Programming in Memory of George Dantzig. Yinyu Ye Department if Management Science and Engineering Stanford University ISMP 2006. Outline. LP in Auction Pricing Parimutuel Call Auction Proving Theorems using LP Uncapacitated Facility Location
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Department if Management Science and Engineering
(Applications presented here are by no means complete)
Argentina, Brazil, Italy, Germany and France
Total Amount Bet = $6
Outcome: Horse 2 wins
Two winners earn $2 per bet plus stake back: Winners have stake returned then divide the winnings among themselvesParimutuel Methods
Cornuejols, Nemhauser & Wolsey .
Guha & Khuller , Sviridenko .
Interpretation:clients share the cost to open a facility, and pay the connection cost.
A bi-factor (Rf,Rc)-approximate algorithm is a max(Rf,Rc)-approximate algorithm
Jain et al 
Introduce a notion of time, such that each event can be associated with the time at which it happened. The algorithm start at time 0. Initially, all facilities are closed; all clients are unconnected; all set to 0. Let C=D
While , increase simultaneously for all , until one of the following events occurs:
(1). For some client , and a open facility , then connect client j to facility i and remove j from C;
(2). For some closed facility i, , then open
facility i, and connect client with to facility i, and remove j from C.
The Bi-Factor Revealing LP
Jain et al , Mahdian et al 
Given , is bounded above by
The problem was first formulated by Leon Walrasin 1874,Elements of Pure Economics, or the Theory of Social Wealth
n players, each with
Can prices be set for all the goods such that the market clears?
Answer by Arrow and Debreu in 1954:
yes, under mild conditions if the utility functions are concave.
Eisenberg and Gale , Scarf , Eaves [1976,1985]
Nenakhov and Primak , Jain 
Codenotti et al. ,
Chen and Deng [2005, 2006],
Many excellent sessions in ISMP 2006 …
IN OUR OWN IMAGE
- a computer science odyssey -
George B. Dantzig
Nach, pale and shaking,rushed in to tell Adam, Skylab’s Captain, that a biogerm plague is sweeping the Earth, killing millions like flies.
In Our Own Image
Copyright © 2003 by
George Bernard Dantzig
All rights reserved
Organized by MS&E, Stanford, November 12, 2004 (Lustig, Thapa, etc)