Friday, March 24, 2006

David Simchi-Levi Presentation

David Simchi-Levi is here at CMU today speaking on inventory systems where the decision maker is not risk neutral. David is a professor at MIT and Editor-in-Chief of Operations Research. He also runs his own company, LogicTools. I think he has given up sleep.

It is surprising that there is so little research on risk-averse decision makers in the operations management context. This clearly is a useful integration of economic theory and operations research and also involves the interface between finance and operations in a firm. In David's work, even marketing comes into play since prices can be set in the model in order to influence demand.

Work like this often spends time in pages of greek letters with subscripts, and this paper is no different (though David is an excellent lecturer, so it was not as mind-numbing as some lectures like this).

With fixed costs for ordering, even models with risk neutral decision makers are hard to solve. Normally, the optimal decisions are set with an (s,S,p) policy: if inventory is under s, order up to S, and set price p. But suppose the inventory level is a bit above s. Should price be set high in order to decrease demand or should the order go up to S, and price be set low. This example shows that the price has a discontinuity, making it hard to get characteristics of the solution.

With risk aversion, things get more complicated. For the case where there is no fixed ordering cost, the optimal policy is a base stock policy, but the base stock level depends on the wealth level of the decision maker. With fixed costs, for exponential utility, the optimal inventory policy is independent of wealth, making things a bit easier (though it is still hard to figure out the exact policy).

One interesting aspect of this that came up in Q&A is the need to combine pricing and inventory decisions. Most companies are not aligned this way: marketing sets price, while operations sets inventory. Even in these complicated models, though, the results generally look like "Operations, do (s,S); Marketing, set price p". This suggests very tight integration is not needed: coordination is enough.

When you add financial hedging aspects, there is still this decoupling aspect: the financial decisions do not affect the operational decisions.

It would take someone more skilled than I to explain these results to a general audience, but I find it interesting that models that contain all of marketing (price setting), operations (inventory setting) and finance (hedging) are amenable to analytical solution. This seems a very rich research area.

Thursday, March 23, 2006

A Stonewall Connection to Operational Research

My parents grew up on farms outside a then-small (now medium) sized town in Manitoba named Stonewall. For a period in the early 1900s, a boy named Charles Goodeve lived in Stonewall. He lived there for about 10 years, before his family moved to Winnipeg. There is an article in the Stonewall Argus (the Gordon Trick mentioned is my father) about his life, including his work during World War II in the British Navy. Among other things, he figured out how to protect ships from underwater mines through a demagnetization process.

The operational research connection? In 1948, Sir Charles Goodeve founded the OR Club, which would later become the Operational Research Society.

Wednesday, March 15, 2006

Tournament Time!

The NCAA Tournament is irresistable to OR types. Predicting the tournament has proven a rich area of application. Jay Coleman of the University of North Florida has a scorecard approach that gives probabilities of wins for every game in the first round. For three of the 32 games, his approach favors the lower seeded team (including number 10 Alabama over number 7 Marquette. As far as number 1 seeds go, his method gives a 99%+ chance to Villanova and Duke in their first game (a number 16 has never beat a number 1) but just 97% for UConn and 95% for Memphis.

Joel Sokol of Georgia Tech has done a lot of work in this area. He has some interesting comments on the 2006 brackets.

INFORMS has some other pointers in this area.

Anyone else like to talk about their OR approaches to this?

Operations Research and CIOs

United Airlines now has a CIO who is also responsible for operations research and other activities. This seems a natural, if somewhat unusual move (OR is often under manufacturing, operations or some other structure). OR is all about using information, and as firms realize the value of information (and CIOs) is in their ability to extract knowledge from information, more OR may be in the hands of the CIO.

Wednesday, March 01, 2006

Applied Mathematical Programming

One of my all time favorite textbooks is Applied Mathematical Programming by Bradley, Hax, and Magnanti. This text is now available on the web!