Category Archives: modeling

decision analysis, modeling

Costs and risks

The “Top Gear” guy had a nice rant in the Times Online about laws to mitigate risks.  Can we think of a way to connect the risk with the costs?  Suppose that we could eliminate a risk entirely if everyone just paid a small price.  Think polio, for example.  Well, then what about this risk, or that risk.  Surely the same solution applies, right?  As Jeremy points out, we all take our shoes off at the airport now, so the terrorists decided to use their underwear.  What will we have to do now, if risk elimination is the goal.

Or are there risks that we just have to live with?  Where do we draw the line?  Can we use probabilities and decision analysis to help make policies a little more bearable?

modeling

Complex software

One of the areas I have worked in is thinking about modeling complex manufacturing systems to try to analyze the cost functions that could be used to approximate the behavior of the system. This required lots of machinery, and reviewers were at a huge disadvantage, wondering what was going on with all my software. I tried to think of ways to “open” the code and the methods, but it was quite difficult. Getting the paper published was not picnic.

The global warming software debate is very similar. I don’t know whose software is more complicated (maybe not mine?). Here’s an article that talks about the lack of (and need for) software reviewing. Academe needs to confront this issue seriously.

decision analysis, modeling

Decision making when you know you will be second guessed

I teach quite a bit about structuring problems to help make decisions. Usually models can help illuminate the tradeoffs, and sometimes it becomes much more clear what the right strategy is.

But sometimes the downside of the “right” decision comes to dominate the thinking of the decision maker. This is a fundamental part of the dilemma facing the contestant on the game show Let’s Make a Deal when they are offered the chance to change their original decision. Even if they are better off changing, the emotional pain of changing and then losing makes them stay with their first choice. They can hear their friends saying “You won the car and then you gave it away.”

Here’s an interesting article about football coaches going for it on fourth down. I am not sure about all the details of the study, but it is probably true that the thought of what the sports writers and talk radio people will say play an important part of the calculations of when to try or punt.

modeling

I choose the BMW

Interesting experiment in fuel economy, pitting a compact hybrid versus a midsize sedan. I don’t know about the methodology, so I don’t know if the results are scientific (ie, repeatable), but it does indicate that there are many solutions to the problems we face.

What are the costs of settling for what seems to be a good solution quickly, if that leads you to miss an even better solution later on? Modeling business decisions can lead managers to stop looking after they’ve found the “optimal” solution, too.

modeling, spreadsheets

New Class for Fall 2008 Semester

I will be teaching a new class, OPIM 4895 Spreadsheet Modeling for Business Decision Making.

The class will focus on the techniques that businesses use to obtain a competitive advantage through analytics. The course will be based in Excel, to learn how the techniques work, and students will be able to translate the skills from the class to special-purpose tools that companies often use for particular problems.

Problem settings will span all of the functional business areas: operations (my background), finance and marketing, and there will be case work involved in the class to look at how analytic modeling fits into the business situation that requires decisions to be made. The right decision is always a function of the business strategy, which is why different companies “solve” problems in different ways (consider that Delta, Southwest and Skybus can all fly you from Hartford, but in very different ways).

Part of the class will focus on “optimization.” In these settings, we will try to represent complex decision settings where there are limits on what the decision maker can do. For example, suppose that as marketing manager, you have to allocate the money for a new product campaign across different channels (print, radio, television, web). What is the best use of the limited dollars? Or suppose you are trying to schedule people in a customer service center in such a way that their schedules are “attractive” and that customers get good service but also that the total cost is as low as possible.

We will also look at “decision analysis” where uncertainty about the world is only revealed after you must make your decision. Think about the poor person on Deal or No Deal, with everyone screaming different decisions. Is there a way to think about making “good” decisions? The answer is yes, by the way.

Part of the class will also be devoted to the increasing use of simulation in business. Older techniques use “scenarios” to evaluate a business decision in the face of different possible outcomes (interest rates rise by some amount, decrease by some amount, stay flat). Within a spreadsheet model, it is possible to create models that can sample thousands of possible scenarios and reveal the patterns of how the business works in those different scenarios. In much the same way that a pilot uses a simulator to practice landing in different weather situations, simulation can be used by businesses to “try out” different strategies against possible future scenarios to better understand how to proceed. Risk analysis is quite often done in this way for financial planning.

Please feel free to email me if you have other questions about the class.

modeling, operations

Traveling Salesman Problem, part 2

Now for non-geeks, what does the cartoon in part one mean? When thinking about finding the optimal solution to a problem, one question is how “hard” is the problem. If there are only two solutions, then you could probably spend the time to evaluate both and pick the better one. Most problems have many solutions, and so any algorithm to find the best is going to have to evaluate some number of potential solutions in order to find the best.

This leads to the “order” notation, O(n). What this says is the problem is “order n” and that while we might not know the exact time to evaluate each possible solution, we know we are going to have to check about “n” of them.

Now the traveling salesman problem (TSP) is one where we have to visit some number of locations, one after the other. Suppose I sell golf balls and want to visit five different golf courses today. I start at my house, and I go to one of the golf courses. From there I can choose one of the remaining four. From there, I choose one of the three, and so on, until I return home at the end of the day. How many different ways are there to do this? Turns out that this is the number of permutations of the five (and if you count your home, actually six) locations, and the number of permutations is given by n! = n(n-1)(n-2)…(2)(1). One way to solve the problem is to check every solution, all n! of them.

Suppose there are 10 locations to visit, and that your laptop computer can figure out the length of a trip with a certain visiting sequence in one thousandth of a second. You can come back to your computer in about an hour for the solution. What happens if you add two locations to visit. The awful truth about factorials is they grow like crazy, and now your computer needs five days to find the solution. What to solve 15 locations? It will take your computer 40 years. Ouch.

So geeks try to find sneaky ways to evaluate all the “good” solutions, and implicitly check the others without doing any work. Dynamic programming is one of the sneaky methods for evaluating only some of the possible solutions, but still knowing that the best of the ones you find is better than all of the possible n! solutions. The algorithm in the cartoon is O(n^2 x 2^n). So for 10 locations, we can solve the problem in about one second (instead of an hour). Twelve locations takes four seconds, and 15 takes about a minute. Much better than 40 years!

So geeks win? Not so fast. Try thirty locations — 12 days. Thirty-five locations? A year. Forty locations? 35 years. Don’t even think about 100 locations…

What does O(1) mean? The third panel guy can sell to 100 golf courses by doing just one thing. Okay, you need to have a particularly warped sense of humor to find that funny. But such senses of humor do exist (me, unfortunately).

If you’ve read this far, thanks. But is this problem really important? Do salesmen really do this? Well think about oil delivery trucks or a beer distributor who restocks convenience stores. Lots of locations, lots of choices about who to visit today, and who to visit tomorrow, and the price of gas for your truck keeps going up.

Or think about making printed circuit boards. A robot arm (usually) picks the chips from a storage position (sometimes attached to a tape) and puts them on the board in a particular location. The optimal sequence (the shortest trip to visit the n chip sites on the board) may take a lot less time than a non-optimal one, increasing costs and reducing capacity. Could there be 100 chips on a board? Sure.

economics, modeling

Subprime mortgage mess

Ok, you have to be warned that there’s a bit of less-than-polite language, but this is an interesting explanation of the subprime mortgage mess. I’m sure there was also some sophisticated modeling involved that, unfortunately, depended on an assumption that gets mentioned in the link. That assumption is not holding, and so the modeling has not played out as expected.