5 ms·

Here's an example of applied math in industry: FedEx had candidate investor General Dynamics (GD), and GD had sent two of their guys, one aero engineer and one

by graycat 12y ago

Here's an example of applied math in industry: FedEx had candidate investor General Dynamics (GD), and GD had sent two of their guys, one aero engineer and one finance guy, to help FedEx. FedEx needed the GD investment. At one point, the Board wanted some revenue projections. I wasn't asked to get involved and didn't want to, but no one had any ideas of how to do the projections except just draw a free hand line on a graph based on hopes, dreams, intentions, guesses, etc. So, I thought: We know (1) the current revenue. We know (2) the revenue when the planned service to 90 US cities with 33 airplanes is full. So, the projections are roughly how interpolate between (1) and (2). For how the interpolation will go, we have (3) current customers and (4) the rest of the customers we will have when we have (2) and are full. Then say that the growth is from current customers (3) talking to the rest of the customers (4). That is, the rate of growth is directly proportional to the number of (happy) customers (3) talking to the rest of the customers we will have (4). So, let t denote time in days with t = 0 corresponding to the present. Let the revenue at time t be y(t). Let the revenue from (2), being full, be b dollars a day. Then at time t, the growth rate is y'(t), that is, d/dt y(t). So, we have that y'(t) = k y(t) ( b - y(t) ) How 'bout that! Maybe it's so simple it's almost just a joke, but the rest of the ideas floating around the office are much worse! So, sure, it's an initial value problem for a first order, linear ordinary differential equation but, really, is so simple can just use freshman calculus directly and find the closed form solution, right, some exponentials I omit here. So, on a Friday the Senior Vice President (SVP) for Planning and I got out some graph paper, picked a value for k, and drew the graph. The next day, Saturday, I was in my office, and at noon I got a phone call asking if I knew about the revenue projections. Well, the SVP was traveling, and, yes, I knew. So, I was asked if I could come over to the HQ offices and explain. So, I got in my Camaro hot rod and drove over. When I got there, people were unhappy. The two GD guys were standing in the hall with their bags packed. I was led to the graph, given a time, and asked to reproduce the value on the graph at that time. So, I had brought my HP scientific calculator, punched the buttons, and got the value on the graph. I did that a few more times, and people started to be happy again. It turned out that the Board meeting had been that Saturday morning; the graph had been presented; and the two GD guys had asked how it had been calculated. Well, all the FedEx people there tried to figure out how the graph had been calculated and went on for a few hours without success, and then GD guys lost patience, got plane reservations back to Texas, went to their rented rooms and packed their bags, and as a last chance returned to the HQ offices to see if FedEx had an explanation for the graph. FedEx was about to die. That's when I arrived and explained the graph. The FedEx guys stayed, and FedEx was saved. I never got thanked! Really my impression was that the rest of the top of FedEx had concluded that I'd been dangerous, maybe had 'hooked' the company. And I'd never been invited to the Board meeting. So, I began to conclude that my contribution was so resented that the top of FedEx would rather see all of FedEx go under than let me help. The promised FedEx stock was already 18 months late. I was in Memphis while my wife was in her Ph.D. program at Johns Hopkins near our home in Maryland. So, to heck with FedEx -- I went home and to Hopkins for my Ph.D. So, that's an example of applied math in US business! E.g., I was the only one around who still knew freshman calculus! And, heck, I'd never even taken freshman calculus, had studied it on my own and started with sophomore calculus! A broad lesson is, for anything very technical, have a tough time just making a contribution in the middle of a lot of operational and management people who forgot freshman calculus -- such people will feel out of control and resentful. So, instead, for technical contributions, need an appropriate organizational structure, maybe be in a research division and out of the main line operations or management, maybe be a respected external vendor, maybe be in a profession complete with legal liability and licensing, etc. And charge a LOT. Of course, broadly, the flip side of such technical incompetence, at the level of just freshman calculus, should be an opportunity! There were several other cases where I did some good technical work on an important problem but resentment by others and competitive office politics kept me from getting credit or actually blocked my contribution. In the field of organizational behavior, such politics is called goal subordination, that is, someone finds it in their interest in the company to hurt the company, subordinate the good of the company to their own good. Broadly, being a really good technical contributor among a lot of less technical people is a great way to create enemies who will sabotage your career, not friends who will help it. So, net, usually have to make a technical contribution from outside the pecking order of the organization. That is, be a vendor. Still better, just sell a product or service the customers will like but where the customers need not be aware of anything technical in the work.

hgibbs 12y ago
What kind of companies would be good to get practical experience in this area? In my experience the bridge between theoretically and actually apply mathematics is very hard to cross. Having started working mathematically recently it seems to me that even though I can propose a solution which isn't the best, they are usually better than what is currently available. Is that a common experience as a working mathematician. That story about FedEx is hilarious!
- graycat 12y ago
  Part I > Having started working mathematically recently it seems to me that even though I can propose a solution which isn't the best, they are usually better than what is currently available. Is that a common experience as a working mathematician. Sure. For the politics, just report the savings. The stuff about the optimal solution, that is, its, say, moral or ethical value, is lost on business people. With some good common sense, the business people just want to know how much has been saved (or extra earned). If you can also have, say, a lower bound on the possible savings and get close to that, then you have in practice a stopping criterion. Or, what in practice is really difficult about the NP-hard problems is usually saving the very last possible tiny fraction of one penny and proving that did that. Instead, just concentrate on saving, say, the first $5 million a month on, say, the $100 million a month of jet fuel for an airline. For a while in optimization, having the optimal solution was made a moral objective with anything that wasted even 0.0001 pennies regarded as a sin. Religious nonsense. Really sloppy work is not good, but close approximation usually is plenty good. For not the best, that's the other time I kept FedEx from going out of business: The founder, Fred W. Smith, spent the afternoon in his office trying to schedule the fleet, staggered out exhausted, said "We need a computer", and a college friend of mine heard that plea and called me. Sure, digging in, I heard a lot about optimal solutions. But I knew that first just get something that helps, say, so can type in a schedule, have the software check it out for, say, planes being over loaded or having to fly too far, get the arrival times, etc., and print out all the details. So, I typed in 6000 lines of code to do that. Right, great circle distances are from just the law of cosines for spherical triangles! Soon the Board wanted a schedule; biggie Board members doubted that the scheduling could even be done; biggie funding was being held up; the company was at risk. So, I got a call from the same guy who called me to the Board meeting for the revenue projections, Roger Frock (he wrote a book about FedEx), and he and one short, easy evening he and I used my software to develop a schedule for the whole planned system of 90 cities and 33 airplanes. It printed out and looked nice. At the next senior staff meeting, Fred's reaction to the printout was "Amazing document -- solved the most important problem facing Federal Express". Our same two guys from General Dynamics went over the schedule carefully and announced "It's a little tight in a few places but it's flyable". The Board was pleased; the funding was enabled. That was the first time I saved FedEx. So, I got into how to do better scheduling. So, for one period from, say, 5 PM to midnight (again from 1 AM to, say, 8 AM) set up a table with one row for each city to be served, 90 cities, and one column for each candidate airplane tour from Memphis and back. So, may have some thousands of columns. Considering all fine details want to account for, and take expectations for random costs, find for each of the candidate tours the cost (first cut, assume that if a plane goes to a city, then it completely serves that city). Then for the schedule, want to pick no more than 33 columns from the 1000s so that all 90 cities are served and total cost is minimized. So, each column covers some cities, and want to pick columns that cover all 90 cities -- so have a set covering problem. Right, it's in NP-complete. Well, that table is essentially the matrix in a 0-1 integer linear programming least cost optimization problem. There have one unknown variable for each of the columns, and the variable is 1 if use that column and 0 otherwise. If relax the 0-1 constraint, then have a fairly routine linear programming problem but will likely end up with some fractional airplanes allocated. Could use branch and bound to get to a good or optimal 0-1 solution. Should have saved FedEx a huge bundle. Now, with software such as the IBM Optimization Subroutine Library (OSL), C-PLEX (now owned by IBM but from Robert Bixby at Rice in Dallas), etc., that would be a fun and likely fairly easy problem. Alas, for proposing that work as my project, I got too much guff and flack back from too much of the top of FedEx, wasn't getting much thanks for the two times I'd saved the company, was not seeing the promised stock, was away from my home and wife, was in a company close to going belly up, saw a lot of dumb work, so went for my Ph.D.

by graycat 12y ago

hgibbs 12y ago

What kind of companies would be good to get practical experience in this area? In my experience the bridge between theoretically and actually apply mathematics is very hard to cross. Having started working mathematically recently it seems to me that even though I can propose a solution which isn't the best, they are usually better than what is currently available. Is that a common experience as a working mathematician. That story about FedEx is hilarious!

graycat 12y ago
Part I > Having started working mathematically recently it seems to me that even though I can propose a solution which isn't the best, they are usually better than what is currently available. Is that a common experience as a working mathematician. Sure. For the politics, just report the savings. The stuff about the optimal solution, that is, its, say, moral or ethical value, is lost on business people. With some good common sense, the business people just want to know how much has been saved (or extra earned). If you can also have, say, a lower bound on the possible savings and get close to that, then you have in practice a stopping criterion. Or, what in practice is really difficult about the NP-hard problems is usually saving the very last possible tiny fraction of one penny and proving that did that. Instead, just concentrate on saving, say, the first $5 million a month on, say, the $100 million a month of jet fuel for an airline. For a while in optimization, having the optimal solution was made a moral objective with anything that wasted even 0.0001 pennies regarded as a sin. Religious nonsense. Really sloppy work is not good, but close approximation usually is plenty good. For not the best, that's the other time I kept FedEx from going out of business: The founder, Fred W. Smith, spent the afternoon in his office trying to schedule the fleet, staggered out exhausted, said "We need a computer", and a college friend of mine heard that plea and called me. Sure, digging in, I heard a lot about optimal solutions. But I knew that first just get something that helps, say, so can type in a schedule, have the software check it out for, say, planes being over loaded or having to fly too far, get the arrival times, etc., and print out all the details. So, I typed in 6000 lines of code to do that. Right, great circle distances are from just the law of cosines for spherical triangles! Soon the Board wanted a schedule; biggie Board members doubted that the scheduling could even be done; biggie funding was being held up; the company was at risk. So, I got a call from the same guy who called me to the Board meeting for the revenue projections, Roger Frock (he wrote a book about FedEx), and he and one short, easy evening he and I used my software to develop a schedule for the whole planned system of 90 cities and 33 airplanes. It printed out and looked nice. At the next senior staff meeting, Fred's reaction to the printout was "Amazing document -- solved the most important problem facing Federal Express". Our same two guys from General Dynamics went over the schedule carefully and announced "It's a little tight in a few places but it's flyable". The Board was pleased; the funding was enabled. That was the first time I saved FedEx. So, I got into how to do better scheduling. So, for one period from, say, 5 PM to midnight (again from 1 AM to, say, 8 AM) set up a table with one row for each city to be served, 90 cities, and one column for each candidate airplane tour from Memphis and back. So, may have some thousands of columns. Considering all fine details want to account for, and take expectations for random costs, find for each of the candidate tours the cost (first cut, assume that if a plane goes to a city, then it completely serves that city). Then for the schedule, want to pick no more than 33 columns from the 1000s so that all 90 cities are served and total cost is minimized. So, each column covers some cities, and want to pick columns that cover all 90 cities -- so have a set covering problem. Right, it's in NP-complete. Well, that table is essentially the matrix in a 0-1 integer linear programming least cost optimization problem. There have one unknown variable for each of the columns, and the variable is 1 if use that column and 0 otherwise. If relax the 0-1 constraint, then have a fairly routine linear programming problem but will likely end up with some fractional airplanes allocated. Could use branch and bound to get to a good or optimal 0-1 solution. Should have saved FedEx a huge bundle. Now, with software such as the IBM Optimization Subroutine Library (OSL), C-PLEX (now owned by IBM but from Robert Bixby at Rice in Dallas), etc., that would be a fun and likely fairly easy problem. Alas, for proposing that work as my project, I got too much guff and flack back from too much of the top of FedEx, wasn't getting much thanks for the two times I'd saved the company, was not seeing the promised stock, was away from my home and wife, was in a company close to going belly up, saw a lot of dumb work, so went for my Ph.D.