What happens when a modeling mindset takes over our everyday activities? Lifestyle management science.
By Brad C. Meyer
Those of us in the management science profession spend a lot of our time in the modeling mindset. All day long we consider inventory mathematics, queuing formulas, linear programs, heuristic search and decision trees. We talk about optimal solutions, shadow prices, expected values and utility as the source of our livelihood. It's not a surprise, therefore, when we find our non-professional life attacked by an uncontrollable urge to analyze. This urge to analyze and to model is what makes the difference between a true management scientist and someone else who is merely performing MS activities. This is the urge that I hope to awaken in some of my students (alas, it will not turn up in all of them) through my teaching of management science.
I realize that not everyone has an analytical personality; it becomes apparent when I teach MS at the MBA level. In every class there are a few who never grasp how management science applies to their lives and to their work. They don't understand that the question is not,"Does management science apply to this situation?" but rather, "Will I apply management science to this situation?"
As for me, I find it hard not to look at the world through the eyes of a modeler. I am always encountering situations that can be described with mathematics or logic and optimized, even in life's daily decisions. It convinces me how practical the field of management science is, not just for business, but for all of life. To illustrate, let me describe the events of a recent morning.
It was 7 a.m., time for the daily assembly operation known as getting dressed. I walked over to the closet where the clothing inventory was stored. The assembly technology in place is highly flexible and can be used to assemble any set of pants, shirt, sweater and tie. The equipment is, however, programmed to accept only those combinations that meet certain aesthetic standards. This morning, there were 10 pairs of pants in the closet, 16 shirts, nine sweaters and 47 ties. An exhaustive enumeration technique would yield 67,680 possible combinations. Unfortunately, the computer used for this task (my brain) was developed in 1956. With such outdated equipment, I have been forced to implement a heuristic search algorithm to determine a feasible outfit.
That morning, the heuristic search was performing more backtracking than usual. Two pairs of pants were removed due to an obsolescence rule, three others failed to meet a waist restriction parameter, one pair's branch was terminated due to the time-of-year criterion. The algorithm was on the third of the remaining four pairs, searching for feasible shirt/sweater combinations, when I realized that something was wrong. Several versatile shirts were missing from inventory. Visions of Goldratt haunted me as I realized that the items I needed were not in inventory, while the items I didn't need were plentiful. Clearly I was not managing my constraints properly. I decided to check out the feeder operation.
I made my way to the laundry work center only to be met by piles and piles of WIP. Of course, I began to analyze the situation to uncover root causes. The work center included four stations: washing, drying, folding and ironing. Some of the equipment was fully automated, requiring only a load and unload operation. The folding and ironing stations, however, were labor intensive. Nonetheless, the work center was staffed with only one operator, who did not seem to be present at the time.
As I stared at the basket-type containers of dirty and clean clothes, my analytical mind was delighted to realize that what we had was a modern "pull" type system! When someone needed clothes they sent a signal (KANBAN) to the laundry work center to initiate processing. This signal was sent vocally, at around 130 decibels, in the standardized format: "Where's my x?" where x is a variable filled in with the clothing item in question.
I was pleased that we were using an up-to-date production philosophy, but somehow the system did not appear very lean. Did we have the optimal number of containers? It was time for a back of the envelope calculation. I used a simple model that I teach in my operations management class. It is taken from Stevenson (1).
N = number of containers
My wife and I have seven children. (We understood from Frank Gilbreth that they are cheaper by the dozen, but when we got to seven we decided that was cheap enough.) I estimated that each person soiled an average of six items of clothing per day. For simplicity, I assumed that a pair of socks was 1 item (we management science types always have to assume something for simplicity). The volume of kitchen and bathroom towels was estimated to be equivalent to two more persons. Thus daily demand on the washing facility was 11 persons * six items per person, or 66 items. The capacity of the container was approximately 25 items. The average time for replenishment was the addition of the processing time and the waiting time. Processing time was estimated to be two hours, waiting time seemed highly variable, which was not a good sign, but seemed to be around 10 hours. The policy variable, X, I set to .50. I considered the day to have 16 working hours. This made the optimal number of containers equal to:
I counted four full containers before the folding station and six containers (including four piles) in front of the washing station. No wonder the system was not lean; we had too many containers!
Now I was worried. "What other problems will I find?" I said to myself. "No, I must change my perspective, what would Deming think if he heard me talking like this. What I meant was, 'What other opportunities for improvement will I find?'" I looked over at the containers of incoming, soiled laundry. At the top of the basket was a pair of pants I had worn yesterday. At the bottom of the basket, the color of a cloth caught my eye. Reaching into the basket, I pulled from the bottom two of my missing shirts. These shirts I had sent to the laundry over a week ago. So that was it! LIFO inventory management! No wonder my shirts weren't clean. Satisfied that I had uncovered the most pressing root causes I went back upstairs to finish getting dressed.
By now, I was falling behind in my morning production schedule, so I loosened my aesthetics constraint enough to find something to wear. Next it was time for some routine maintenance and then breakfast. Checking the breakfast raw material storage revealed that the purchaser was using the old-fashioned lowest cost supplier strategy. I was struggling, trying to find something appetizing enough to bring customer delight, when I had a spark of inspiration: maybe I should do a make-buy analysis. It just may be more economical to buy my breakfast than to make it! I estimated some of the following values for the make option:
I was not sure how long it would take me to make breakfast, I first assumed 15 minutes, then 10 then 20. Fortunately, my training as a management scientist came in handy. This was a perfect context for the use of sensitivity analysis. I let the time to make the meal be the variable, T, and set up the equation:
I dashed over to my computer and brought up my spreadsheet. Before long I had the graph shown in Figure 1.
Figure 1 - The break-even analysis of making breakfast vs. buying breakfast shows that it is better to buy breakfast if it saves 4 minutes or more of time.
The McDonald's extra value breakfast meal costs $3.25. Thus, the break-even point of time to make breakfast is four minutes. More correctly, the additional time to make breakfast as opposed to the time to purchase breakfast must be four minutes or less to justify making breakfast at home. Clearly, the most economical decision was to buy breakfast. Having thus justified myself, in every sense of the word, I put on my coat and headed out to the car.
As I drove across town, I had the nagging feeling that somehow the $5 I had spent analyzing breakfast options (12 minutes at $25 per hour) was more than the amount I was saving by going to McDonald's. But I was comforted to realize that this analysis allows me to make decisions in the future. If I am wasting money by eating at home, think of all the money I will save by eating out each day for breakfast. The payback period for those 12 minutes of research is clearly less than one week! But then again, payback period has been shown to be an inferior criterion for evaluating investments, perhaps I should calculate a rate of return on my investment. By now, I could see the McDonald's just ahead so I decided that the 12 minutes was a sunk cost and dropped the issue.
As I drove into the parking lot, I was faced with a simple, single-phase decision. Do I stop my car and go inside to the M/M/4 system or do I stay in my car and try the M/M/1 system? Then again, maybe it's M/G/4 vs. M/G/1. Oh, if only I had perfect information! Even some sample information would be nice right now. "Too much of life is a case under uncertainty," I muttered to myself. There was no time to debate, the car behind me was honking, so I pulled into a parking space and got out of the car.
Inside, I looked for the shortest queue. I was surprised to find the restaurant so busy. I thought I was quite ingenious to have performed the make-buy analysis this morning, but apparently, many others had discovered the optimal solution long before. Fortunately, the lines were moving quickly, though not quickly enough for everyone. When I made it to the front of the line the employee asked me for my order. "A number 2, hold the cheese," I said, and then without thinking continued, "You really ought to tell your manager to increase the number of channels in the system. I have just observed several transactions renege." She looked at me like I was from another planet and said, "That will be $3.39." I paid her kindly and before I had time to compute the cost per ounce of the three sizes of orange juice, she handed me my meal.
I found an empty table and took a seat. While I downed my English muffin and eggs I began to ponder whether it was more appropriate to constrain my meal cost and try to optimize my satisfaction or to constrain my satisfaction and minimize cost. Of course, I must not forget nutritional value. Perhaps I would have to form a goal-programming model to determine my menu choice for tomorrow morning. Looking at my watch, I realized it was time to get to work, so I finished my juice and walked out to the car.
My car is a 1977 Chevrolet Suburban. It is a part of my ongoing research in the field of equipment replacement. A common estimate made in equipment replacement is the gradient of increasing costs over the life of the equipment item. When gathering empirical data to verify the estimated gradients, researchers are often hampered by a phenomenon similar to the Heisenberg uncertainty principle. You can't both replace an item at the right time and know that you replaced the item at the right time. Once you replace it, you are unable to know what the costs would have been had you retained it. On the other hand, if you retain the item and continue to gather the cost data you will soon realize that you should have replaced it earlier. Since I have more of a commitment to furthering knowledge than furthering my own economic well being, I have chosen to retain the vehicle and collect data.
As I drove toward my office, I noticed that the quantity on hand of fuel had dropped below the reorder point. In an analysis several years ago I had discovered the optimal quantity and time to fill the car with gas. I used a modification of the EOQ model with no stockouts allowed. It only took three pages of formulas to prove that when I purchase gas for the car, I should fill the tank to the top. The reorder point depends on whether I am doing city driving or highway driving. The lead-time in the city is short enough that I begin to look for a gas station when the quantity on hand drops below one-eighth of a tank. On the highway, the reorder point is one-fourth of a tank. I am proud to say that using this model I have not had a stockout occur in the past 10 years.
After I filled the car with gas, I took out my data register and recorded the amount and the odometer reading. As usual, I calculated the miles per gallon since the last fill. I was disturbed to find that again the mileage was very poor, less than 8 MPG. The mileage had dropped after a mechanic recently replaced the valve cover gaskets. I had hoped it was a fluke, but now continued readings were confirming the fact. However, before I accused the mechanic, I decided that I had better consider more of the historical data. It was February, and cold months do lead to poorer MPG. Luckily for me, I had most of my gas data on a spreadsheet. When I arrived at my office that morning I had a little bit of time before my first responsibility so I added the recent readings to update the spreadsheet. Then I plotted the graph. (See Figure 2.) Clearly the data evidence a seasonal pattern. Every January/February the mileage hits a low value. But this year the low was lower than usual. I decided I would have to talk to the mechanic.
Figure 2 - The MPG of my 1977 Chevrolet Suburban during my time of ownership evidences a seasonal pattern with reduced MPG in winter months.
I looked at the clock to find that it was now a few minutes after 9 a.m. which meant that I was bumping into a constraint on the number of hours I must work in a day. Realizing that continuing to analyze my car costs at this time was infeasible, I closed the spreadsheet, and left my personal life. It was time to be a management scientist again.
Brad C. Meyer is an associate professor and chairman of the Department of Management at Drake University in Des Moines, Iowa.
OR/MS Today copyright © 2000 by the Institute for Operations Research and the Management Sciences. All rights reserved.
Lionheart Publishing, Inc.
506 Roswell Street, Suite 220, Marietta, GA 30060, USA
Phone: 770-431-0867 | Fax: 770-432-6969
Web Site © Copyright 2000 by Lionheart Publishing, Inc. All rights reserved.