As weight issues plagued my mind, I had a discussion with students about what would occur if a system had no bottlenecks. The answer is, obviously, an infinite level of benefits (an unbounded system). I immediately recognized that the body has limited benefits and so there are bottlenecks. Consequently, I could attempt to optimize losing weight. After six months of experiments and analysis, I discovered an optimized dieting strategy that enabled me to lose 25 pounds and to keep the weight off.

When I began optimizing weight loss, I never imagined I would write a diet book. This attitude changed the day I derived a mathematical proof that showed that a proper implementation of my operations research dieting strategy theoretically results in weight loss. Thus, this dieting strategy was not specific to me and could be applied to anyone. So I wrote "The When Diet: Mathematically Optimizing Eating and Exercise for Weight Loss" [1] to convey my analysis and, hopefully, help others lose weight. This article describes some of the major topics covered in this book.

It is important to point out that this is not a health article, but rather an analysis of weight loss. The American Dietetic Association [2] and the American Heart Association [3] have the answer for the healthiest method to maintain and lose weight. It is to eat according to the food pyramid, consume the suggested number of calories and perform 30 minutes of a moderately intense exercise five days a week. Since about two-thirds of the U.S. is overweight [4], most people do not follow this suggested lifestyle.

Prior to solving a problem, one must understand why the problem exists. Individuals are primarily overweight because they enjoy eating too much food, eating high calorie foods and avoiding additional exercise. Diets attempt to help people lose weight by modifying some or all of these habits. For my purposes, a diet is defined as a modification to a person's chosen lifestyle that is intended to result in weight loss.

Modifying a person's chosen lifestyle results in some dissatisfaction, misery and possibly pain. From a decision theory point of view, a rational decision-maker remains on a diet as long as the diet's misery is less than the benefit received from the weight loss. Consequently, a diet should seek to minimize the misery of losing weight, while maximizing the weight loss.

One of the primary causes of being overweight is the amount and type of food people eat. Identifying the probabilistic properties of hunger enables an argument that optimizes eating for weight loss.

First, I conjecture that today's hunger is independent from the food consumed yesterday. That is, the amount eaten yesterday has little to no impact on today's hunger. If not, then people would not be overweight. For instance, most individuals eat far too much food on Thanksgiving and if there is perfect correlation between the foods consumed on the previous day, then the Friday following Thanksgiving would be spent with most people eating almost nothing. Consequently, overeating one day would be immediately offset by under eating the next, and periods of rapid weight gain or loss would rarely occur. Thus, hunger between days can be assumed to be independent.

Second, hunger on a single day is conjectured to be nonmemoryless. In other words, knowing just the most recently eaten item is not sufficient to determine one's hunger. Rather the hunger is determined by what has been eaten all day prior to a moment in time. For instance, at 4 p.m. a person having eaten a large lunch and a candy bar at 3 p.m. would be less hungry than if the person ate a low calorie lunch and a candy bar at 3 p.m.

Optimizing these two properties results in a concept called "When to Eat." When to Eat states that if a person wants to reduce the number of calories consumed per day by a certain amount, say 200 calories, then the individual should eliminate the last 200 calories that would have been consumed on that day.

A common argument from scheduling theory describes why skipping calories earlier in the day cannot be optimal. Consider a person trying to lose weight by eating fewer calories (skipping a morning snack) at 10 am. The individual has elevated hunger at lunch and the natural response is to consume a larger lunch. If the person gives in to this urge and eats a large lunch, then the person does not lose weight as there is not a decrease in calories for the day, and so the dieter incurred hunger with no weight loss benefit, which is a terrible outcome.

Alternately, the dieter could consume a normal amount for lunch. Due to the nonmemoryless property of hunger on a single day, the person would still be a little hungry immediately after lunch. The individual must remain vigilant throughout the remainder of the day and only eat the normal amount for each snack and meal. Consequently, the person has elevated hunger levels from 10 a.m. until the person goes to sleep.

In contrast, if the person skipped the snack after dinner (the final calories that would have been consumed), then the person would have elevated hunger from about 8 p.m. until the dieter goes to sleep. Clearly, this results in less dissatisfaction than attempting to control this hunger throughout the entire day, and so skipping daytime snacks or meals to lose weight cannot be optimal.

With eating optimized for weight loss, it is natural to analyze exercise for weight loss. Exercise burns additional calories [5], but also increases a person's appetite. (Exercise may diminish one's hunger immediately after exercise, but within a few hours the body desires to replenish the spent calories and hunger escalates.) Consequently, exercise harms weight loss if the exercise causes an individual to consume more calories than the person expended during exercise.

Following the previous arguments regarding eating, it can be seen that a method to guarantee that exercise positively impacts weight loss is to exercise after the final food is consumed for the day. This concept is called When to Exercise, which states that some exercise should be performed after the final meal. The exercise need not be excessive, and my standard exercise is about 25 pushups or as many arm curls as possible in each arm using a 25-pound weight. Either of these options can be done in less than five minutes.

Combining When to Eat and When to Exercise results in The When Diet. The basic steps are to consume every meal and snack during the day, eat a reduced calorie dinner about five hours prior to going to sleep, consume no food after dinner and perform some exercise after the final meal.

One of the best properties of The When Diet is that no misery or dissatisfaction is wasted. An individual can eat whatever he or she wants from morning until the evening and so the dieter incurs no dissatisfaction during the day. The dissatisfaction begins with a low calorie meal for dinner and increases by not eating after dinner. Some exercise after dinner further escalates the dissatisfaction. The highest level of dissatisfaction (hunger) occurs while the dieter is asleep and is oblivious to its impact. Thus, The When Diet should cause a manageable level of dissatisfaction.

The nighttime exercise, particularly strength training, increases one's metabolism [6] and so more calories are burned while the person sleeps. Consequently, The When Diet should have a high weight loss per unit of dissatisfaction and can be considered an optimized diet. (I am not claiming that The When Diet is the optimal diet. It is just optimized in the same sense a heuristic optimizes a problem as there is no proof of optimality.)

The When Diet can theoretically show weight loss and be considered an optimized dieting strategy, but that does not imply that this diet will be effective. Since each individual has different preferences and annoyances, there still remains one critical question that each individual who attempts The When Diet must answer. Is the dissatisfaction caused by being on The When Diet less than the weight loss benefit received by being on this diet? If the answer is yes and the dieter is rational, then following The When Diet would allow the dieter to achieve his or her weight loss goals.



Todd Easton (teaston@ksu.edu) is an associate professor in the Industrial and Manufacturing Systems Engineering Department at Kansas State University.

References

1. Easton, T., 2009, "The When Diet: Mathematically Optimizing Eating and Exercise for Weight Loss," Ithaca Press, Dryden, N.Y., ISBN 978-0-9815116-5-8.
2. The American Dietetic Association, MyPyramid Web page: www.eatright.org/cps/rde/xchg/ada/hs.xsl/nutrition_fgp_ENU_HTML.htm.
3. The American Heart Association, exercise and fitness Web page: www.americanheart.org/presenter.jhtml?identifier=1200013.
4. The Center For Disease Control, National Health and Nutrition Examination Survey, www.cdc.gov/nchs/data/nhanes/databriefs/adultweight.pdf.
5. The Center For Disease Control, Healthy Weight — "It's not a diet, it's a lifestyle!" www.cdc.gov/healthyweight/physical_activity/.
6. Fenicchia, L., Kanaley, J., Azevedo, J., Miller, C., Weinstock, R., Carhart, R., Ploutz-Snyder, L., 2004, "Influence of resistance exercise training on glucose control in women with type 2 diabetes." Metabolism, March 2004, Vol. 53, No. 3, pp. 284-289.

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