Information Technology Reference
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batter ingredients on the final baked product has been studied at length [
25
]; the
effects can be traced back to the nutrients that the ingredients contain. A formula
for ice cream [
26
] constrains the proportions of five groups of nutrients (fat, milk
solids that are not fat, sugar, other solids, and water) within certain ranges, regardless
of the actual ingredient types. It is shown that irrespective of whether the fructose
comes from corn syrup, strawberry, or carrot—as long as one follows the formula
and the general instructions to make such a frozen dessert, one will obtain a properly
balanced ice cream. Following the nutrient ratios of existing recipes is clearly a key
factor in determining ingredient proportions for a new recipe.
It is important to note that dishes that do not fall in the above category should be
prepared using a different template. For instance, adding one more carrot or one more
cup of stock to a stew will not compromise the structure of the dish; measurements
of this sort are often approximated by chefs. In these cases, the relative proportions
of the various ingredient types such as the meat-to-vegetable or the sauce-to-meat
ratios are more crucial.
Our system uses the notion of balancing ingredients to determine the proportions.
The essence of the idea is that ingredient proportions are determined so that the
proportions of each nutrient (protein, fat, carbohydrate, etc.) and each ingredient
type (meat, vegetable, herb, etc.) of the new recipe appropriately conform to the
distributions of those proportions in the existing recipes of the same dish. A major
advantage of our method is that it is data-driven, i.e. the required information is
acquired entirely from the data. It should be noted that additional expertise and
ontological information could easily be used in conjunction with our method.
We now describe the mathematical model behind our system's ingredient propor-
tions algorithm. We assume that the dish and the ingredient bill for the new recipe
have already been determined. Suppose that all existing recipes for the dish in the
database have been identified. We introduce the notation in Table
16.1
.
Since our method determines the ingredient proportions,
x
represents the vec-
tor of decision variables. These are determined as the output of an optimization
Table 16.1
Mathematical notation for the ingredient proportion model
Notation
Description
M
Number of ingredients in new recipe
P
Number of nutrients in new recipe
Q
Number of ingredient types in new recipe
c
mp
Percentage of
p
th nutrient in
m
th ingredient
t
mq
Indicator which is 1 only if
m
th ingredient is of
q
th ingredient type
nutrient
p
μ
Mean percentage of
p
th nutrient in existing recipes
nutrient
p
˃
Standard deviation of percentage of
p
th nutrient in existing recipes
ing type
q
μ
Mean percentage of
q
th ingredient type in existing recipes
ing type
q
˃
Standard deviation of percentage of
q
th ingredient type in existing
recipes
x
= {
x
m
:
m
=
,...,
M
}
1
Percentage of ingredients in the new recipe
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