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11
Dynamic Programming
Dynamic programming is a useful mathematical technique for making a sequence of in
terrelated decisions. It provides a systematic procedure for determining the optimal com
bination of decisions.
In contrast to linear programming, there does not exist a standard mathematical for
mulation of "the" dynamic programming problem. Rather, dynamic programming is a gen
eral type of approach to problem solving, and the particular equations used must be de
veloped to fit each situation. Therefore, a certain degree of ingenuity and insight into the
general structure of dynamic programming problems is required to recognize when and
how a problem can be solved by dynamic programming procedures. These abilities can
best be developed by an exposure to a wide variety of dynamic programming applications
and a study of the characteristics that are common to all these situations. A large number
of illustrative examples are presented for this purpose.
11.1 A PROTOTYPE EXAMPLE FOR DYNAMIC PROGRAMMING
EXAMPLE 1 The Stagecoach Problem
The STAGECOACH PROBLEM is a problem specially constructed1
to illustrate the fea
tures and to introduce the terminology of dynamic programming. It concerns a mythical
