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FIGURE 7.15 If the respective values of goal A and goal B are equal,
there are no time restraints and no other considerations, then it is more
efficient to complete goal A first and then proceed to goal B.
Regardless, if there is no detriment to putting off goal B (or goal A for that mat-
ter) until we can get around to it, there is really nothing to consider. In fact, what
is to stop us from taking the scenic route and going all the way over to goal B first
and then backtracking to goal A? Of course, if there is no time limit, then the value
of the time spent getting there is not really relevant. So let's make it relevant…
C HANGES IN U TILITY OVER T IME
To make this problem far more interesting, let's assume that the values of accom-
plishing goals A and B will diminish over time. For simplicity's sake, let's assume
that the rate of decay ( r ) for the goal values is the same for both A and B. This
change causes an inherent utility in the time spent (or saved) in traveling to goals
A and B. We can no longer take a leisurely approach. Again, this puts us back in the
mindset of taking the shortest route through the two goals. There is one caveat,
however… what if goal B was so important that it couldn't wait? Is there a point
where accomplishing goal B quickly is urgent enough that we would postpone
accomplishing goal A until later despite the fact that we are relatively close to it?
Let's construct our formula and test a couple of cases.
The components that we need to consider are:
V a
The value of goal A
V b
The value of goal B
V ab
The total value of goals A and B
T a
The time to move to goal A
T b
The time to move to goal B
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