able time while simultaneously making sure that outside constraints were
also satisfied—such as making sure the space capsule was rotated so it did
not overheat. Thus was born the branch of mathematics known as sched-
uling, and with it the discovery of how improving the individual compo-
nents that go into an ensemble can result in counterproductive—and
counterintuitive—outcomes.So Why Is Your Car Never Ready When They Promised?
Whether your neighborhood garage is in Dallas, Denver, or Des Moines,
it encounters basically the same problem. On any given day, there are a
bunch of cars that need work done, and equipment and mechanics avail-
able to do the job. If only one car comes into the shop, there’s no problem
with scheduling, but if several cars need repairs, it’s important to do
things efficiently. There may be only one diagnostic analyzer and only
two hydraulic lifts—ideally, one would want to schedule the repair se-
quence so that everything is simultaneously in operation, as idle time
costs money. The same thing can be said about the available mechanics;
they’re paid by the hour, so if they are sitting on the sidelines while cars
are waiting to be serviced, that costs money, too.
One critical aspect of scheduling is a method of displaying the tasks to
be done, how they relate to one another, and how long they will take. For
instance, to determine if a tire has a leak, the tire must be removed before
checking it in the water bath. The standard way of displaying the tasks,
their times, and their relationships to each other is by means of a digraph.
A digraph is a diagram with squares and arrows indicating the tasks to be
done, the order in which they are to be done, and the time required—one
such is indicated below.
T1-4 T2-6 T3-5 T6-7T4 -10 T5 -2Task 1 requires 4 time units (hours, days, months—whatever), and tasks
1 and 2 must be completed before task 4, which requires 10 time units, is
undertaken. Similarly, task 3 must be completed before task 5 is begun.
Prologue 3