9781118041581

Optimal Search 559

apparently simple association? The investigative panel pointed to one impor-

tant reason. NASA diligently compiled a checklist of over 4,500 “critical” risk

factors. However, all these factors were treated equally, with no effort to dis-

tinguish the “most critical” factors. NASA should have set priorities according

to the likelihood of each factor leading to system failure. Indeed, tests con-

ducted for the presidential panel after the shuttle disaster showed that O-ring

failure was much more sensitive to changes in temperature than had been pre-

viously imagined. If NASA had recognized the need to acquire this test infor-

mation in advance, it would have certainly abandoned the cold-weather launch.

OPTIMAL SEARCH

Many management decisions involve a number of opportunities that can be

pursued, each yielding an unknown payoff (i.e., profit). Uncertainty about the

payoff can be eliminated at a cost. Each option has its own cost and probabil-

ity distribution concerning possible payoffs, independent of the other options.

Options are explored (or searched) in sequence in whatever order is preferred.

When management stops exploring new options, it selects the most profitable

one from among its current options. Management’s task is to find the best

sequential search strategy, that is, the order in which to pursue options and

when to stop.

Optimal Stopping

The sequential R&D decision in Chapter 12 nicely illustrates optimal search.

There, the drug company could pursue (at a cost) either of two highly uncer-

tain scientific methods, in either order. After learning the results, it commer-

cialized only one process: the one that proved most profitable. A related R&D

problem offers another example of optimal search.

ESCALATING INVESTMENTS IN R&D An electronics firm can initiate an

important R&D program by making a $3 million investment. There is a 1/5

chance that the program will meet with immediate success (i.e., within the

year), earning the firm a return of $10 million for a net profit of $7 million. If

success does not come, the firm can invest another $3 million with the chance

of success now 1/4. If this second stage fails, the firm can invest again, and so

on, up to a total of five investments. The investment cost for each stage is $3 mil-

lion, the ultimate return from a successful completion of the program (sooner

or later) is $10 million, and the chances of success are 1/5, 1/4, 1/3, 1/2, and

1 for the investments. Should a risk-neutral firm pursue this program, and if so,

at what stage (if any) should it stop?

This kind of decision is called an optimal-stoppingproblem. When (if

ever) should the firm stop reinvesting? In a moment, we will use a decision

tree to solve the problem. First, use your unaided judgment to select the best

c13TheValueofInformation.qxd 9/26/11 11:02 AM Page 559