9.2 Multistage Decision Processes 545
technique suffers from a major drawback, known as thecurse of dimensionality. How-
ever, despite this disadvantage, it is very suitable for the solution of a wide range of
complex problems in several areas of decision making.
9.2 Multistage Decision Processes
9.2.1 Definition and Examples
As applied to dynamic programming, a multistage decision process is one in which
a number of single-stage processes are connected in series so that the output of one
stage is the input of the succeeding stage. Strictly speaking, this type of process should
be called aserial multistage decision processsince the individual stages are connected
head to tail with no recycle. Serial multistage decision problems arise in many types
of practical problems. A few examples are given below and many others can be found
in the literature.
Consider a chemical process consisting of a heater, a reactor, and a distillation tower
connected in series. The objective is to find the optimal value of temperature in the
heater, the reaction rate in the reactor, and the number of trays in the distillation tower
such that the cost of the process is minimum while satisfying all the restrictions placed
on the process. Figure 9.1 shows a missile resting on a launch pad that is expected to
hit a moving aircraft (target) in a given time interval. The target will naturally take
evasive action and attempts to avoid being hit. The problem is to generate a set of
commands to the missile so that it can hit the target in the specified time interval.
This can be done by observing the target and, from its actions, generate periodically a
new direction and speed for the missile. Next, consider the minimum cost design of a
water tank. The system consists of a tank, a set of columns, and a foundation. Here the
tank supports the water, the columns support the weights of water and tank, and the
foundation supports the weights of water, tank, and columns. The components can be
Figure 9.1 Ground-radar-controlled missile chasing a moving target.
