550 Dynamic Programming
Figure 9.6 Water tank system.Example 9.1 Explain the concept of suboptimization in the context of the design of
the water tank shown in Fig. 9.6a. The tank is required to have a capacity of 100,000
liters of water and is to be designed for minimum cost [9.10].SOLUTION Instead of trying to optimize the complete system as a single unit, it
would be desirable tobreakthe system into components which could be optimized
more or less individually. For this breaking and component suboptimization, a logical
procedure is to be used; otherwise, the procedure might result in a poor solution. This
concept can be seen by breaking the system into three components: componenti(tank),
componentj(columns), and componentk(foundation). Consider the suboptimization
of componentj(columns) without a consideration of the other components. If the cost
of steel is very high, the minimum cost design of componentj may correspond to
heavy concrete columns without reinforcement. Although this design may be accept-
able for columns, the entire weight of the columns has to be carried by the foundation.
This may result in a foundation that is prohibitively expensive. This shows that the
suboptimization of componentjhas adversely influenced the design of the following
componentk. This example shows that the design of any interior component affects the
designs of all the subsequent (downstream) components. As such, it cannot be subop-
timized without considering its effect on the downstream components. The following
mode of suboptimization can be adopted as a rational optimization strategy. Since the
last component in a serial system influences no other component, it can be suboptimized
independently. Then the last two components can be considered together as a single
(larger) component and can be suboptimized without adversely influencing any of the
downstream components. This process can be continued to group any number of end
components as a single (larger) end component and suboptimize them. This process of