578 Dynamic Programming
Figure 9.18 Multibay cantilever truss.For specificness, consider a three-bay truss for which the following relationships
are valid (see Fig. 9.18):yi+ 1 =yi+di, i= 1 , 2 , 3 (9.41)Since the value ofy 1 is fixed, the problem can be treated as an initial value problem.
If theycoordinate of each node is limited to a finite number of alternatives that can
take one of the four values 0.25, 0.5, 0.75, 1 (arbitrary units are used), there will be
64 possible designs, as shown in Fig. 9.19. If the cost of each bay is denoted byRi,
the resulting multistage decision problem can be represented as shown in Fig. 9.5a.Figure 9.19 Possible designs of the cantilever truss.