Engineering Optimization: Theory and Practice, Fourth Edition

9.6 Example Illustrating the Tabular Method of Solution 563 Figure 9.14 Various stages of suboptimization of Example 9.3: (a) su ...

564 Dynamic Programming Specific value x 1 ∗(type of foundation f 1 ∗ Corresponding value ofs 2 (kgf) for minimum cost) ($) ofs ...

9.6 Example Illustrating the Tabular Method of Solution 565 quantities (i.e.,f 2 ∗andx 2 ∗)correspondingto the various discrete ...

566 Dynamic Programming Now, we retrace the steps to collect the optimum values ofx∗ 3 ,x∗ 2 , andx∗ 1 and obtain x 3 ∗= ype (c) ...

9.7 Conversion of a Final Value Problem into an Initial Value Problem 567 Figure 9.15 Conversion of a final value problem to an ...

568 Dynamic Programming wherex 1 andx 2 indicate the number of drilling machines manufactured in thefirst month and the second m ...

9.8 Linear Programming as a Case of Dynamic Programming 569 9.8 Linear Programming as a Case of Dynamic Programming A linear pro ...

570 Dynamic Programming such that ∑n j= 1 aijxj≤bi, i= 1 , 2 ,... , m (9.29) xj≥ 0 , j= 1 , 2 ,... , n (9.30) The recurrence rel ...

9.8 Linear Programming as a Case of Dynamic Programming 571 whereβ 1 ,β 2 , andβ 3 are the resources available for allocation at ...

572 Dynamic Programming we obtain max 0 ≤x 2 ≤ 002 [ 100 x 2 + 0 min 5 ( 2500 − 5 x 2 10 , 2000 − 10 x 2 4 , 450 − 1. 5 x 2 )] = ...

9.9 Continuous Dynamic Programming 573 These comments are equally applicable for all dynamic programming problems involving many ...

574 Dynamic Programming periodt 1 tot 2 is given by f= ∫t 2 t 1 [ p ( a+ b p ) −c ( p, dp dt , t ) −x(t) ] dt (E 1 ) wherep=p{x( ...

9.9 Continuous Dynamic Programming 575 to the solution of continuous decision problems, consider the following simple (uncon- st ...

576 Dynamic Programming In Eqs. (9.37) to (9.39),θoryiis a continuous variable. However, for simplicity, we treatθ oryias a disc ...

9.10 Additional Applications 577 Figure 9.17 Continuous beam on rigid supports. be applicable. Accordingly, the complete bending ...

578 Dynamic Programming Figure 9.18 Multibay cantilever truss. For specificness, consider a three-bay truss for which the follow ...

9.10 Additional Applications 579 9.10.3 Optimal Design of a Gear Train Consider the gear train shown in Fig. 9.20, in which the ...

580 Dynamic Programming Figure 9.21 Typical drainage network. 1 2 3 R 1 R 2 R 3 h 0 h 1 h 2 h 3 D 1 D 2 D 3 h 0 h 1 h 2 D 3 Elem ...

References and Bibliography 581 element consists of selecting values for the diameter of the pipe, the slope of the pipe, and th ...

582 Dynamic Programming 9.17 W. S. Duff, Minimum cost solar thermal electric power systems: a dynamic programming based approach ...