{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture 11

# Lecture 11 - Dynamic Programming 1 Investment Problem...

This preview shows pages 1–6. Sign up to view the full content.

1 Dynamic Programming

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Investment Problem Decision variable X ij =1 means we allocate j units of investment to opportunity i y = unused investment 0 }, 1 , 0 { 8 ,..., 1 for , 1 10 subject to 5 . 0 max 4 0 8 1 4 0 8 1 4 0 = = = + + ∑∑ ∑∑ = = = = = y X i X y jX y X r ij j ij i j ij i j ij ij
3 The DP Method Solve the problem sequentially At each stage, one investment opportunity is considered Let f ( i , s ) be the maximum total profit from stage i , i +1,…, to stage 8, given s Dynamic Programming recursion f ( i , s ) = max d { r id + f ( i +1, s d ) | 0 ≤ d ≤ 4, d s } Initial condition f ( 8, s ) =max d { r 8d +0.5( s d ) | 0 ≤ d ≤ 4, d s } The optimal solution of the problem is obtained from f (1,10) : the maximum profit from stage 1 to stage 8 with 10 units of money initially available

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4 Dynamic Programming Formulation Problem includes a series of decisions Over “real” time, or simply a decision sequence Stage, state, decision, and value function Sometimes naturally, sometimes not obviously A recursive equation To link different stages An initial condition to make calculation of DP feasible
5 Advantages of DP DP formulation is often the best way to gain understanding of a problem and its solution Computational efficiency The number of states we have to consider: 8*11, or I*S , where I is the number of stages and S is the number of possible states For each state, we need to compare up to 5 possible actions, or D decisions, in general Overall calculation: I * S * D More information can be obtained What happens if we only have 7 units of money?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern