Lecture 11.ppt

Lecture 11 - Dynamic Programming 1 Investment Problem Decision variable Xij =1 means we allocate j units of investment to opportunity i y = unused

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
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? We only need to see the value of

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.

This note was uploaded on 01/05/2011 for the course IELM IELM202 taught by Professor D during the Fall '10 term at HKUST.

Page1 / 17

Lecture 11 - Dynamic Programming 1 Investment Problem Decision variable Xij =1 means we allocate j units of investment to opportunity i y = unused

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online