{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 21 suppose we were interested in using simulation to

This preview shows pages 141–145. Sign up to view the full content.

21. Suppose we were interested in using simulation to compute θ =E [e u ]. Here, a natural variant to use as a control is the random number U. Discuss what sort of improvement over the raw estimator is possible. (20 marks) Solution θ = E[e U ] By using raw estimator, ( ) [] [ ] ( ) 0.2420 1 - e - dx e x e E - U E e Var 1 0 2 x 2 U 2U U = = = By using antithetic variable U, ( ) [ ] [ ] [ ] 0.14086 2 1 - e - 1 2 1 - e - dx e x e E U E - e U E U , e Cov 1 0 x U U U = = = = And then, () [] [ ] ( ) ( ) 0.0039 0.2380 - 0.2420 0.14086 12 - e Var 1/2 - U c e Var Y Var Y X, Cov - X Var μ - Y c X Var have we 1/12 U E - U E U Var 2 U * U 2 y * 2 2 = = = + = + = = Therefore, the use of control variate U can lead to a variance reduction of up to 98.4 percent.

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

View Full Document
Computer Integrated Manufacturing IT 4036 for Second Semester Sample Question

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

View Full Document
11. Master production schedule for products P1 are 50 at 8 th week and 100 at 10 th week and for product P2 are 50 at 7 th week and 100 at 9 th week. Product structure for P1 and P2 are as follows: C4(1) & C6(2) = S3(1) = P2 C4(2) & C6(1) = S2(2) = P1 Component of raw material is M4. Two unit of M4 is needed to produce one unit of C4. The raw material used in component C 6 is M6. One unit of C6 is obtained from two units of M6. Lead times are as follows: P1: assembly lead time = 1 week P2: assembly lead time = 1 week S2: assembly lead time = 1 week S3: assembly lead time = 1 week Week number 6 7 8 9 10 Product P 1 50 100 Product P 2 70 80 25 etc, Period 1 2 3 4 5 6 7 Item: Raw Matl M 4 Gross Requirements Schedule Receipts 40 On Hand 50 90 Net Requirements Planned Order Release P2 S4 S3 C4 C6 C7 C2 C8 (1) (1) (2) (2) (2) (1) (1) Figure
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page141 / 168

21 Suppose we were interested in using simulation to...

This preview shows document pages 141 - 145. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online