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21 suppose we were interested in using simulation to

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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.
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Computer Integrated Manufacturing IT 4036 for Second Semester Sample Question
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1. Explain with the block diagram showing various functions of CAD and their relationships to design CAD and manufacturing operations. (20 marks) 2. Draw “Overview of CAM” and explain briefly the “Direct computer application” in manufacturing. (10 marks) 3. Sketch the scope of CAD/CAM. (10 marks) 4. Discuss briefly the “Direct application” in computer aided- manufacturing. (10 marks) 5. Explain the computerized elements of a CIM system. (20 marks) 6. Explain the Computer Aided Process Planning. (10 marks) 7. What are the benefits of Computer Aided Process Planning ? (10 marks) 8. Explain the fundamental concept in Material Requirements Planning. (10 marks) 9. What are the output reports and benefits of the MRP (Materials Requirements Planning)? (10 marks) 10. To illustrate how MRP works let us consider the requirements planning proceeded for one of the components of product PI. The components we will consider a C4. This part happens to be used also on one other product P2 (see figure). However, only one of item C4 is used on each P2 produced. The product structure of P2 is given in Figure 1. Component C4 is made out of raw materials M4. One unit of M4 is needed to produce 1 unit of C4. Find the ordering and manufacturing lead times and make the MRP computations? (20 marks) The current inventory order and status of item M4 is in Figure. There are no stocks or orders for any of the other items listed below: P1: assembly lead time = 1 week P2: assembly lead time = 1week S2: assembly lead time = 1week S3: assembly lead time = 1 week C4: manufacturing lead time = 2 weeks M4: ordering lead time = 3weeks
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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
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21 Suppose we were interested in using simulation to...

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