IE 416 Quiz Date: 1-22-98
Total Page：16
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IE 416 Quiz Date: 1-13-03 Last name: First name:
1- Did you have a chance to watch Video 1, which is Tape 1 on Chapters 1 to 3 and Tape 2 on Chapter 4? If not explain why.
2- Which version did you watch? Video from Reserve Lib ….. On Internet from home ….. On Internet at School labs ….. Others …..
3- How was the quality of tape? Very good …… Acceptable …… Not good ……
4- How (in what ways, if any) the video-lecture helped you in your learning process?
5- Would like to watch tape instead of having a lecture in class and spend the class time on more discussions? Explain why.
6- What is nonbonding constraint and how it is important?
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IE 416 Quiz Date: 1-13-03 Last name: First name:
1- What is “Big M” method? What is the motivation for applying (when do we use) “Big M” method?
1 2- What does a multi-optimal solution mean? How is that useful from practical point of view? How often we can reach a multi-optimal solution in real problems?
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IE 416 Quiz Date: 1-27-03 Last name: First name:
Define “reduced cost” and provide an example. What is its application?
What is the application of “artificial variable” from practical point of view?
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IE 416 Quiz Date: 2-19-03 Last name: First name:
The following is transportation tableau. Use MC method to find the initial bfs.
Destination 1 Destination 2 Destination 3 Destination 4 4 5 7 6 source 1 9000
7 1 2 3 source 2 1000
2 5 3 5 source 3 5500
6000 4000 4000 1500
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IE 416 Quiz Date: 2-26-03 Last name: First name:
2 The following is a transportation tableau with its initial bfs using MC method. Perform one iteration of simplex transportation. Write the new tableau. What is the value of Z for the new tableau.
Destination 1 Destination 2 Destination 3 Destination 4 4 5 7 6 source 1 500 3000 4000 1500 9000
7 1 2 3 source 2 1000 1000
2 5 3 5 source 3 5500 5500
6000 4000 4000 1500
The result of the above iteration will be written below: Destination 1 Destination 2 Destination 3 Destination 4 4 5 7 6 source 1 9000
7 1 2 3 source 2 1000
2 5 3 5 source 3 5500
6000 4000 4000 1500
IE 416 Quiz Date: 3-5-03 Last name: First name:
3 Create a balanced transportation tableau for the following transshipment network, use Winston style. 5 Point X Prod: 300
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IE 416 Quiz Date: 3-12-03 Last name: First name:
Assume there is an attempt to solve a TSP problem applying Branch-and-Bound method. The objective is to find the minimum cost. One of the subproblems and its solution is given below. What are the next steps to complete this process (branches and the subproblems to be solved at each branch, do not solve)?
Subproblem 5:
Store Store Store Store Store Store 6 1 2 3 4 5 Store 1 M 23 14 40 36 17 Store 2 23 M 53 M 37 51 Store 3 14 53 M 16 11 25 Store 4 40 62 16 M M 21 Store 5 36 37 11 33 M 44 Store 6 M 51 25 21 44 M
Solution: X15=X46=X52=X21=X63=X34=1
IE 416 Quiz 9-25-01 Last name: First name: ID:
Solve the following linear system of equations. 6X1 + 2X2 + 10X3 = 18 2X1 + 2X2 + 3X3 = 8
IE 416 Quiz 10-2-01 Last name: First name: ID:
4 Leather Limited manufactures two types of belts: the deluxe model and the regular model. Each type requires 1.5 sq yd of leather. A regular belt requires 3 hours of skilled labor, and a deluxe belt requires 5 hours. Each week, 50 sp yd of leather and 180 hours of skilled labor are available. Each regular belt costs $8 and each deluxe belt, $11. Each regular belt can be sold for $14 and each deluxe belt, $23. Formulate the problem to be able to find number of belts to produce so that to maximize the profit.
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IE 416 Quiz 1-18-01 Last name: First name: ID:
A version of Giapetto problem is below with its solution. X1 = number of soldiers X2 = number of trains Variable --> X1 X2 Direction R. H. S. Maximize 5 6 C1 3 1 <= 130 hours of finish labor C2 2 4 <= 111 hours of carpenter labor C3 1 <= 50 demand of soldier Combined Report for Giapetto-new
Variable Value Profit c(j) Contribution Cost Status Min. c(j) Max. c(j)
1 X1 40.9000 5.0000 204.5000 0 basic 3.0000 18.0000 2 X2 7.3000 6.0000 43.8000 0 basic 1.6667 10.0000
Objective Function (Max.) = 248.3000
Left Hand Right Hand Slack Shadow Allowable Allowable Constraint Side Direction Side or Surplus Price Min. RHS Max. RHS
1 C1 130.0000 <= 130.0000 0 0.8000 27.7500 152.7500 2 C2 111.0000 <= 111.0000 0 1.3000 86.6667 520.0000 3 C3 40.9000 <= 50.0000 9.1000 0 40.9000 M a) What is the new objective function value if there are 140 hours available for finish labor?
b) What is the new objective function value if the sales profit of a soldier is $7?
c) What is the new objective function value if the sales profit of a train is $11?
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5 IE 416 Quiz 10-16-01 Last name: First name: ID:
A version of Giapetto problem is below with its solution. X1 = number of soldiers X2 = number of trains Variable --> X1 X2 Direction R. H. S. Maximize 5 6 C1 3 1 <= 130 hours of finish labor C2 2 4 <= 111 hours of carpenter labor C3 1 <= 50 demand of soldier Combined Report for Giapetto-new
Variable Value Profit c(j) Contribution Cost Status Min. c(j) Max. c(j)
1 X1 40.9000 5.0000 204.5000 0 basic 3.0000 18.0000 2 X2 7.3000 6.0000 43.8000 0 basic 1.6667 10.0000
Objective Function (Max.) = 248.3000
Left Hand Right Hand Slack Shadow Allowable Allowable Constraint Side Direction Side or Surplus Price Min. RHS Max. RHS
1 C1 130.0000 <= 130.0000 0 0.8000 27.7500 152.7500 2 C2 111.0000 <= 111.0000 0 1.3000 86.6667 520.0000 3 C3 40.9000 <= 50.0000 9.1000 0 40.9000 M
You had to make a decision in regards to increasing the number of hours of carpenter labor to 200 hours. However, the carpenters will request 80 cents/hour more for working overtime. What would be your decision? How much change will there be in your total profit?
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IE 416 Quiz 10-30-01 Last name: First name: ID:
Create a balanced transportation tableau, with all the necessary information, for the following problem.
Source Capacity Demand Capacity A 250 B 40 C 100 D 120 E 180 Distance From To B D E A 2 4 7 C 5 3 6
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6 IE 416 Quiz 11-6-01 Last name: First name: ID:
The following transportation tableau shows the initial bfs. What is the value of objective function at this step. Perform only one iteration of transportation simplex method.
Destination 1 Destination 2 Destination 3 Destination 4 4 2 7 6 source 1 5000 5000
7 1 2 3 source 2 1000 0 1000
2 5 3 5 source 3 2000 2000 1500 5500
6000 2000 2000 1500
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IE 416 Quiz 11-13-01 Last name: First name: ID:
Below is the optimal solution to a transportation problem. How much we can change the cost of shipment from source 2 to destination 1 so that there is no change in the basis?
Destination 1 Destination 2 Destination 3 Destination 4 4 2 7 6 source 1 2500 1500 4000
7 1 2 3 source 2 2500 3000 1500 7000
2 5 3 5 source 3 2500 2500
5000 4000 3000 1500
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IE 416 Quiz 11-29-01 Last name: First name: ID:
7 Assume there is an attempt to solve a TSP problem applying Branch-and-Bound method. The objective is to find the minimum cost. One of the subproblems and its solution is given below. What are the next steps to complete this process (branches and the subproblems to be solved at each branch, do not solve)?
Subproblem 5:
Store Store Store Store Store Store 6 1 2 3 4 5 Store 1 M 23 14 40 36 17 Store 2 23 M 53 M 37 51 Store 3 14 53 M 16 11 25 Store 4 40 62 16 M M 21 Store 5 36 37 11 33 M 44 Store 6 M 51 25 21 44 M
Solution: X15=X41=X53=X26=X62=X34=1
------IE 416 Quiz 11-20-01 Last name: First name: ID:
Find the reduced cost matrix for the problem 2 on page 379 as below.
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