1. Dynamic programming divides problems into
a. nodes. b. arcs.
c. decision stages. d. branches.
e. variables.
2. Possible beginning situations or conditions of a dynamic programming problem are called
a. stages. b. state variables.
c. decision variables. d. optimal policy.
e. transformation.
3. The statement concerning the objective of a dynamic programming problem is called
a. stages. b. state variables.
c. decision variables. d. optimal policy.
e. decision criterion.
4. The first step of a dynamic programming problem is to
a. define the nodes.
b. define the arcs.
c. divide the original problem into stages.
d. determine the optimal policy.
e. none of the above.
5. Working forward from the first stage to the ending stage
a. is done for large dynamic programming problems to achieve a solution.
b. is done for any dynamic programming problem.
c. is the first step of a dynamic programming problem solution.
d. is the last step of a dynamic programming problem solution.
e. none of the above.
6. An algebraic statement that reveals the relationship between stages is called
a. the transformation. b. state variables.
c. decision variables. d. the optimal policy.
e. the decision criterion.
7. In this chapter, dynamic programming was used to solve what type of problem?
8. In dynamic programming terminology, a period or logical subproblem is called
a. the transformation. b. a state variable.
c. a decision variable. d. the optimal policy.
e. a stage.
9. The statement that the distance from the beginning stage is equal to the distance from the preceding stage to the last node plus the distance from the given stage to the preceding stage is called
a. the transformation. b. state variables.
c. decision variables. d. the optimal policy.
e. stages.
10. In dynamic programming, snis a. the input to the stage n.
b. the decision at stage n.
c. the return at stage n.
d. the output of stage n.
e. none of the above.
11. The relationship that the distance from the beginning stage is equal to the distance from the preceding stage to the last node plus the distance for the given stage to the preceding stage is used to solve which type of problem?
a. knapsack b. JIT
c. shortest-route d. minimal spanning tree e. maximal flow
12. In dynamic programming, rnis a. the input to the stage n.
b. the decision at stage n.
c. the return at stage n.
d. the output of stage n.
e. none of the above.
13. In dynamic programming, onis a. the input to the stage n.
b. the decision at stage n.
c. the return at stage n.
d. the output of stage n.
e. none of the above.
14. In dynamic programming, dnis a. the input to the stage n.
b. the decision at stage n.
c. the return at stage n.
d. the output of stage n.
e. none of the above.
Discussion Questions and Problems Discussion Questions
M2-1 What is a stage in dynamic programming?
M2-2 What is the difference between a state variable and a decision variable?
M2-3 Describe the meaning and use of a decision criterion.
M2-4 Do all dynamic programming problems require an optimal policy?
M2-5 Why is transformation important for dynamic programming problems?
Problems
M2-6 Refer to Figure M2.1. What is the shortest route between Rice and Dixieville if the road between Hope and Georgetown is improved and the distance is reduced to 4 miles?
M2-7 Due to road construction between Georgetown and Dixieville, a detour must be taken through country roads (Figure M2.1). Unfortunately, this detour has increased the dis-tance from Georgetown to Dixieville to 14 miles. What should George do? Should he take a different route?
M2-8 The Rice Brothers have a gold mine between Rice and Brown. In their zeal to find gold, they have blown up the road between Rice and Brown. The road will not be in service for five months. What should George do? Refer to Figure M2.1.
M2-9 Solve the shortest-route problem of Figure M2.11.
Discussion Questions and Problems M2-21
FIGURE M2.11 (for Problem M2-9)
1 5
2
3
7 4
8
6
9 5
4 11
10
4
12
6
10
4 6 2
4
6
••
••
••
••
M2-11 Mail Express, an overnight mail service, delivers mail to customers throughout the United States, Canada, and Mexico. Fortunately, Mail Express has additional capacity on one of its cargo planes. To maximize profits, Mail Express takes shipments from local manufacturing plants to warehouses for other companies. Currently, there is room for another 6 tons. The following table shows the items that can be shipped, their weights, the expected profit for each, and the number of available parts. How many units of each item do you suggest that Mail Express ship?
ITEMS TO BE SHIPPED
M2-12 Leslie Bessler must travel from her hometown to Denver to see her friend Austin. Given the road map of Figure M2.13, what route will minimize the distance that she travels?
M2-22 Module 2 DY N A M I C PR O G R A M M I N G
•M2-10 Solve the shortest-route problem of Figure M2.12.
M2-13 An air cargo company has the following shipping requirements. Two planes are avail-able with a total capacity of 11 tons. How many of each item should be shipped to maximize profits?
M2-14 Because of a new manufacturing and packaging procedure, the weight of item 2 in Problem M2-13 can be cut in half. Does this change the number or types of items that can be shipped by the air transport company?
M2-15 What is the shortest route through the network of Figure M2.14?
Discussion Questions and Problems M2-23
FIGURE M2.14
•••M2-16 The road between node 6 and node 11 is no longer in service due to construction.
(Refer to Problem M2-15.) What is the shortest route given this situation?
M2-24 Module 2 DY N A M I C PR O G R A M M I N G
Case Study United Trucking
Like many trucking operations, United Trucking got started with one truck and one owner—Judson Maclay. Judson is an individ-ualist and always liked to do things his way. He was a fast driver, and many people called the 800 number on the back of his truck when he worked for Hartmann Trucking. After two years with Hartmann and numerous calls about his bad driving, Judson de-cided to go out on his own. United Trucking was the result.
In the early days of United Trucking, Judson was the only driver. On the back of his truck was the message: How do you like my driving? Call 1-800-AMI-FAST. He was convinced that some people actually tried to call the number. Soon, a number of truck operators had the same or similar messages on the back of their trucks. After three years of operation, Jud-son had 15 other trucks and drivers working for him. He traded his driving skills for office and management skills. Al-though 1-800-AMI-FAST was no longer visible, Judson de-cided to never place an 800 number on the back of any of his trucks. If someone really wanted to complain, they could look up United Trucking in the phone book.
Judson liked to innovate with his trucking company. He knew that he could make more money by keeping his trucks full. Thus he decided to institute a discount trucking service.
He gave substantial discounts to customers that would accept delivery to the West Coast within two weeks. Customers got a great price, and he made more money and kept his trucks full.
Over time, Judson developed steady customers that would usually have loads to go at the discounted price. On one
ship-ment, he had an available capacity of 10 tons in several trucks going to the West Coast. Ten items can be shipped at discount.
The weight, profit, and number of items available are shown in the following table.
1. What do you recommend Judson should do?
2. If the total available capacity was 20 tons, how would this change Judson’s decision?