Each day, a company makes deliveries to four restaurants. The service uses one truck that starts at its warehouse, makes a delivery to each restaurant in turn, and then returns to the warehouse. The distance (km) between each location is shown in the following table: Location Location 1 2 3 4 5 1 10 15 20 40 2 10 12 16 24 - 3 15 12 10 20 4 20 16 10 16 - 5 40 24 20 16 The warehouse is Location 1 and the restaurants are Locations 2-5. The goal is to determine the route the truck should take to start at the warehouse, visit each restaurant once, and return to the warehouse while minimising the total distance traveled. a. Formulate this as an integer programming problem. In your answer you must - introduce any variables needed to describe the quantities in the problem, and briefly explain what they mean. state the objective function. write down all constraints that apply, and briefly explain what they mean. b. Solve the problem to find the route and and the minimum distance. You may use a linear programming tool or a manual method to solve this problem. All working or computer input and output must be shown, and you must include a brief concluding sentence describing your findings.
Each day, a company makes deliveries to four restaurants. The service uses one truck that starts at its warehouse, makes a delivery to each restaurant in turn, and then returns to the warehouse. The distance (km) between each location is shown in the following table: Location Location 1 2 3 4 5 1 10 15 20 40 2 10 12 16 24 - 3 15 12 10 20 4 20 16 10 16 - 5 40 24 20 16 The warehouse is Location 1 and the restaurants are Locations 2-5. The goal is to determine the route the truck should take to start at the warehouse, visit each restaurant once, and return to the warehouse while minimising the total distance traveled. a. Formulate this as an integer programming problem. In your answer you must - introduce any variables needed to describe the quantities in the problem, and briefly explain what they mean. state the objective function. write down all constraints that apply, and briefly explain what they mean. b. Solve the problem to find the route and and the minimum distance. You may use a linear programming tool or a manual method to solve this problem. All working or computer input and output must be shown, and you must include a brief concluding sentence describing your findings.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Transcribed Image Text:Each day, a company makes deliveries to four restaurants. The service uses one truck
that starts at its warehouse, makes a delivery to each restaurant in turn, and then
returns to the warehouse. The distance (km) between each location is shown in the
following table:
Location
Location
1
2
3
4
5
1
10
15
20
40
2
10
12
16
24
3
15
12
10
20
4
20
16
10
16
5
40
24
20
16
The warehouse is Location 1 and the restaurants are Locations 2-5.
The goal is to determine the route the truck should take to start at the warehouse, visit
each restaurant once, and return to the warehouse while minimising the total distance
traveled.
a. Formulate this as an integer programming problem. In your answer you must
introduce any variables needed to describe the quantities in the problem,
and briefly explain what they mean.
state the objective function.
write down all constraints that apply, and briefly explain what they mean.
b. Solve the problem to find the route and and the minimum distance. You may use a
linear programming tool or a manual method to solve this problem. All working or
computer input and output must be shown, and you must include a brief
concluding sentence describing your findings.
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