Formulate an integer programming model to identify a feasible deployment plan to the sales representatives. What is the minimum number of representatives that can cover this region? What are their home cities?
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PharmaCo wants to determine how to deploy sales representatives across its Western U.S. region to support a new drug for obesity. Sales representatives will be located in a "home city", which they serve, in addition to cities with feasible commuting distance, with the objective that all cities must be served by at least one sales representative. The feasible connections between each city in the region are listed below (1 indicates a feasible connection, potential home cities are shown in columns, and cities served in rows):
|
Potential Rep Home |
|||||||||||
|
City Served? |
Albuquerque |
El Paso |
Denver |
Phoenix |
San Diego |
Los Angeles |
San Francisco |
Portland |
Seattle |
Las Vegas |
Salt Lake City |
|
Albuquerque |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
El Paso |
1 |
1 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Denver |
1 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
|
Phoenix |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
1 |
1 |
|
San Diego |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
1 |
0 |
|
Los Angeles |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
1 |
0 |
|
San Francisco |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
1 |
|
Portland |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
|
Seattle |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
|
Las Vegas |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
0 |
0 |
1 |
1 |
|
Salt Lake City |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
- Formulate an integer programming model to identify a feasible deployment plan to the sales representatives. What is the minimum number of representatives that can cover this region? What are their home cities?
- Suppose PharmaCo wants to have a backup for each city (two sales reps for each city). What is the minimum number of representatives that can cover this region in that case? What are their home cities? (Assume you can’t have more than one sales rep in a city.
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