BADM515 - Case study no. 2

PROBLEM NO. 1

American Parcel Service (APS) has determined that it needs to add several new package distribution hubs to service cities east of the Mississippi River. The company wants to construct the minimum set of new hubs in the following 12 cities so that there is a hub within 300 miles of each city (i.e. every city is covered by a hub): CityCities within 300 miles AtlantaAtlanta, Charlotte, Nashville BostonBoston, New York CharlotteAtlanta, Charlotte, Richmond CincinnatiCincinnati, Detroit, Indianapolis, Nashville, Pittsburgh DetroitCincinnati, Detroit, Indianapolis, Milwaukee, Pittsburgh IndianapolisCincinnati, Detroit, Indianapolis, Milwaukee, Nashville, St. Louis MilwaukeeDetroit, Indianapolis, Milwaukee NashvilleAtlanta, Cincinnati, Indianapolis, Nashville, St. Louis New YorkBoston, New York, Richmond PittsburghCincinnati, Detroit, Pittsburgh, Richmond RichmondCharlotte, New York, Pittsburgh, Richmond St. LouisIndianapolis, Nashville, St. Louis

For example, the cities of Atlanta, Charlotte, and Nashville exist within a diameter of 300 miles. APS Company wants to recognize in which cities to construct new hubs and which cities should not include new hubs in a way that there is a hub within 300 miles of each city.

Requirements:

1.Formulate the suitable integer programming model for this problem. 2.Create the necessary tables using Excel and QM for Windows 3.Solve this model using Excel and QM for Windows.

PROBLEM NO. 2

MJ Cleaning Experts Company is trying to determine the number of salespeople it should allocate to its three regions-the East, the Midwest, and the West. The company has 100 salespeople that it wants to assign to the three regions. The annual average unit sales volume achieved by a salesperson in each region is as follows: RegionUnits per salesperson East25,000 Midwest18,000 West31,000

Because travel distance, costs of living, and other factors vary among the three regions, the annual cost of having a salesperson is $5000 in the East, $11000 in the Midwest, and $7000 in the West. The company has $700,000 budgeted for expenses. To ensure nationwide exposure for its product, the company has decided that each region must have at least 10 salespeople. The company wants to know how many salespeople to allocate to each region to maximize total average units sold.

Requirements:

1.Formulate the suitable integer programming model for this problem. 2.Create the necessary tables using Excel and QM for Windows 3.Solve this model using Excel and QM for Windows.

PROBLEM NO. 3

The artisans at Ghina Jewelry are preparing to make gold jewelry during a 2-month period for the Valentine season. They can make bracelets, necklaces, and pins. Each bracelet requires 6.3 ounces of gold and 17 hours of labor, each necklace requires 3.9 ounces of gold and 10 hours of labor, and each pin requires 3.1 ounces of gold and 7 hours of labor. Ghina Jewelry has available 125 ounces of gold and 320 hours of labor. A bracelet sells for $1650, a necklace for $850, and a pin for $790. The store wants to know how many of each item to produce to maximize revenue.

Requirements:

1.Formulate the suitable integer programming model for this problem. 2.Create the necessary tables using Excel and QM for Windows 3.Solve this model using Excel and QM for Windows. 4.If it is not the case of integer programming, solve the same model without the integer constraint and round down the values of decision variables, then explain the difference between the answers in both scenarios.