### Single facility location problem

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##### Reference no: EM13950

Purdue Clinic at Waldron Street was established in 1966 as West Lafayette's community health care center. The center decided to initiate its "Intoxication Treatment Program" due to recent public demand and increased budget from the city council.

Intoxication treatment includes administration of IV fluids and B complex vitamins for dehydration and vitamin deficiency that can cause serious brain injuries. In severe cases the patient will be intubated to support respiration and to protect the lungs from filling with vomit.

The center's manager was recommended to allocate a facility room for the new program. Due to current physical layout constraints the manager has identified only five possible rooms that could be remodeled to serve the program. The coordinates of these rooms in the Cartesian coordinate system are:

 X Y Room 1 30 25 Room 2 45 20 Room 3 55 30 Room 4 50 30 Room 5 60 35

Table 1: Cartesian coordinate of possible rooms

The manager also identified other rooms that would have high travel frequency to the facility room of the new program. The coordinates of these rooms and their expected travel frequency to the new facility room per day are as follows.

 X Y Expected travel frequency per day Main office 30 40 30 Nurses room 50 45 35 Doctor room 60 45 20 Supplies room 30 25 12 File room 40 35 25

Table 2: Cartesian coordinates of "other rooms" with expected travel frequency per day

Problem 1.

Treat this problem as a discrete facility location problem. Select a possible room that:

• minimizes the maximum travel distance per trip using rectilinear distance;
• minimizes the total travel distance per day using rectilinear distance;
• minimizes the total travel distance per day using Euclidean (straight-line) distance.

The manager considers allocating more than one facility room for the new program.

• How many room(s) should be allocated to the program in order to minimize the total cost (total cost = travel cost + fixed cost)? Which room(s) should be used? Plot ONE graph to show the relationship between travel costs, fixed costs, total costs and the number of facility rooms for the program.

Use rectilinear distance for this problem. Consider each trip as a round trip. The cost for each traveling distance unit of one-way trip is \$0.50, and the fixed cost is \$1100 for each facility room per month (assume 30 days per month). Base your calculation on per day, NOT per month.

Problem 2.

Treat this problem as a continuous single facility location problem. Determine the location of the room that minimizes

• The total travel distance per day using rectilinear distance
• The total travel distance per day using straight-line distance

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