4. (Western Pennsylvania Milk Company) The western Pennsylvania Milk Company is

Question

4. (Western Pennsylvania Milk Company) The western Pennsylvania Milk Company is producing milk at a fixed rate of 5000 gallons/hour. The company’s clients request 100,000 gallons of milk over the course of one day. This demand is spread out uniformly from 8 a.m. to 6 p.m. If there is no milk available, clients will wait until enough is produced to satisfy their requests.

The company starts producing at 8 a.m. with 25,000 gallons in finished goods inventory. At the end of the day, after all demand has been fulfilled, the plant keeps on producing until the finished goods inventory has been restored to 25,000 gallons.x

When answering the following questions, treat trucks/milk as a continuous flow process. Begin by drawing a graph indicating how much milk is in inventory and how much milk is “back-ordered” over the course of the day.

At what time during the day will the clients have to start waiting for their requests to be filled?

At what time will clients stop waiting?

Assume that the milk is picked up in trucks that hold 1,250 gallons each. What is the maximum number of trucks that are waiting?

Assume the plant is charged $50 per hour waiting truck. What are the total waiting time charges on a day?

9. (Paris Airport) Kim Opim, an enthusiastic first-year MBA student, is on her flight over from Philadelphia (PHL) to Paris (CDG), where she will spend some time at INSEAD in Fontainebleau, France. Kim reflects upon how her educational experiences from her operations courses could help explain the long wait time that she experienced before she could enter the departure area of Terminal A at PHL. As an airline representative explained to Kim, there are four types of travelers in Terminal A:

Experienced short-distance (short distance international travel destinations are Mexico and various islands in the Atlantic) travelers: The passengers check in online and do not speak with any agent nor do they take any time at the kiosks.

Experienced long-distance travelers: These passengers spend 3 minutes with an agent.

Inexperienced short-distance travelers: These passengers spend 2 minutes at a kiosk; however, they do not require the attention of an agent.

Inexperienced long-distance travelers: These passengers need to talk 5 minutes with an agent.

All passengers must pass through security, where they need 0.5 minutes independent of their type. From historical data, the airport is able to estimate the arrival rates of the different customer types at Terminal A of Philadelphia International:

Experience short distance travelers: 100 per hour

Experienced long distance travelers: 80 per hour

Inexperienced short distance travelers: 80 per hour

Inexperienced long-distance travelers: 40 per hour

At this terminal, there are four security check stations, six agents, and three electronic kiosks. Passengers arrive uniformly from 4 p.m. to 8 p. m. , with the entire system empty prior to 4p.m. (the “midafternoon lull”) and no customers after 8p.m. All workers must stay on duty until the last passenger is entirely through the system (e.g., has passed through security).

What are the levels of implied utilization at each resource?

At what time has the last passenger gone through the system? Note: If passengers of one type have to wait for a resource, passengers do not require service at the resource can pass by the waiting passengers!

Kim, an experienced long distance traveler, arrived at 6p.m. at the airport and attempted to move through the check-in process as quickly as she could. How long did she have to wait before she was checked at security?

The airline considers showing an educational program that would provide information about the airport’s check-in procedures. Passenger surveys indicate that 80 percent of the inexperienced passengers (short or long distance) would subsequently act as experienced passengers (i.e., the new arrival rates would be 164 experienced short distance, 112 experienced long distance, 16 inexperienced short distance, 8 inexperienced long distance [passengers/hour]). At what time has the last passenger gone through the system?

Explanation / Answer

Solution
Part 4
1. The day is started with 25,000 gallons of milk in inventory. Production per hour from 8 am = 5,000 gallons per hour.
Demand = 100,000 gallons from 8am to 6pm i.e. 10 hours. Thus demand per hour = 100,000 gallons/10 hours = 10,000 gallons.
Thus the inventory of 25,000 is being depleted at the rate of 10,000 (demand) - 5,000 (production) = 5,000 gallons per hour.
The beginning inventory of 25,000 will get entirely depleted in 25,000 gallons/5,000 gallons per hour = 5 hours.
5 hours from 8 am = 1pm.
Thus from 1 pm onwards the clients will have to start waiting for their requests to be fulfilled.
2. At 6pm there will be a backlog of 25,000 gallons. Clients will stop waiting when the milk company has removed its backlog of 25,000 gallons (this is the level to which the finished goods has to be restored). Time taken for this = 25,000 gallons/5,000 gallons per hour = 5 hours.
Thus 5 hours from 6 pm = 11pm.
3. Finished goods invenory has to be restored to 25,000 gallons. At 11 pm all backlog is cleared and so only 25,000 units that is required to bring the ending inventory to desired levels has to be produced. Time required = units to be produced/production rate
Production rate = 5,000 gallons per hour. Thus the inventory will be restored to 25,000 gallons in 25,000/5,000 = 5 hours.
Thus time = 11pm+5 hours = 4 am.

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