Case Presentation 2 Chapter 4 CASE SCENARIO: BOULEVARD INDUSTRIES Boulevard Industries has decided to provide safety training to its 1,500+ employees who work in the Boulevard main office. Part of this training is a 60-minute presentation by a member of the Boulevard human resources (HR) department and is held in a conference room at the main office building. Boulevard plans to complete this process by holding five sessions a day on Thursdays (Th) and Fridays (F) each week for the next 4 months. During the first week of sessions, the HR department recorded the following information concerning attendance. Questions 1. During this first week of sessions, what was the mean error of the HR department’s forecasts (ME)? What was the mean absolute deviation (MAD)? What was the mean absolute percent error (MAPE)? 2. Assume that the HR department’s forecast for the Thursday 9 a.m. session was 10, as shown in the table. If HR had used simple exponential smoothing with an alpha (α) of 0.2 to forecast the remainder of the sessions that week, what would the forecast for the Friday 9 a.m. session have been? 3. Someone in HR noticed that overall attendance on Friday was somewhat less than on Thursday and believes this pattern will continue. Calculate the two seasonal relatives that express this fluctuation, based on this data. 4. Using your answer from question 3, how many people would you forecast to attend next Friday’s sessions, if a total of 100 people were forecast to attend all 10 sessions next week? CASE SCENARIO: HOLIDAY CRUISE LINES Holiday Cruise Lines is evaluating the cost of operating its newest ship, the Caribbean Summer. In its first year of operation, the Caribbean Summer completed 25 short cruises along the same route, but with varying numbers of passengers on board. The chief operating officer of Holiday Cruise Lines collected the total cost of operating each short cruise, as well as the number of passengers on board, and summarized the data: Assume that Y in this information is the total cost of operating the ship on a short cruise, in millions of US dollars, while X is the number of passengers on that cruise stated in thousands. Questions 1. According to the information, what was the average total cost of operating the Caribbean Summer on one of its 25 short cruises? 2. Use this information to find the linear regression equation that best explains the relationship of the total cost of a short cruise to the number of passengers on that cruise. What is that equation? Using that equation, what total cost would you predict for a Caribbean Summer short cruise carrying 2,500 passengers? 3. What percent of the variation in the total cost of operating the ship on these 25 short cruises is explained by your regression equation? 4. The chief operating officer is particularly interested in understanding the fixed cost of operating the Caribbean Summer on a short cruise, which represents the expenses that would be incurred regardless of whether there are no, few, or many passengers aboard. The Caribbean Summer was built to eventually replace its sister ship the Tropical Equinox, which requires a fixed cost of about $2 million to complete a short cruise similar to those being evaluated here. What does your regression equation indicate about this issue? Does the newer Caribbean Summer have lower fixed costs than the Tropical Equinox? Chapter 5 CASE SCENARIO: WORLD TRANSPORTATION PARTNERS World Transportation Partners (WTP) offers three different intermodal container sizes that clients rent and pack with freight for shipping over- seas. Intermodal containers are measured in TEUs (twenty-foot equivalent units), and WTP offers three sizes. The 1 TEU container can hold 1,100 cubic feet of freight, while a 2 TEU container can hold 2,200 cubic feet and a 2.5 TEU container can hold 2,750 cubic feet. Every container in WTP’s inventory weighs approximately 4,000 lbs. per TEU when empty and is designed to be safely loaded with 50,000 lbs. of additional weight per TEU. In addition, WTP does not allow a container of any size to be loaded past a total combined weight of 60,000 lbs., allowing each container the option of being transferred to a truck trailer for delivery, without violating maximum weight limits for roadways in most countries. WTP charges $800 per TEU to ship containers along its major routes, and rents those containers for $150 per container, per shipment. Questions 1. Prepare a table that provides both the design and the effective capacity of each container size, in terms of the weight of cargo it can hold. Which container size has the greatest effective capacity in terms of weight? 2. Suppose a 2.5 TEU container were filled to its effective weight capacity with cargo that weighed 25 lbs. per cubic foot. What would the utilization of that container be, in terms of weight? What would its utilization be in terms of volume? 3. One of WTP’s clients, Bankston Industries, must ship 120,000 lbs. of cargo on one of WTP’s major routes. This cargo weighs 50 lbs. per cubic foot. Which container size would be best for Bankston Industries to rent for this shipment, based on cost? 4. Bankston Industries is trying to convince WTP that restricting a container’s loaded weight to a total of 60,000 lbs. should not apply to the shipment mentioned in ques- tion 3, because that shipment will be delivered by railroad car after its arrival in port, and one railcar can legally handle over 280,000 lbs. in weight. If WTP agrees to waive its policy of restricting a container to 60,000 lbs. total weight, which container size would be best for Bankston Industries to rent for this shipment, and how much will Bankston be saving from this agreement? CASE SCENARIO: DRIVER’S DONUTS Driver’s Donuts is a bakery and coffee shop that depends on morning commuters for 80% of its daily business. During the morning rush from 5:30 a.m. to 8:30 a.m., an average of 35 cars arrive at the Driver’s Donuts drive- through lane every hour, to purchase donuts and coffee through a single store window. The employee who staffs that window can serve each car in an average of 90 seconds, although this speed is partially due to the fact that a second employee talks to the car behind the one being served, inputting that car’s order so that the window employee knows the order and its cost when the second car arrives at the window. Without that assistance, it takes the window employee an average of 2 minutes to serve any car, which is the practice outside of the morning rush hours, as customer traffic in the drive-through lane drops to an average of four cars an hour. Assuming that Driver’s Donuts drive-through lane meets the assumptions of the M/M/1 model, answer the following questions. Questions 1. On average, how many cars are in the drive-through lane during the morning rush? (This includes any car being served). During the morning rush, how much time does the average Driver’s Donuts customer spend in the drive-through lane? 2. If a car arrived between 1:00 p.m. and 2:00 p.m., how much time could the customer expect to spend in the drive-through lane? What is the probability that the customer would find no other cars in the lane, and be able to pull up to the window immediately? 3. If a customer arrives at the drive-through lane during the morning rush, what is the probability that the customer will have to wait until a Driver’s Donuts employee takes their order?
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