QUESTION 3
In part 2, based on average check-in waiting time, what course of action should Too Late take?
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Implement Method 1
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Implement neither Method 1 nor Method 2
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Implement Method 2
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Implement Method 1 and Method 2
QUESTION 4
In part 2, if instead of considering the average waiting times, we consider the proportion of customers that wait in line, what course of action should Too Late take?
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Implement Method 1
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Implement Method 1 and Method 2
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Implement neither method 1 nor method 2
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Implement Method 2
QUESTION 5
In part 2, Too Late hired a consulting firm to help make sense of the situation. The firm concluded that total waiting time was the most important factor, and assigned a value of $150 for each second of total waiting time saved. Based on this value, which of the below statements is supported?
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We should not use Method 2 because the benefit is less than the cost.
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We should not use Method 2 because the cost is less than the benefit.
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We should use Method 2 because the benefit is less than the cost.
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We should use Method 2 because the cost is less than the benefit.
Part 2 The rental procedure for customers is a two-step process. First customers arrive at the rental counter to check-in and pay for their rental, and then they go to the parking garage to have the car inspected. The time between customer arrivals at the rental counter is distributed as follows: Figure 3: Time Between 180 240 300 360 Arrivals (Seconds) Probability 0.1 0.2 0.5 0.2 Upon arrival, customers go to an electronic check-in machine, enter their reference number, (electronically) sign a waiver, and make a payment. If a customer arrives at the check-in machine and finds that it is being used by another customer, the incoming customer must wait in line until the machine is open. Once the machine is open, the customer's transaction time at the check-in machine is distributed as follows: Figure 4: Check-In Time 120 180 240 300 (Seconds) Probability 0.2 0.3 0.2 0.3 After checking in, the customer enters the parking garage for vehicle inspection. There is only one attendant who works at the inspection station, so an inspection cannot begin until the previous inspection is completed, and thus, there is a chance that customers will need to wait in line for the inspection. Once the inspection begins, the inspection times are distributed as follows: Figure 5: Inspection Time 240 300 360 420 (Seconds) Probability 0.4 0.3 0.2 0.1 This system was repeatedly simulated for 50 customers (roughly the average daily demand) and the waiting times for the check-in machine and for inspection were recorded. The below table shows the mean times. Figure 6: Average Wait Time Check-In Inspection Total 15 Sec 441 Sec 456 Sec Too Late's management conducted a brain storming session to consider improvements to their system. Two methods were considered viable. In the first method, improvements to the check-in machine could be made that would decrease the times in Figure 4 by 25%. In the second method, the inspection procedure could be streamlined so that the times in Figure 5 would decrease by 10%. Although both methods are viable by themselves, it would be cost prohibitive to do both. The cost of the first method is $25,000 and the cost of the second method is $50,000. Prior to deciding which (if any) of the methods to move forward with, both scenarios were repeatedly simulated for 50 customers. The below table shows the mean times from these simulations. Figure 7: Average Wait Time Check-In Inspection Total Method 1 1 Sec 454 Sec 455 Sec Method 2 14 Sec 122 Sec 136 Sec One other idea was brought up to management, which was to consider the proportion of customers who have to wait. Too Late examined the results of the previous simulations and created the below table which shows, for the current method and both proposed methods, the proportion of customers who have to wait for both Check-in and Inspection. Figure 8: Proportion of Customers Who Wait Check-In Inspection Current 0.16 0.89 Method 1 0.03 0.89 Method 2 0.16 0.68 Upon reviewing the values in Figure 8, a member of management pointed out that, if a customer arrives at the rental counter and finds that they have to wait in line, they may leave Too Late and try one of its competitors. The same cannot be said about customers who find that they must wait in line for inspection, as these customers have already committed to renting from Too Late. Too Late's management team found this argument compelling and agreed that the proportion of customers waiting in line at check-in was a much more serious issue than the proportion of customers waiting in line at inspection Part 2 The rental procedure for customers is a two-step process. First customers arrive at the rental counter to check-in and pay for their rental, and then they go to the parking garage to have the car inspected. The time between customer arrivals at the rental counter is distributed as follows: Figure 3: Time Between 180 240 300 360 Arrivals (Seconds) Probability 0.1 0.2 0.5 0.2 Upon arrival, customers go to an electronic check-in machine, enter their reference number, (electronically) sign a waiver, and make a payment. If a customer arrives at the check-in machine and finds that it is being used by another customer, the incoming customer must wait in line until the machine is open. Once the machine is open, the customer's transaction time at the check-in machine is distributed as follows: Figure 4: Check-In Time 120 180 240 300 (Seconds) Probability 0.2 0.3 0.2 0.3 After checking in, the customer enters the parking garage for vehicle inspection. There is only one attendant who works at the inspection station, so an inspection cannot begin until the previous inspection is completed, and thus, there is a chance that customers will need to wait in line for the inspection. Once the inspection begins, the inspection times are distributed as follows: Figure 5: Inspection Time 240 300 360 420 (Seconds) Probability 0.4 0.3 0.2 0.1 This system was repeatedly simulated for 50 customers (roughly the average daily demand) and the waiting times for the check-in machine and for inspection were recorded. The below table shows the mean times. Figure 6: Average Wait Time Check-In Inspection Total 15 Sec 441 Sec 456 Sec Too Late's management conducted a brain storming session to consider improvements to their system. Two methods were considered viable. In the first method, improvements to the check-in machine could be made that would decrease the times in Figure 4 by 25%. In the second method, the inspection procedure could be streamlined so that the times in Figure 5 would decrease by 10%. Although both methods are viable by themselves, it would be cost prohibitive to do both. The cost of the first method is $25,000 and the cost of the second method is $50,000. Prior to deciding which (if any) of the methods to move forward with, both scenarios were repeatedly simulated for 50 customers. The below table shows the mean times from these simulations. Figure 7: Average Wait Time Check-In Inspection Total Method 1 1 Sec 454 Sec 455 Sec Method 2 14 Sec 122 Sec 136 Sec One other idea was brought up to management, which was to consider the proportion of customers who have to wait. Too Late examined the results of the previous simulations and created the below table which shows, for the current method and both proposed methods, the proportion of customers who have to wait for both Check-in and Inspection. Figure 8: Proportion of Customers Who Wait Check-In Inspection Current 0.16 0.89 Method 1 0.03 0.89 Method 2 0.16 0.68 Upon reviewing the values in Figure 8, a member of management pointed out that, if a customer arrives at the rental counter and finds that they have to wait in line, they may leave Too Late and try one of its competitors. The same cannot be said about customers who find that they must wait in line for inspection, as these customers have already committed to renting from Too Late. Too Late's management team found this argument compelling and agreed that the proportion of customers waiting in line at check-in was a much more serious issue than the proportion of customers waiting in line at inspection
