Case Study 1 - Abu Dhabi Equipment, Inc.
Abu Dhabi Equipment, Inc. (AEI) leases automatic mailing machines to business customers in Abu Dhabi, UAE. The company built its success on a reputation for providing timely maintenance and repair service. Each AEI service contract states that a service technician will come to a customer's business site within an average of three hours from the time that the customers informs AEI of an equipment problem.
Currently, AEI has 10 customers with service contracts. One service technician is responsible for handling all service calls. A statistical analysis of historical service records shows that a customer requests a service call at an average rate of one call per 50 hours of operation. If the service technician is available when a customer calls for service, it takes the technician an average of 1 hour of travel time to reach the customer's office and an average of 1.5 hours to complete the repair service. However, if the service technician is busy with another customer when a new customer calls for a service, the technician completes the current service call and any other waiting service calls before responding to the new service call. In such cases, once the technician is free from all existing service commitments, the technician takes an average of 1 hour of travel time to reach the new customer's office and an average of 1.5 hours to complete the repair service. The cost of one service technician is $80 per hour. The downtime (wait time and service time) for customer is $100 per hour.
AEI is planning to expand its business. Within a year, AEI projects that it will have 20 customers, and within two years, AEI projects that it will have 30 customers. Although AEI is satisfied that one service technician can handle the 10 existing customers, management is concerned about the ability of one technician to meet the average three-hour service guarantee when the AIE customer base expands. In a recent planning meeting, the marketing manager made a proposal to add a second service technician when AEI reaches 20 customers and to add a third service technician when AEI reaches 30 customers. Before making a final decision, management would like an analysis of AEI service capabilities. AEI is particularly interested in meeting the average three-hour waiting time guarantee at the lowest possible total cost.
Required:
Develop a managerial report summarizing your analysis of the AEI service capabilities. Make recommendations regarding the number of technicians to be used when AEI reaches 20 customers and AEI reaches 30 customers. Include a discussion of the following in your report.
1. What is the arrival rate for each customer per hour?
2. Which queuing model will you use? What is arrival rate for each customer per hour?
3. What is the service rate in terms of the number of customers per hour? Note that the average travel time of 1 hour becomes part of the service time because the time that the service technician is busy handling a service call include the travel time plus the time required to complete the repair.
4. AEI is satisfied that one service technician can handle the 10 existing customers. Use a waiting line model to determine the following information:
a. Probability that no customers are in the system
b. Average number of customers in the waiting line
c. Average number of customers in the system
d. Average time a customer waits until the service technician arrives
e. Average time a customer waits until the machine is back in operation
f. The number of hours a week the technician is not making service calls. A technician works 40 hours a week.
g. The total cost per hour for the service operation
Do you agree with AEI management that one technician meet the average three-hour service call guarantee?(The average time a customer spends in the waiting line is the average time for the service technician to complete all previous service call commitments and be ready to travel to the new customer. Since the average travel time is 1 hour for the service technician to reach the new customer's office, the total customer waiting time is Wq + 1)
5. What is your recommendation for the number of service technicians to hire when AEI expands to 20 customers? Use the information that you developed in part (4) to justify your answer.
6. What is your recommendation for the number of service technicians to hire when AEI expands to 30 customers? Use the information that you developed in part (4) to justify your answer.
7. What are the annual savings of your recommendation in part (6) compared to the planning committee's proposal that 30 customers will require three service technicians? Assume 250 days of operation per year.
Case Study 2 - Speedy Tires
Salem, the Transport Manager at Speedy Tires, has just returned from a meeting with the Managing Director. Apparently the police received complaints from local residents about the parking of heavy trucks in the side streets near the factory. This is occurring because there is insufficient room in the depot for trucks to wait to be loaded/unloaded.
To reduce the congestion it has been suggested a second bay be built. However, before this is done a simulation of the current system is to be developed and you have been asked to take on this project.
Your first task was a data collection exercise, and this gave you the following information:
(i) The depot is open from 08:00 to 18:00 Sundays to Thursdays.
(ii) Trucks require either loading or unloading (not both).
|
Type of Service
|
Frequency (%)
|
|
Loading
|
70
|
|
Unloading
|
30
|
(iii) The frequency distribution of the loading/unloading operations found by timing a large number of trucks were shown in the following tables.
|
Loading Time (min)
|
Frequency (%)
|
|
0 to under 30
|
20
|
|
30 to under 40
|
35
|
|
40 to under 50
|
22
|
|
50 to under 60
|
15
|
|
60 to under 70
|
8
|
|
Unloading Time (min)
|
Frequency (%)
|
|
0 to under 30
|
30
|
|
30 to under 40
|
40
|
|
40 to under 50
|
25
|
|
50 to under 60
|
4
|
|
60 to under 70
|
1
|
The frequency distribution of the inter-arrival time; that is, the time between successive arrivals, was shown in the following table.
|
Inter-arrival Time (min)
|
Frequency (%)
|
|
0 to under 10
|
15
|
|
10 to under 20
|
40
|
|
20 to under 30
|
30
|
|
30 to under 40
|
5
|
|
40 to under 50
|
5
|
|
50 to under 60
|
3
|
|
60 to under 70
|
2
|
You have also made the following assumptions:
(i) A second bay would be used like the first, that is, loading and unloading.
(ii) A single queue of trucks would form and a truck could use either bay on a first-come, first-served basis.
Required:
1. Explain why simulation is a better method than experimenting on the real system for this problem.
2. Using the random numbers which will be e-mailed to each group separately, manually simulate the depot operations with one bay and find the average waiting time of the 10 trucks?DO NOT USE EXCEL.
3. Repeat the simulation using 2 bays.
Case Study - Local Bank
A local bank has a single drive-through window with arrival times and service times that follow the distributions from the following tables:
|
Time between arrivals (min)
|
(%)
|
|
1
|
15
|
|
2
|
24
|
|
3
|
27
|
|
4
|
22
|
|
5
|
12
|
|
Service Time (min)
|
Unloading Frequency (%)
|
|
1
|
15
|
|
2
|
35
|
|
3
|
22
|
|
4
|
28
|
Use Excel (RAND, LOOKUP, Data Tables) to simulate the arrival of 200 customers to compute each of the following measures:
a) Average time a customer waits for service
b) Average time a customer is in the system (wait plus service time)
c) Percentage of time the server busy with customers (utilization factor)
Replicate each measure 20 times to compute the average.