Quality Management - Sampling and Tolerance Acceptance
1. The temperature control of the dying process of the ABC Textile Company has to be controlled. The target temperature is 140 degrees F. A +/- 5 degrees can be tolerated. The company's goal is to have 99.7% of all dyeing processes be within the acceptable temperature range. The process statistics show that standard deviation of the dye process temperature to be 2.14 degrees. Evaluate the process capability.
2. The temperature control of the dying process of the ABC Textile Company has to be controlled. The target temperature is 140 degrees F. A +/- 5 degrees can be tolerated. The company's goal is to have 99.7% of all dying processes be within the acceptable temperature range. The process statistics show that standard deviation of the dye process temperature to be 2.14 degrees and the mean temperature in reality 142 degrees instead of 140. Evaluate the process capability provided that the tolerance of the temperature requirement is non-bias (i.e. below specification is just as bad as above). What if the process is more tolerable for lower-than-specification temperature than otherwise? Would your conclusion be different? Show your evaluation based on the reliance of the process capability index.
3. BHC produces bags of cement. The stated weight for a bag of cement is 100 lbs. Customers will accept an occasional bag weighing as little as 98 lbs. as long as the average weight is at least 100 lbs. At the same time, BHC doesn't want to give away cement, so it has set an upper tolerance limit of close to 102 lbs. Such setting results in the current filling process having an actual process mean of 101 lbs. and a standard deviation of 0.7 lb.
a. Does the company have the capability of meeting the tolerance limits more than 99.7% of the time? Show your computations and briefly explain your calculated results.
b. Now suppose BHC re-centers the manufacturing process so that the process mean is exactly 100 lbs, while the standard deviation remains the same. Calculate the process capability ratio. Is the process still capable of meeting the tolerance limits more than 99.7% of the time? Show your calculation and briefly explain your answer.
Project Management - Program Evaluation and Review Technique (PERT)
1. What is the earliest that activity D can start if A is 3 days, B is 5, days C is 7 days, and D is 4 days long?
2. What is the latest that activity B can start if A is 3 days, B is 5, days C is 7 days, and D is 4 days long?
3. By which time can activity D be completed if A is 3 days, B is 5, days C is 7 days, and D is 4 days long?
4. The project has activity lengths in days, precedence and crash costs as shown in the table below. Evaluate the project by mapping out the network, computing the ES/EF and LS/LF times for all activities, identifying the critical path, and the slack that each activity may have. What is the cheapest completion cost for the project if the contractor must complete all work in 45 days?
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Activity
|
Duration (Days)
|
Precedence
|
Max # Days of Reduction
|
Crash Cost per Day
|
|
A
|
10
|
None
|
2
|
$250
|
|
B
|
16
|
A
|
4
|
$400
|
|
C
|
12
|
A
|
3
|
$100
|
|
D
|
17
|
B, C
|
1
|
$320
|
|
E
|
14
|
B
|
1
|
$300
|
|
F
|
6
|
D, E
|
2
|
$350
|
Inventory Management
1. Ollah's Organic Pet Shop sells about 4,000 bags of free-range dog biscuits every year. The fixed ordering cost is $15, and the cost of holding a bag in inventory for a year is $2. What is the economic order quantity for the biscuits?
Suppose Ollah decides to order 200 bags at a time while keeping a safety stock at the level of 100 units. What would the total ordering and holding costs for the year be?
2. Pam runs an e-Bay business for gym equipment. Annual demand for the TricoFlexers is 16,000. Pam is currently paying $30 per unit. The annual holding cost per unit is 15% of its cost, and the cost to place an order is $500. In order to save some ordering cost, Pam currently orders 4,000 units each time. What is the total inventory cost to Pam?
Pam's friend, who is an MBA, suggests her to consider using the EOQ as the ordering size. What is the economic order quantity for Pam based on the current demand and costs? Will changing from the current order size to EOQ save her some inventory expenses?
Assuming the same holding and ordering costs, suppose demand is now changed to 32,000. Will the EOQ be different? Is it going to be double? Why or why not?
The manufacturer of TricoFlexers has agreed to offer Pam a price discount of 1% if she buys 8,000 units each time. Assuming annual demand is still 16,000 units and that the holding cost per unit remains the same as normal, should Pam order based on the discount-order size?
Waiting-Line Questions
1. Wong runs a small hot dog stand in downtown Miami. On average, it takes Wong 2 minutes to serve a hot dog. During lunchtime, customers randomly arrive at the rate of one per five minutes.
Required:
a. On average, how many customers are in the hot dog stand and how many are waiting to be served?
b. On average, how much time, in minutes, does a customer spend at the hot dog stand?
c. On average, how much time, in minutes, does a customer have to wait for service?
2. The following arrival and service data were taken from one of the groups' class projects. Table 1 is sample arrival data capturing the number of cars arrived per each 5-minute interval. Table 2 is sample service data capturing the number of seconds a service station spent on servicing each car.
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Table 1
|
|
Table 2
|
|
Interval of 5 min
|
# of Cars
|
Service #
|
Service Time
(sec)
|
|
1
|
5
|
1
|
56
|
|
2
|
4
|
2
|
67
|
|
3
|
3
|
3
|
59
|
|
4
|
5
|
4
|
32
|
|
5
|
3
|
5
|
35
|
|
6
|
5
|
6
|
37
|
|
7
|
4
|
7
|
6
|
|
8
|
1
|
8
|
4
|
|
9
|
1
|
9
|
64
|
|
10
|
2
|
10
|
55
|
Based on the sample data provided in Table 1 and Table 2, complete the 'Answer' column of the following:
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|
Supporting Work
|
Answer
|
|
Utilization
|
ρ
|
|
|
Arrival Rate
|
λ
|
|
|
Service Rate
|
µ
|
|
|
Average Customers in System
|
Cs
|
|
|
Average Customers in Waiting
|
Cw
|
|
|
Average Time Spent in System (in seconds)
|
|
|
Average Time Spent in Waiting (in seconds)
|
|