A critical dimension of the service quality of a call center is the wait time of a caller to get to a sales representative. Periodically, random samples of 6 customer calls are measured for time. Results from the last five samples are shown in the table.
Observation (seconds)
Sample
1
2
3
4
5
6
1
435
408
422
436
410
401
2
440
410
431
427
422
430
3
400
426
419
424
433
425
4
411
406
395
442
436
410
5
408
407
407
435
411
405
a) Management is willing to use three-sigma limits. Using the factors in Table 5.1, determine upper and lower limits for mean and range charts.
b) Plot sample means and ranges on their respective control charts. Is the process in control?
2. (Chapter 6) Larry’s Wickets, Inc. is producing two types of products: A and B. Both are produced at the same machining operation. The machines operate on two 8-hour shifts, 5 days per week, and 50 weeks per year. The manager wants to maintain a 20 percent capacity cushion. Because of demand uncertainties, the operations manager obtained three demand forecasts (pessimistic, expected, and optimistic). The demand forecasts, lot sizes, processing times, and setup times are given in the below table. Determine the minimum, expected, and maximum number of machines needed.
Time Standards
Demand Forecast
Product
Processing (hr/unit)
Setup (hr/lot)
Lot Size (units/lot)
Pessimistic
Expected
Optimistic
A
0.30
1
200
100,000
120,000
150,000
B
0.25
2
100
190,000
210,000
230,000
3. (Chapter 7) The figure below shows the process for paying tuition at a major university. Students are provided their bill for the next term for review, and then routed to different tables for questions to be answered before finally paying their tuition at E. The numbers in parentheses are the times in minutes for each step of the process.
a) What is the capacity for the A-B-C-E process route?
b) What is the capacity for the A-B-D-E process route?
c) If 60% of the students are routed to C and 40% are routed to D, what is the average capacity per hour for the process?
d) Where would you expect student wait times to occur? Why?
Please explain your solutions clearly.
4. (Chapter 15) Complete the MPS record in Figure 15.27 on page 569 of your textbook. Explain how you determined projected on-hand inventory, MPS quantity, and MPS start.
A
(2)
C
(6)
D
(10)
E
(4)
B
(5)
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To answer these questions, we will use the given information and apply relevant concepts and formulas from the specified chapters. Let's go step by step.
1a) To determine the upper and lower limits for mean and range charts, we need to calculate the mean and range for each sample.
Mean Chart:
1. Calculate the average of each sample by adding up the seconds and dividing by 6:
Sample 1 mean = (435 + 408 + 422 + 436 + 410 + 401) / 6 = 419.67
Repeat this calculation for the other samples.
2. Calculate the overall mean by taking the average of all sample means:
Overall mean = (mean of sample 1 + mean of sample 2 + mean of sample 3 + mean of sample 4 + mean of sample 5) / 5
Range Chart:
1. Calculate the range for each sample by subtracting the minimum value from the maximum value:
Sample 1 range = 436 - 401 = 35
Repeat this calculation for the other samples.
2. Calculate the overall range by taking the average of all sample ranges:
Overall range = (range of sample 1 + range of sample 2 + range of sample 3 + range of sample 4 + range of sample 5) / 5
Now that we have the means and ranges, we can calculate the control limits using the factors in Table 5.1. The control limits for the mean chart are given by:
Upper limit = Overall mean + (3 * A2 * Overall range)
Lower limit = Overall mean - (3 * A2 * Overall range)
The control limits for the range chart are given by:
Upper limit = D4 * Overall range
Lower limit = D3 * Overall range
The values of A2, D3, and D4 can be found in Table 5.1 in your textbook.
1b) To plot the sample means and ranges on their respective control charts, you would typically set up the x-axis for the mean chart to represent the sample number (1-5 in this case) and the y-axis to represent the mean values. You would then plot the mean values and connect them with a line.
Similarly, for the range chart, you would set up the x-axis to represent the sample number and the y-axis to represent the range values. Again, you would plot the range values and connect them with a line.
To determine if the process is in control, you need to check if the plotted points fall within the calculated control limits. If most of the points are within the control limits and there is no obvious pattern or trend, then the process is considered in control. If any points fall outside the control limits or exhibit patterns, further investigation may be needed.
2. To determine the minimum, expected, and maximum number of machines needed, we can use the following formulas:
Minimum number of machines = (Optimistic demand forecast * Lot size) / (8 hours per shift * 5 days per week * 50 weeks per year)
Expected number of machines = (Expected demand forecast * Lot size) / (8 hours per shift * 5 days per week * 50 weeks per year)
Maximum number of machines = (Pessimistic demand forecast * Lot size) / (8 hours per shift * 5 days per week * 50 weeks per year)
Substitute the values from the given table into the formulas to calculate the minimum, expected, and maximum number of machines for products A and B.
3a) To determine the capacity for the A-B-C-E process route, we need to sum up the times for each step in the process. The capacity can be calculated as the inverse of the total time required for one complete cycle:
Capacity = 1 / (A + B + C + E)
Substitute the given times into the formula to calculate the capacity for the A-B-C-E process route.
3b) To determine the capacity for the A-B-D-E process route, follow the same steps as in part 3a, but include the time for step D in the calculation.
3c) To calculate the average capacity per hour for the process when 60% of the students are routed to C and 40% are routed to D, you can use the following formula:
Average capacity per hour = (60% * capacity of A-B-C-E route) + (40% * capacity of A-B-D-E route)
Substitute the calculated values from parts 3a and 3b into the formula to find the average capacity per hour.
3d) Student wait times would most likely occur at steps C and D, as these are the tables where the questions are answered before students can proceed to pay their tuition at step E. These steps involve interaction and potential delays due to the number of students, complexity of questions, and available staff.
4. To complete the MPS record in Figure 15.27, you would need to determine the projected on-hand inventory, MPS quantity, and MPS start for each item.
Projected on-hand inventory can be calculated by subtracting the forecasted demand from the beginning inventory for each period.
MPS quantity is the planned production quantity for each period, which can be determined based on factors such as demand, safety stock, and production capacity.
MPS start refers to the beginning of the planned production period. It can be calculated by subtracting the lead time (time required for production and delivery) from the period start date.
By using the given information in Figure 15.27 and applying the relevant concepts from Chapter 15, you can calculate the projected on-hand inventory, MPS quantity, and MPS start for each item.