Name:______ID:______
Production Management 73-604 Fall 2000
Faculty of Business Administration
University of Windsor
Midterm Exam 1 Solution
Thursday, October 5, 6:00 – 8:00 pm
Instructor: Mohammed Fazle Baki
Aids Permitted: Calculator, straightedge, and a one-sided formula sheet.
Time available: 2 hours
Instructions:
· This exam has 11 pages.
· Please be sure to put your name and student ID number on each page.
· Show your work.
Grading:
Question Marks:
1 /5
2 /5
3 /4
4 /4
5 /7
6 /5
7 /12
8 /8
Total: /50
Question 1: (5 points)
True/False Questions (1 point each)
1.1 The idea of Supply-Chain Management is to apply a total system approach to managing the entire flow of information, materials, and services from raw-materials suppliers through factories and warehouses to the end users.
Answer: True
1.2 We should match Functional Products with a Responsive supply-chain.
Answer: False
1.3 Capacity can be defined in a production management context as the amount of resource inputs available relative to output requirements over a particular period of time.
Answer: True
1.4 Typically, Master production Schedule is prepared before Aggregate Production Plan.
Answer: False
1.5 When considering the frequency of production capacity additions we need to consider the two costs of upgrading too frequently with the costs of upgrading too infrequently.
Answer: True
Question 2: (5 points)
Multiple Choice Questions (1 point each)
2.1 Which of the following products includes fashionable cloths and personal computers that typically have a life cycle of just a few months?
a. Functional products
b. Innovative products
c. Bullwhip products
d. Value density products
2.2 When adding production capacity to a plant, which of the following issues should be considered?
a. Maintaining system balance
b. The frequency of capacity additions
c. Use of external capacity
d. All of the above
2.3 Which of the following statements about bottlenecks is best?
a. Bottlenecks are created by uniform demand.
b. When capacities are perfectly balance, it can be said that every operation is a bottleneck.
c. Increasing bottleneck capacity does not increase plant capacity.
d. Bottlenecks are most likely to occur in a plant that produces functional products.
2.4 Capacity decisions are usually linked with other decision areas. If a system is well balanced, which of the following changes requires a larger capacity cushion?
a. A new technology results in a faster production process.
b. Schedules for production are more stable.
c. The company promises faster delivery times to customers.
d. The capital intensity of the process is increased.
2.5 Matching the production rate to the order rate by hiring and laying off employees as the order rate varies is which of the following Production Planning Strategies?
a. Stable workforce, with overtime
b. Stable workforce, with subcontract
c. Chase
d. Level
Question 3 (4 points)
The manager of a custom manufacturer has just completed an order of two large turbines. The first unit took 30,000 direct labor hours and the second one required only 27,000 hours. Next month 4 units will be produced. Estimate the number of direct labor hours required next month. The following table reproduces some parts of Exhibits 2.5 and 2.6.
Unit / Unit Improvement Factor / Cumulative Improvement Factor80% / 85% / 90% / 95% / 80% / 85% / 90% / 95%
1 / 1.0000 / 1.0000 / 1.0000 / 1.0000 / 1.0000 / 1.0000 / 1.0000 / 1.0000
2 / 0.8000 / 0.8500 / 0.9000 / 0.9500 / 1.8000 / 1.8500 / 1.9000 / 1.9500
3 / 0.7021 / 0.7729 / 0.8462 / 0.9219 / 2.5021 / 2.6229 / 2.7462 / 2.8719
4 / 0.6400 / 0.7225 / 0.8100 / 0.9025 / 3.1421 / 3.3454 / 3.5562 / 3.7744
5 / 0.5956 / 0.6857 / 0.7830 / 0.8877 / 3.7377 / 4.0311 / 4.3392 / 4.6621
6 / 0.5617 / 0.6570 / 0.7616 / 0.8758 / 4.2994 / 4.6881 / 5.1008 / 5.5380
7 / 0.5345 / 0.6337 / 0.7439 / 0.8659 / 4.8339 / 5.3217 / 5.8447 / 6.4039
8 / 0.5120 / 0.6141 / 0.7290 / 0.8574 / 5.3459 / 5.9358 / 6.5737 / 7.2612
Answer1
Rate of learning is 27,000/30,000 = 0.90 » 90% (1 point)
Unit Labor hour required
3 30,000(0.8462)
4 30,000(0.8100)
5 30,000(0.7830)
6 30,000(0.7616) (2 points)
Total 30,000(0.8462+0.8100+0.7830+0.7616) = 30,000(3.2008) = 96,024 hrs (1 point)
Answer 2
Rate of learning is 90% (1 point)
Cumulative number of hours required to produce
first 6 units = 30,000(5.101) = 153,030 hrs (1 point)
first 2 units = 30,000(1.900) = 57,000 hrs (1 point)
units 3, 4, 5, 6 = 96,030 hrs (1 point)
Question 4 (4 Points)
Kelly construction wants to get in on the boom of student condominium construction. The company must decide whether to purchase enough land to build a 100-, or 300-unit condominium complex. Many other complexes are currently under construction, so Kelly is unsure how strong demand for its complex will be. If the company is conservative and builds only a few units, it loses potential profits if the demand turns out to be high. On the other hand, many unsold units would be costly to Kelly. The net dollar returns associated with low and high levels of demand are shown below.
Decision
/Demand
Low
/High
Build 100
/ $400,000 / $400,000Build 300 / -200,000 / 1,200,000
If P(Low) = 0.55, and P(High) = 0.45
a. (1 point) What is the maximum expected net dollar return?
b. (1 point) Which decision will maximize the expected net dollar return?
c. (2 points) Construct a decision tree.
Answer
Expected net dollar return, Build 100 = 0.55(400,000) + 0.45(400,000) = $400,000
Expected net dollar return, Build 300 = 0.55(-200,000) + 0.45(1200,000) = $430,000
Hence, maximum expected net dollar return = $430,000 (1 point)
Build 300 maximizes expected net dollar return. (1 point)
Question 5 (7 points)
Your manager has given you two forecasting models and asks you to determine which one to use, if any. Using the models on the last 4-month period, you find the following forecasts.
Month /Actual Demand
/ ForecastMethod 1 / Method 2
1 / 190 / 174 / 180
2 / 220 / 179 / 189
3 / 205 / 191 / 207
4 / 210 / 195 / 215
For each method, compute MAD and tracking signal. Comment on which method to use, if any. Assume that acceptable limit of the TS value is ±3.0.
Method 1
Month / Forecast / Actual / Deviation / RSFE(1 point) / Abs Dev / Sum(Abs Dev) / MAD
(1 point) / TS
(1 point)
1 / 174 / 190 / 16 / 16 / 16 / 16 / 16.00 / 1.00
2 / 179 / 220 / 41 / 57 / 41 / 57 / 28.50 / 2.00
3 / 191 / 205 / 14 / 71 / 14 / 71 / 23.67 / 3.00
4 / 195 / 210 / 15 / 86 / 15 / 86 / 21.50 / 4.00
Method 2
Month / Forecast / Actual / Deviation / RSFE(1 point) / Abs Dev / Sum(Abs Dev) / MAD
(1 point) / TS
(1 point)
1 / 180 / 190 / 10 / 10 / 10 / 10 / 10.00 / 1.00
2 / 189 / 220 / 31 / 41 / 31 / 41 / 20.50 / 2.00
3 / 207 / 205 / -2 / 39 / 2 / 43 / 14.33 / 2.72
4 / 215 / 210 / -5 / 34 / 5 / 48 / 12.00 / 2.83
Method 2 has less MAD than Method 1. Furthermore, TS for Method 2 is 2.83. If acceptable limit of the TS value is ±3.0, Method 2 can be accepted. (1 point)
Question 6 (5 points)
Here are the data for the past 4 months of actual sales of a particular product:
Month / Actual Demand1 / 100
2 / 103
3 / 104
4 / 107
Calculate the exponential smoothing with trend component forecast for months 2-4 using an initial trend forecast (T1) of 2, an initial exponential smoothing forecast (F1) of 98, an a of 0.30, and a d of 0.30.
Answer
Month, t / Actual, At / Ft / Tt / FITt1 / 100 / 98 / 2 / 100.00
2 / 103 / 100.00 + 0.30(100-100.00) = 100.00(1 point) / 2.00+0.30(100.00-100.00) = 2.00(1 point) / 102.00(1 point)
3 / 104 / 102.00 + 0.30(103-102.00) = 102.30 / 2.00+0.30(102.30-102.00) = 2.09 / 104.39
4 / 107 / 104.39 + 0.30(104-104.39) = 104.27 / 2.09+0.30(104.27-104.39) = 2.06 / 106.33(2 points)
Question 7 (12 points)
Use regression analysis on deseasonalized demand to forecast demand in fall 2000, given the following historical demand data:
Year /Season
/ Actual Demand1998 / Winter / 49
Spring
/ 36Summer / 44
Fall / 31
1999 / Winter / 33
Spring / 22
Summer / 28
Fall / 18
Answer
1. Seasonal factors / 2. Desea- / 3. Regressionx / y / Average / Seasonal / sonalized / x*Deseaso- / x^2
from same / factor / demand / nalized
quarterly / demand
period
1 / 49 / 41.0 / 1.257 / 39.0 / 39.0 / 1
2 / 36 / 29.0 / 0.889 / 40.5 / 81.0 / 4
3 / 44 / 36.0 / 1.103 / 39.9 / 119.6 / 9
4 / 31 / 24.5 / 0.751 / 41.3 / 165.1 / 16
5 / 33 / 1.257 / 26.3 / 131.3 / 25
6 / 22 / 0.889 / 24.8 / 148.5 / 36
7 / 28 / 1.103 / 25.4 / 177.6 / 49
8 / 18 / 0.751 / 24.0 / 191.8 / 64
Total / 36 / 261 / 1053.91414 / 204
Average / 4.5 / 32.625
n / 8
b / -2.9
a / 45.5
4. Projection / 5. Reseasonalize
x / Deseasona- / Seasonal / Forecast
lized demand / Factor
9 / 19.7 / 1.257 / 24.76
10 / 16.8 / 0.889 / 14.96
11 / 14.0 / 1.103 / 15.41
12 / 11.1 / 0.751 / 8.33
Common mistakes:
· Incorrect seasonal factors (-1)
· Using regression on actual demand instead of deseasonalized demand (-3)
· Replacing regression by another technique (-2)
· Missing or incorrect projection (-2)
· Missing or incorrect reseasonalization (-2)
Question 8 (8 points)
Harold Grey owns a small farm in Salinas Valley that grows apricots. The apricots are dried on the premises and sold to a number of large supermarket chains. Based on past experience and committed contracts, he estimates that sales over the next three years in thousands of packages will be as follows:
Year / Forecasted Demand (thousands of packages)1 / 300
2 / 120
3 / 200
Assume that Grey currently has 3 workers on the payroll. He estimates that he will have 20,000 packages on hand at the end of the current year. Assume that, on the average, each worker is paid $25,000 per year and is responsible for producing 30,000 packages. Inventory costs have been estimated to be 4 cents per package per year, and shortages are not allowed.
Based on the effort of interviewing and training new workers, Farmer Grey estimates that it costs $500 for each worker hired. Severance pay amounts to $1,000 per worker.
a. (2 points) Assuming that shortages are not allowed, determine the minimum constant workforce that he will need over the next three years.
b. (6 points) Evaluate the cost of the plan found in part (a).
Answer
Computation of the workforce required for avoiding shortages (2 points)Year / Forecast / Beginning / Production / Cumulative / Cumulative / Workers
Inventory / Requirement / Production / Units produced / Required
Requirement / Per worker
1 / 300000 / 20000 / 280000 / 280000 / 30000 / 10
2 / 120000 / 120000 / 400000 / 60000 / 7
3 / 200000 / 200000 / 600000 / 90000 / 7
Workers hired / 7 / Initial hiring cost / 3500 / (1 point)
Workers fired / 0 / Initial firing cost / 0
Total workers / 10 / Initial recruitment cost / 3500
Straighttime cost / 750000
(1 point)
Computation of cost
Year / Forecast / Beginning / Actual / Ending / Inventory
Inventory / Production / Inventory / Holding cost
1 / 300000 / 20000 / 300000 / 20000 / 800
2 / 120000 / 20000 / 300000 / 200000 / 8000
3 / 200000 / 200000 / 300000 / 300000 / 12000
(1 point) / (1 point) / (1 point)
Total cost / 774300 / (1 point)
10