Name:______ID:______

Production Management 73-604 Fall 2007

Odette School of Business

University of Windsor

Midterm Exam 1 Solution

Thursday, October 11, 5:30 pm – 6:50 pm

Instructor: Mohammed Fazle Baki

Aids Permitted: Calculator, straightedge, and a one-sided formula sheet.

Time available: 1 hour 20 minutes

Instructions:

  • This exam has 12 ages including this cover page.
  • Please be sure to put your name and student ID number on each page.
  • Show your work.

Grading:

QuestionMarks:

1/10

2/7

3/8

4/10

5/15

6/15

Total:/65

Question 1: (10 points) Multiple choice questions: circle the most appropriate answer

1.1In working to a solution to a Decision Tree problem, we start at the ______of the tree and calculate ______.

  1. start, forward
  2. start, backwards
  3. end, forward
  4. end, backwards

1.2Chance nodes in a Decision Tree is

  1. rectangular
  2. square
  3. circular
  4. triangular

1.3(i) Capacity can be defined as the ability to hold, receive, store, or accommodate. (ii) The capacity utilization rate is found by dividing Best Operating Level by Capacity used.

  1. (i) true, (ii) false
  2. (i) false, (ii) true
  3. Both true
  4. Both false

1.4If the payoff of selecting Machine A is $46,000 with a probability of 90% and the payoff of selecting Machine B is $80,000 with a probability of 50%, which machine would you select if maximizing payoff is your objective?

  1. Machine A
  2. Machine B
  3. Both
  4. None

1.5We should match ______products with a ______supply-chain.

  1. functional, responsive
  2. functional, efficient
  3. innovative, effective
  4. innovative, efficient

1.6Demand for products or services can be broken down into which of the following components of demand?

  1. Random variation
  2. Autocorrelation
  3. A trend
  4. All of the above

1.7(i) RSFE stands for Readable Safety Function for Error detection. (ii) MAD statistics can be used to generate Tracking Signals.

  1. (i) true, (ii) false
  2. (i) false, (ii) true
  3. Both true
  4. Both false

1.8Maintaining a stable workforce working at a constant output rate while shortages and surpluses are absorbed by fluctuating inventory levels, order backlogs and allowing lost sales is which of the following Production Planning Strategies?

  1. Stable workforce, variable work hours
  2. Chase
  3. Level
  4. All of the above

1.9Linear Programming (LP) is appropriate to Aggregate Planning if the cost and variable relationships are ______and demand can be treated as ______.

  1. linear, stochastic
  2. non-linear, deterministic
  3. linear, deterministic
  4. non-linear, stochastic

1.10An Exponential Smoothing method requires which of the following pieces of data to forecast the future?

  1. The most recent forecast
  2. The actual demand that occurred for a forecasted future period
  3. The value of the smoothing constant Alpha
  4. All of the above

Question 2: (7 points)

Alpha Computer Products competed for and won a contract to produce two prototype units of a new type of computer that is based on laser optics rather than on electronic binary bits. The first unit produced by Alpha took 6,000 hours to produce and required $200,000 worth of materials, equipment usage, and supplies. The second unit took 5,400 hours and used $160,000 worth of materials, equipment usage, and supplies. Labor is $30 per hour. Alpha was asked to present a bid for 3 additional units as soon as the second unit was completed. Production would start immediately. What would this bid be? The following table reproduces some parts of Exhibits 2.5 and 2.6.

Unit / Unit Improvement Factor / Cumulative Improvement Factor
80% / 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

Rate of learning for labor hour = (1 point)

Rate of learning for materials, equipment usage and supplies = (1 point)

Unit / Labour hour
(1 point) / Materials, equipment usage and supplies (1 point)
3 / 6,000  0.8462 = / $5,077.2 / 200,000  0.7021 = / $140,420
4 / 6,000  0.8100 = / 4,860.0 / 200,000  0.6400 = / 128,000
5 / 6,000  0.7830 = / 4,698.0 / 200,000  0.5956 = / 119,120
Total
(1 point) / 14,635.2 / 387,540

The total labor cost = 14,635.2  30 = $439,056.0 (1 point)

Materials, equipment usage and supplies are 387,540.0

Hence, the total cost = $826,596.0 (1 point)

Alternate solution

Labour hour = 6,000(4.3392-1.9000) = 14,635.2

Materials, equipment usage and supplies = 200,000(3.7377-1.8000) = $387,540.

Question 3: (8 points)

Observed weekly sales of ball peen hammers at the town hardware store over a five-week period have been 16, 12, 28, 24, 32.

  1. (3 points) Suppose that three-week moving averages are used to forecast sales, Determine the one-step-ahead forecasts for weeks 4 and 5.
  1. (3 points) Suppose that exponential smoothing is used to with a smoothing constant of Find the exponential smoothing forecasts for weeks 4 and 5. (To get the method started, use the same forecast for week 4 as you used in part a.)
  1. (2 points) Based on the MAD, which method did better?

Thus, moving average is better.

Question 4: (10 points)

Lakeroad, a manufacturer of hard disks for personal computers, was founded in 2005 and has sold the following number of disks:

Year / Numbers Sold (in 000s)
2005 / 24
2006 / 35
2007 / 47
  1. (7 points) Calculate the exponential smoothing with trend component forecast for years 2006 and 2007 using an initial trend forecast (T1) of 12, an initial exponential smoothing forecast (F1) of 13, an  of 0.20, and a  of 0.20.

Yeart / Actual At / Ft / Tt / FITt
2005 / 24 / 13 / 12 / 13+12= 25.00
2006 / 35 / 0.20(24)+0.80(25) = 24.80
(2 points) / 0.20(24.80-13)+0.80(12) = 11.96
(2 points) / 24.80+11.96 = 36.76(2 points)
2007 / 47 / 0.20(35)+0.80(36.76)= 36.408 / 0.20(36.408-24.80)+0.80(11.96)= 11.89 / 36.408+11.89 = 48.298(1 point)
  1. (3 points) What is the sales forecast for the year 2009 made at the end of 2007?
Question 5: (15 points)

Use regression analysis on deseasonalized demand to forecast demand in Fall 2007, given the following historical demand data:

Year /

Season

/ Actual Demand
2005 / Winter / 61

Spring

/ 77
Summer / 79
Fall / 64
2006 / Winter / 69
Spring / 86
Summer / 90
Fall / 76

Quarterly average demand = (61+77+79+64+69+86+90+76)/8 = 75.25

Season / Average demand / Seasonal Index
Winter / (61+69)/2 = 65.0 / 65.0/75.25 = 0.8640
Spring
/ (77+86)/2 = 81.5 / 81.5/75.25 = 1.0830
Summer / (79+90)/2 = 84.5 / 84.5/75.25 = 1.1230
Fall / (64+76)/2 = 70.0 / 70.0/75.25 = 0.9300
4.0000
Period
/
Demand
/ Deseasonalized Demand
/ /
1 / 61 / 70.6 / 70.6 / 1
2 / 77 / 71.1 / 142.2 / 4
3 / 79 / 70.4 / 211.1 / 9
4 / 64 / 68.8 / 275.2 / 16
5 / 69 / 79.9 / 399.4 / 25
6 / 86 / 79.4 / 476.4 / 36
7 / 90 / 80.1 / 561.0 / 49
8 / 76 / 81.7 / 653.6 / 64
=36 / =602.0 / =2789.5344 / =204
=4.5 / =75.25

Forecast, fall 2007, reseasonalized = 89.6313(0.9300) = 83.3571

Question 6 (15 points)

Mr. Meadows Cookie Company makes a variety of chocolate chip cookies in the plant in Albion, Michigan. Based on orders received and forecasts of buying habits, it is assumed that the demand for the next three months is 1100, 1300 and 1000, expressed in thousands of cookies. During a 50-day period when there were 150 workers, the company produced 2.5 million cookies. Assume that the numbers of workdays over the three months are respectively 25, 20 and 21. There are currently 70 workers employed. Beginning inventory is 100 thousand and it is required that there be at least 200 thousand units in the inventory at the end of three months.

  1. (9 points) What is the minimum constant workforce required to meet demand (i.e., shortages not allowed) over the next three months?

Productivity = 2.5/50/150 = 333.33 cookies/worker/day

Month / Net Production Required
(000) / Cumulative net production required
(000) / #Days
Per Month / Production
Per Worker / Cumulative
Production
Per Worker / # of Workers Needed
1 / 1100-100
=1000 / 1000 / 25 / 8333.33 / 8333.33 /
2 / 1300 / 2300 / 20 / 6666.67 / 15000.00 /
3 / 1000+200
=1200 / 3500 / 21 / 7000.00 / 22000.00 /
Maximum / 160

Minimum constant workforce = 160 workers

  1. (6 points) Assume that the inventory holding cost is 15 cents per cookie per month, hiring cost is $200 per worker, and firing cost is $300 per worker. Evaluate the cost of the plan derived in a.

Month / Beginning Inventory
(000) / Production
Per Worker / Production by 160 workers
(000) / Demand
(000) / Ending Inventory
(000)
1 / 100 / 8333.33 / 1333.3333 / 1100 / 100+1333.33-1100 = 333.33
2 / 333.33 / 6666.67 / 1066.6667 / 1300 / 333.33+1066.66-1300=100
3 / 100 / 7000.00 / 1120.0000 / 1000 / 100+1120-1000=220
Total = 653.3333

Number of workers hired = 160-70 = 90 workers

Hiring cost = 90(200) = $18,000

Inventory holding cost = 653.3333(1000)(0.15) = $98,000

Total cost = $18,000+$98,000 = $116,000

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