BMGT 311: Exam 1 Study Guide

Discussion questions: Review all the assigned discussion questions from the back of the chapters.

  1. Name three major contributors to Operations Management and describe their contribution.
  2. What are the basic functions of all firms?
  3. What are the ways in which productivity can be improved?
  4. What are the competitive priorities a firm may pursue?
  5. Describe the characteristics of a Job Shop and an Assembly line.
  6. How would you describe a critical path of a project?
  7. How is slack time of an activity calculated?
  8. What are the three activity times used in a PERT project? How are they used?
  9. How is project variance calculated in a PERT project?
  10. List the qualitative forecasting methods and describe each.
  11. What are advantages and disadvantages of associative forecasting methods?
  12. List and describe the four components of a time series.
  13. Under what condition would exponential smoothing forecast be the same as a naive forecast?
  14. What is the primary purpose of the mean absolute deviation (MAD) in forecasting?
  15. What is the difference between MAD and MAPE?

PROBLEMS

  1. Mabel's Ceramics spent $3000 on a new kiln last year, in the belief that it would cut energy usage 25% over the old kiln. This kiln is an oven that turns "greenware" into finished pottery. Mabel is concerned that the new kiln requires extra labor hours for its operation. Mabel wants to check the energy savings of the new oven, and also to look over other measures of their productivity to see if the change really was beneficial. Mabel has the following data to work with:

The year before / Year just ended
Production (finished units) / 4000 / 4100
Labor (hrs) / 350 / 375
Capital ($) / 15000 / 18000
Energy (kWh) / 3000 / 2600

Also, suppose that the average labor cost is $12 per hour and cost of energy is $0.40 per kwh.

  1. Were the modifications beneficial? (Compute labor, energy, and capital productivity for the two years and compare.)
  2. Compute percentage change in multi-factor productivity of the year just ended from that of year before.
  3. If the multifactor productivity must be restored next year to what is was the year before, assuming the same output next year as the year just ended, by how the input must be reduced from what it is this year?
  1. An Appliance Service company made house calls and repaired 10 lawn-mowers, 2 refrigerators, and 3 washers in an 8-hour day with his standard crew of 3 workers. The retail price for each respective service is $50, $200, and $120. The average wage for the workers is $12 per hour. The materials cost for a day was $200 while the overhead cost was $50.
  2. What is the company’s labor productivity?
  3. What is the multifactor productivity?
  4. How much of a reduction in input is necessary for a 5% increase in multifactor productivity?
  1. Consider the tasks, durations, and predecessor relationships in the following network. Draw the AON network and answer the questions that follow.

Activity Description / Immediate
Predecessor(s) / Optimistic
(Weeks) / Most Likely
(Weeks) / Pessimistic
(Weeks)
A / --- / 4 / 7 / 10
B / A / 2 / 8 / 20
C / A / 8 / 12 / 16
D / B / 1 / 2 / 3
E / D, C / 6 / 8 / 22
F / C / 2 / 3 / 4
G / F / 2 / 2 / 2
H / F / 6 / 8 / 10
I / E, G / 4 / 8 / 12
J / I / 1 / 2 / 3
  1. Schedule the activities of this project and determine (i) the expected project completion time, (ii) the earliest and latest start and finish times, and the slack for all the activities, and (iii) all the critical paths.
  2. What is the probability of completion of the project before week 42?
  3. What is the probability of completion of the project before week 35?
  4. With 99% confidence what is your estimate for the project completion time.
  1. Consider the following project. All activity times are in weeks.

Activity / Immediate
Predecessor(s) / Normal Time / Crash time / Normal cost / Crash cost
A / - / 7 / 4 / 20000 / 38000
B / - / 8 / 5 / 50000 / 74000
C / A / 9 / 7 / 80000 / 110000
D / A, B / 8 / 8 / 30000 / 30000
E / B / 9 / 8 / 10000 / 12000
F / C / 10 / 8 / 90000 / 124000
G / D, E / 5 / 5 / 25000 / 25000
H / E / 10 / 8 / 32000 / 40000
I / F, G / 5 / 4 / 28000 / 35000
  1. Draw an AON network.
  2. Identify all the unique paths from start to finish and determine the critical path, normal project completion time, and normal project cost.
  3. Compute MTR, Cost of crashing/week.
  4. Which activity would you crash first and by how many weeks?
  5. Determine the project time and cost after crashing the activity selected in (d).
  1. Consider the following CPM Solver model.

a)Determine the successor activities in cells I2 to I10.

b)Determine the Excel formulas for the following cells: F2, G2, C15, C18, D18, D21, C25, G19, G16, G15, H15, B27, B28, and B29.

c)What is the Solver Target cell for minimizing the project completion time?

d)What is the Solver changing cell range?

e)What are the Solver constraints?

  1. What is the forecast for May based on a 3-period MA and a weighted 3-period moving average applied to the following past demand data? Let the weights be, 3, 3, and 4 (last weight is for most recent data). Compute MAD and MAPE for both cases and compare.

Nov. / Dec. / Jan. / Feb. / Mar. / April
37 / 36 / 40 / 42 / 47 / 43
  1. Sales of music stands at the local music store over the past ten days are shown in the table below. Forecast demand using exponential smoothing with an of .6 (initial forecast = 16).

a)Compute the forecast for period 11 and the MAD.

b)Compute the tracking signal for periods 1 to 10. What do you recommend for this forecasting process?

t / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
Demand / 13 / 21 / 28 / 37 / 25 / 29 / 36 / 22 / 25 / 28
  1. Weekly sales of copy paper at Cubicle Suppliers are in the table below. Forecast week 8 with a trend projection model.

WeekSales (cases)

117

222

327

432

535

637

741

  1. The quarterly sales for specific educational software over the past three years are given in the following table. Compute the four seasonal indices and find forecast for Year 4 if the annual demand for year 4 is estimated to be 10% more than that of year 3.

YEAR 1 / YEAR 2 / YEAR 3
Quarter 1 / 1690 / 1800 / 1850
Quarter 2 / 940 / 900 / 1100
Quarter 3 / 2625 / 2900 / 2930
Quarter 4 / 2500 / 2360 / 2615
  1. Arnold Tofu owns and operates a chain of 12 vegetable protein "hamburger" restaurants in northern Louisiana. Sales figures and profits for the stores are in the table below. Sales are given in millions of dollars; profits are in hundred thousand dollars. Calculate a regression line for the data. What is your forecast of profit for a store with sales of $24 million? $30 million?

Store / Sales /

Profits

1 / 7 / 15
2 / 2 / 10
3 / 6 / 13
4 / 4 / 15
5 / 14 / 25
6 / 15 / 27
7 / 16 / 24
8 / 12 / 20
9 / 14 / 27
10 / 20 / 44
11 / 15 / 34
12 / 7 / 17

Answers:

1.The energy modifications did not generate the expected savings; labor and capital productivity decreased.

Given data / Last year / Now
Production / 4000 / 4100
Labor / 350 / 375
Capital = / 15000 / 18000
Energy = / 3000 / 2600
Change / Change %
Labor productivity (Units/hr) = / 11.4286 / 10.9333 / -0.4952 / -4.33%
Capital productivity (units/$) = / 0.2667 / 0.2278 / -0.0389 / -14.58%
Energy productivity (Units/KWH) = / 1.3333 / 1.5769 / 0.2436 / 18.27%
Labor cost = Hours x $12 = / 4200 / 4500
Capital $ = / 15000 / 18000
Energy $ = $0.40 x Energy = / 1200 / 1040
Total input $ = / 20400 / 23540
Multifactor productivity (Units/$) = / 0.1961 / 0.1742 / -0.0219 / -11.17%
Target productivity = / 0.1961
Target input = / 20910
Reduction in input needed = 23540 – 20910 = / 2630
#2 / LM / R / W
Number serviced / 10 / 2 / 3
Dollar value/unit / 50 / 200 / 120
Production in $ / 500 / 400 / 360 / 1260 / <-- Total $
Labor hours = 3 workers x 8 hrs. = / 24 / per day
Labor productivity = 1260/24 = / $ 52.50 / per hour of labor
Multifactor productivity
Labor cost = 3x8x$12 = / 288
Material = / 200
Overhead = / 50
Total input cost = / 538 / = 288 + 200 + 50
Productivity = 1260/538 = / $ 2.3420 / per $ input
5% improvement in MF productivity = / 0.1171
Target productivity after 5% improvement = / 2.4591
Input for improved productivity = / $ 512.38 / <-- Output/Productivity = 1260/2.4591
Reduction in input needed = / $ 25.62 / <-- 538 –512.38

3. (a)

Task / a / m / B / t / Variance
A / 4 / 7 / 10 / 7 / 1.0000
B / 2 / 8 / 20 / 9
C / 8 / 12 / 16 / 12 / 64/36
D / 1 / 2 / 3 / 2
E / 6 / 8 / 22 / 10 / 256/36
F / 2 / 3 / 4 / 3
G / 2 / 2 / 2 / 2
H / 6 / 8 / 10 / 8
I / 4 / 8 / 12 / 8 / 64/36
J / 1 / 2 / 3 / 2 / 4/36
Task / t / ES / EF / LS / LF / Slack
Start / 0 / 0
A / 7 / 0 / 7 / 0 / 7 / 0 / Critical
B / 9 / 7 / 16 / 8 / 17 / 1
C / 12 / 7 / 19 / 7 / 19 / 0 / Critical
D / 2 / 16 / 18 / 17 / 19 / 1
E / 10 / 19 / 29 / 19 / 29 / 0 / Critical
F / 3 / 19 / 22 / 24 / 27 / 5
G / 2 / 22 / 24 / 27 / 29 / 5
H / 8 / 22 / 30 / 31 / 39 / 9
I / 8 / 29 / 37 / 29 / 37 / 0 / Critical
J / 2 / 37 / 39 / 37 / 39 / 0 / Critical
Finish / 39 / 39

Critical path =A-C-E-I-J, Project completion time TE = 39

Variance for project completion time = 2p = 1 + 388/36 = 11.7778; p =3.4319

b.For P(T <=42), Z = (42 – 39)/3.4319 = 0.87, Table area = 0.80785, Probability = 0.80785

c. For P(T <=35), Z = (35 – 39)/3.4319 = -1.17, Table area = .879; Probability = 1 - .879 = 0.121

d.Z for 99% confidence = 2.325, T = 39 + 2.325(3.4319) = 46.98

4.

Activity / Normal Time / Crash time / Normal cost / Crash cost / MTR / Crashing cost/week / Predecessor(s)
A / 7 / 4 / 20000 / 38000 / 3 / 6000 / -
B / 8 / 5 / 50000 / 74000 / 3 / 8000 / -
C / 9 / 7 / 80000 / 110000 / 2 / 15000 / A
D / 8 / 8 / 30000 / 30000 / 0 / A, B
E / 9 / 8 / 10000 / 12000 / 1 / 2000 / B
F / 10 / 8 / 90000 / 124000 / 2 / 17000 / C
G / 5 / 5 / 25000 / 25000 / 0 / D, E
H / 10 / 8 / 32000 / 40000 / 2 / 4000 / E
I / 5 / 4 / 28000 / 35000 / 1 / 7000 / F, G
Sum = / 365,000
Paths / Path time
A - C - F - I / 31 / Critical path
A - D - G - I / 25 / Normal project time = 31 weeks
Normal project cost = 365,000
B - D - G - I / 26
B - E - G - I / 27
B - E - H / 27

Activity to crash = A – among the critical activities (A, C, F, I) the crashing cost/week for A is the smallest.

Weeks to crash =Minimum{MTR of A, Project time – time of second longest path}

i.e. =Minimum{3, 31-27} = 3

Project time after crashing A 3 weeks = 31 – 3 = 28 weeks

Project cost after crashing A = 365,000 + 3 x 6,000 = 383,000

5.

(a)

Activity / Successors(s)
A / C, D
B / D, E
C / F
D / G
E / G, H
F / I
G / I
H / Finish
I / Finish

(b)

F2 / B2-C2
G2 / (E2-D2)/F2
C15 / B2-B15
D18 / Max(E15,E16)
E18 / D18+C18
D21 / Max(E18,E19)
C25 / Max(E22,E23)
G19 / Min(F21,F22)
F19 / G19-C19
G16 / Min(F18,F19)
G15 / Min(F17,F18)
H15 / F15-D15 or G15-E15
B27 / Sum(D2:D10)
B28 / Sumproduct(BG15:B23,G2:G10)
B29 / B27+B28

(c)Solver Target cell for minimizing the project completion time = C25

(d)Changing cell range = B15:B23

(e)What are the Solver constraints?

B15:B23 <= F2:F10
B15:B23 = Integer (Optional)

6.

Month / Demand (At) / 3-MA Forecast / |Et| / |Et|/At / Weight / Weighted 3-MA / |Et| / |Et|/At
Nov. / 37 / 3
Dec. / 36 / 3
Jan. / 40 / 4
Feb. / 42 / 37.67 / 4.33 / 0.1031 / 37.90 / 4.1 / 0.0976
Mar. / 47 / 39.33 / 7.67 / 0.1632 / 39.60 / 7.4 / 0.1574
April / 43 / 43.00 / 0 / 0.0000 / 43.40 / 0.4 / 0.0093
Forecast = / 44.00 / MAD = 4 / MAPE = 8.88% / Forecast = / 43.90 / MAD = 3.97 / MAPE = 8.81%

7.

Period / Demand / Ft / Et / |Et| / CFEt / CAEt / MADt / TS
1 / 13 / 16.00 / -3.00 / 3.00 / -3.00 / 3.00 / 3 / -1
2 / 21 / 14.20 / 6.80 / 6.80 / 3.80 / 9.80 / 4.9 / 0.78
3 / 28 / 18.28 / 9.72 / 9.72 / 13.52 / 19.52 / 6.51 / 2.08
4 / 37 / 24.11 / 12.89 / 12.89 / 26.41 / 32.41 / 8.1 / 3.26
5 / 25 / 31.84 / -6.84 / 6.84 / 19.57 / 39.25 / 7.85 / 2.49
6 / 29 / 27.74 / 1.26 / 1.26 / 20.83 / 40.51 / 6.75 / 3.09
7 / 36 / 28.50 / 7.50 / 7.50 / 28.33 / 48.01 / 6.86 / 4.13
8 / 22 / 33.00 / -11.00 / 11.00 / 17.33 / 59.01 / 7.38 / 2.35
9 / 25 / 26.40 / -1.40 / 1.40 / 15.93 / 60.41 / 6.71 / 2.37
10 / 28 / 25.56 / 2.44 / 2.44 / 18.37 / 62.85 / 6.29 / 2.92
F11 = / 27.02 / MAD = / 6.29

8.

Week / Sales / XY / X2
1 / 17 / 17 / 1 / n = / 7 / X2 = / 140
2 / 22 / 44 / 4 / X = / 28 / XY = / 954
3 / 27 / 81 / 9 / Y = / 211 / b = / 3.9286
4 / 32 / 128 / 16 /  = / 4.0000 / a = / 14.4286
5 / 35 / 175 / 25 /  = / 30.14
6 / 37 / 222 / 36
7 / 41 / 287 / 49
28 / 211 / 954 / 140
Regression equation: Ŷ = 14.4286 + 3.9286t
F8 = 14.4286 + 3.9286(8) = / 45.8571

9.

Demand
Quarter / Year 1 / Year 2 / Year 3 / Average / Index
1 / 1690 / 1800 / 1850 / 1780.00 / 0.8823
2 / 940 / 900 / 1100 / 980.00 / 0.4857
3 / 2625 / 2900 / 2930 / 2818.33 / 1.3969
4 / 2500 / 2360 / 2615 / 2491.67 / 1.2350
Overall average = / 2017.50
Year 3 sum = / 8495
Annual demand for year 4 = 1.1 x 8495 =9345
Demand/season =2336
Forecast for year 4
Quarter / Average demand / Seasonal Index / Forecast
1 / 2336 / 0.8823 / 2061
2 / 2336 / 0.4857 / 1135
3 / 2336 / 1.3969 / 3263
4 / 2336 / 1.2350 / 2885

10.

Store / Sales (X) / Profits (Y) / XY / X2
1 / 7 / 15 / 105 / 49
2 / 2 / 10 / 20 / 4
3 / 6 / 13 / 78 / 36
4 / 4 / 15 / 60 / 16
5 / 14 / 25 / 350 / 196
6 / 15 / 27 / 405 / 225 / n = / 12 / X2 = / 1796
7 / 16 / 24 / 384 / 256 / X = / 132 / XY = / 3529
8 / 12 / 20 / 240 / 144 / Y = / 271 / b = / 1.5930
9 / 14 / 27 / 378 / 196 /  = / 11 / a = / 5.0601
10 / 20 / 44 / 880 / 400 /  = / 22.5833
11 / 15 / 34 / 510 / 225 / Ft = 5.0601 + 1.593 X
12 / 7 / 17 / 119 / 49
Sum = / 132 / 271 / 3529 / 1796
X / Y / Estimated profit
24 / 43.2923 / $ 4,329,230
30 / 52.8503 / $ 5,285,030