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1. ISQS 3344 Introduction to Production andOperations ManagementSpring 2014

   Quantitative Review I
2. SUPPLEMENT 7 Capacity and Constraint Management (Break-Even Analysis)
3. Portland Radio Company (PRC) is trying to decide whether or not to introduce a new model. If they introduce it, there will be additional fixed costs of $400,000 per year. The variable costs have been estimated to be $30 per radio. If PRC sells the new radio model for $40 per radio, how many must they sell to break even?
4. Which Year to Break Even (BE) Which Month of Year 3 to Break Even Yearly Demand = 60,000 Monthly Demand = 60,000/12 = 5,000 BE = 5,000 x 11 months = 55,000 or Month 11 of Year 3 OR 55,000/60,000 = 0.9167 0.9167 x 12 = 11
5. CHAPTER 1 Operations and Productivity
6. Productivity
7. Labor Productivity Three workers paint twenty-four tables in eight hours Inputs: 24 hours of labor (3 workers x 8 hours) Outputs: 24 painted tables
8. Multifactor Productivity Convert all inputs & outputs to $ value Example: 200 units produced sell for $12 each materials cost $6 per unit 40 hours of labor were required at $10 an hour
9. Productivity Index Can be used to compare a process’ productivity at a given time (P2) to the same process’ productivity at an earlier time (P1)
10. Productivity Growth Rate Example: Last week, a company produced 150 units using 200 hours of labor. This week, the same company produced 170 units using 240 hours of labor.
11. If inputs increase by 25% and outputs decrease by 10%, what is the percentage change in productivity? Assume P1 = 1/1.
12. Production increased to 75 from 65 pieces per day. Defective items have dropped from 12 to 5 pieces per day. Production facility operates eight hours per day. Seven people work daily in the plant. What is the change in productivity? Period 1 Output = 65 Defects = 12 Net Output = 53 Period 2 Output = 75 Defects = 5 Net Output = 70 Period 1 Input = 8 hours x 7 workers = 56 Period 2 Input = 8 hours x 7 workers = 56 P1 = 53/56 = 0.95 P2 = 70/56 = 1.25 Change = (1.25-0.95)/0.95 = 0.32
13. CHAPTER 2 Revenue Management Systems
14. Revenue Management Systems (Hotel) Contribution to profit and overhead ($) = [(Selling Price – Variable Cost) x Demand]1 + [(Selling Price – Variable Cost) x Demand]2 +… + [(Selling Price – Variable Cost) x Demand]n Hotel management effectiveness (%) = Actual hotel revenue Maximum possible hotel revenue = Actual prices for each room night x Actual number of room nights rented Maximum legal price for each room night x Maximum number of room nights available in hotel
15. Hotel Management
16. Hotel Management Contribution to profit and overhead ($) = [(Selling Price – Variable Cost) x Demand] = [($200 - $50) x 400] + [($120 - $50) x 800] = ($150 x 400) + ($70 x 800) = $116,000 Hotel management effectiveness (%) = Actual prices for each room night x Actual number of room nights rented Maximum legal price for each room night x Maximum number of room nights available in hotel = ($200 x 400 rooms) + ($120 x 800 rooms) ($250 x 500 rooms) + ($150 x 900 rooms) = ($80,000 + $96,000) / ($125,000 + $135,000) = 67.69%
17. Revenue Management Systems (Airlines) A regional airline that operates a 50-seat jet prices the ticket for one popular business flight at $250. If the airline overbooks the reservations, overbooked passengers receive a $300 travel voucher. The airline is considering overbooking by up to 5 seats, and the demand for the flight always exceeds the number of reservations it might accept. The probabilities of the number of passengers who show up is given in the following table:
18. Overbooking Strategies and Analysis Expected revenue for 50 reservations = $250 x (45*.1 + 46*.15 + 47*.15 + 48*.2 + 49*.3 + 50*.1) = $11,937.50 Expected re venue for 51 reservations = [$250 x (45*.08 + 46*.13 + 47*.18 + 48*.15 + 49*.25 + 50*.11)] – ($300 x .1) = 10,717.50 Expected re venue for 52 reservations = [$250 x (45*.06 + 46*.125 + 47*.175 + 48*.2 + 49*.25 + 50*.1)] – [$300 x (.05+.04)] = $10,854.25 Expected re venue for 53 reservations = [$250 x (45*.04 + 46*.05 + 47*.07 + 48*.2 + 49*.25 + 50*.15)] – [$300 x (.1+.08+.06)] = $9,113 Expected revenue for 54 reservations = $6,306.50 Expected revenue for 55 reservations = $4,180.50
19. CHAPTER 4 Forecasting
20. Lauren's Beauty Boutique has experienced the following weekly sales. Calculate a 3 period moving average for Week 6. Week Sales 1 2 3 4 5 6 432 396 415 478 460 451
21. A firm has the following order history over the last 6 months. What would be a 3-month weighted moving average forecast for July, using weights of 60% for the most recent month, 20% for the month preceding the most recent month, and 20% for the month preceding that one? January 120 February 95 March 100 April 75 May 100 June 50 July 65
22. Exponential Smoothing Last period’s actual value (At) Last period’s forecast (Ft) Select value of smoothing coefficient, between 0 and 1.0
23. Summary of Single Exponential Smoothing Milk-Sales Forecasts with α = 0.2 F2 = .2(172) + .8(172) =172 F3 = .2(217) + .8(172) = 181 F4 = .2(190) + .8(181) = 182.8 F5 = .2(233) + .8(182.8) = 192.84 F6 = .2(179) + .8(192.84) = 190.07 F7………. You start with past data and calculate forecasts working forward.
24. Determine forecast for periods 7 and 8exponential smoothing with alpha = 0.2 and the period 6 forecast being 375. Exponential Smoothing Period 7 = 0.2(360) + 0.8(375) = 72 + 300 = 372.0 Period 8 = 0.2(375) + 0.8(372) = 75 + 297.6 = 372.6 375.0 372.0 372.6
25. Quarterly Forecasting Expected total demand in 2012 is 3,000 units. Given the historical sales figures below, derive a forecast for each quarter in 2012. 750 x 0.43 250/587.5 Q1Q2 Q3 Q4 2009 250 500 700 900 0.43 0.85 1.19 1.53 2010 270 530 800 970 0.42 0.82 1.25 1.51 2011 310 600 850 1000 0.45 0.87 1.23 1.45 0.43 0.85 1.22 1.50 2012 324 636 917 1123 Total 2350 2570 2760 3000 (1.53+1.51+1.45)/3 Quarter 587.5 642.5 690 750
26. The Regression Equation or Trend Forecast = trend forecast or y variable a = estimate of Y-axis intercept where X = 0 b = estimate of slope of the demand line X = period number or independent variable
27. Linear Regression Identifydependent (y) and independent (x) variables Solve for the slope of the line Solve for the y intercept Develop your equation for the trend line Tx or y = a + bX
28. A maker of golf shirts has been tracking the relationship between sales and advertising dollars. Use linear regression to find out what sales might be if the company invested $60,000 in advertising next year.
29. a = 147.25-3.579(51.25) = -36.17 Y = a + bX Y = -36.17 + 3.579X Y = -36.17 + 3.579(60) Y = 178.57 or $178,570 in sales
30. Tracking Forecast Error Over Time Mean Absolute Deviation (MAD) A good measure of the actual error in a forecast Tracking Signal (TS) Exposes bias (positive or negative) Positive TS = under-forecasting Negative TS = over-forecasting
31. Mean Absolute Deviation MAD sums only absolute values errors, both positive and negative errors add to the sum and the average size of the error (whether positive or negative) is determined. n = number of periods of data F = forecast of demand in period i A = actual demand in period i
32. A company is comparing the accuracy of two forecasting methods. Forecasts using both methods are shown below along with the actual values for January through May. The company also uses a tracking signal with ±4 limits to decide when a forecast should be reviewed. Which forecasting method is best?
33. Supplement 7 Capacity and Constraint Management
34. Capacity Utilization Theoretical Capacity: Maximum output rate under ideal conditions Effective Capacity: Maximum output rate under normal (realistic) conditions
35. Computing Capacity Utilization In the bakery example, the design capacity is 60 custom cakes per day. On average, this bakery can make 40 custom cake per day. Currently, the bakery is producing 56 cakes per day. What is the bakery’s capacity utilization relative to both theoretical and effective capacity?
36. Computing Capacity Utilization In the bakery example, the design capacity is 60 custom cakes per day. On average, this bakery can make 40 custom cake per day. Currently, the bakery is producing 56 cakes per day. What is the bakery’s capacity utilization relative to both theoretical and effective capacity?
37. A clinic has been set up to give flu shots to the elderly in a large city. The theoretical capacity is 80 seniors per hour, and the effective capacity is 55 seniors per hour. Yesterday the clinic was open for ten hours and gave flu shots to 350 seniors. What is the effective utilization? What is the theoretical utilization?
38. Decision Trees Build from the present to the future: Distinguish between decisions (under your control) & chance events (out of your control, but can be estimated to a given probability) Solve from the future to the present: Generate an expected value for each decision point based on probable outcomes of subsequent events
39. Should you expand large or small? .40 x $60,000 = $24,000 $24,000 + $60,000 = $84,000 .60 x $100,000 = $60,000 .40 x $50,000 = $20,000 $20,000 + $42,000 = $62,000 $70,000 > $45,000 .60 x $70,000 = $42,000
40. Capacity Analysis Capacity analysis determines the throughput capacity of workstations in a system. A bottleneck is a limiting factor or constraint. A bottleneck has the lowest effective capacity in a system or takes the most time.
41. Station A (50 seconds) What is the bottleneck? What is the maximum production per hour?
42. That’s all, folks! Thanks for today!