【正文】 1. Deseasonalize current (July) actual demand 2. Use exponential smoothing to project deseasonalized data one period ahead (? = .2) 3. Reseasonalize forecast for desired month (August) = Deseasonalized forecast 180。 seasonal factor = 180。 = or 21 (36) ()() ())F (1 D F T T 1 T ? ? ? ? ? ? ? ? ? Integrative Example: Calculating a Forecast with Seasonal Indexes and Exponential Smoothing ?? 3 6 .1 73 4 /0 .9 4 in d e x S e a s o n a ld e a n d A c tu a l ?? ?? ?34 Supply Chain Engineering MN 799 58 Exercise ? Boler Corp has the following sales history: ? Quarter Year1 Year2 ? 1 140 210 ? 2 280 350 ? 3 70 140 ? 4 210 280 ? What seasonal index for each quarter could be used to forecast the sales of the product for Year 3? ? What would be a forecast for year 3 using an a= and assuming the forecast for year 2 was 1000? What would be the forecast for each quarter in this forecast? Supply Chain Engineering MN 799 59 Source: Adapted from CPIM Inventory Management Certification Review Course (APICS, 1998). 9 5 . 4 4 %9 9 . 7 4 %6 8 . 2 6 %xNormal Distribution Using the Measures of Variability Supply Chain Engineering MN 799 60 Standard Deviation (sigma) F= A = Actual Error (Sales – Error Period Forecast Sales Forecast) Squared 1 1,000 1,200 200 40,000 2 1,000 1,000 0 0 3 1,000 800 – 200 40,000 4 1,000 900 – 100 10,000 5 1,000 1,400 400 160,000 6 1,000 1,200 200 40,000 7 1,000 1,100 100 10,000 8 1,000 700 – 300 90,000 9 1,000 1,000 0 0 10 1,000 900 – 100 10,000 10,000 10,200 200 400,000 Supply Chain Engineering MN 799 61 Standard Deviation — Continued Standard Deviation ( ) ( ) 200 10 400,000 n F A 211 9 400,000 1 n F A 2 i i 2 i i = = = = = = ? ? NOTE: About the use of n or n 1 in the above equations n Use with a large population ( 30 observations) n 1 Use with a small population ( 30 observations) Standard Deviation Supply Chain Engineering MN 799 62 Cumulative sum of error = Bias = Mean Absolute Deviation (MAD) = ( ) 2 0 0FA ii ???Bias and MAD ( ) 10 n 20 200 F A i i = = ? 1600 F 10 n 160 A i i = = ? F = A = Actual Error (Sales – Absolute Period Forecast Sales Forecast) Error 1 1,000 1,200 200 200 2 1,000 1,000 0 0 3 1,000 800 – 200 200 4 1,000 900 – 100 100 5 1,000 1,400 400 400 6 1,000 1,200 200 200 7 1,000 1,100 100 100 8 1,000 700 – 300 300 9 1,000 1,000 0 0 10 1,000 900 – 100 100 10,000 10,200 200 1,600 Supply Chain Engineering MN 799 63 ? Cumulative Sum of Error ? Bias ? Mean Absolute Deviation (MAD) ? Standard Deviation= MAD or NOTE: About the use of n or n1 in the above equations n Use with a large population ( 30 observations) n1 Use with a small population ( 30 observations) Measures of Forecast Error F ( ) ? i i A ( ) n F A i i ? n F A i i ? ( ) 1 n F A 2 i i ? ( ) n F A 2 i i ? or Supply Chain Engineering MN 799 64 ? Definition A confidence interval is a measure of distance, increments of which are represented by the z value ? Formulas ? Relationship ? 1 standard deviation (s) = 180。 MAD ? In the example data s = 180。 MAD = 180。 160 = 200 Source: Raz and Roberts, ―Statistics,‖ 1987 Confidence Intervals ( ) ( ) ( ) s s s z x x or x x Deviation Standard Mean Distance z n F A OR 1 n F A Dev Std 1 i i 2 i i 2 i i + = = = = ? ? Supply Chain Engineering MN 799 65 Expressing z Values (for +ve probabilities) Probabilit y D +1 SD +2 SD +3 SD Cumulative normal distribution from left side of distribution (x + z) z .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 .5000 .5398 .5793 .6179 .6554 .6915 .7257 .7580 .7881 .8413 .8643 .8849 .9032 .9192 .9332 .9452 .9554 .9641 .9773 .9821 .9861 .9893 .9918 .9938 .9953 .9965 .9974 .9987 .9990 .9930 .9995 .9997 .9998 .9998 .9999 .9999 .8159 .9713 .9981 .9999 Back Supply Chain Engineering MN 799 66 Application Problem — Service Level ? Given Average sales for item P is 50 units per week with a standard deviation of 4 ? Required What is the probability that more than 60 units will be sold? a. .006 b. .494 c. .506 d. .994 Supply Chain Engineering MN 799 67 Homework Q1 2. A demand pattern for ten periods for a certain product was given as 127, 113, 121, 123, 117, 109, 131, 115, 127, and 118. Forecast the demand for period 11 using each of the following methods: a threemonth moving average, a threemonth weighted moving average using weights of , , and , exponential smoothing with a smoothing constant of , and linear regression. Compute the MAD for each method to determine which method would be preferable under the circumstances. Also calculate the bias in the data, if any, for all four methods, and explain the meaning. Q2 The following information is presented for a product: ? 2022 2022 ? Forecast Demand Forecast Demand ? Quarter I 200 226 210 218 Quarter II 320 310 315 333 ? Quarter III 145 153 140 122 ? Quarter IV 230 212 240 231 ? a) What are the seasonal indicies that should be used for each quarter? ? What is the MAD for the data above? Supply Chain Engineering MN 799 68 Supply Chain Network Fundamentals William T. Walker, CFPIM, CIRM, CSCP Practitioner, Author, and Supply Chain Architect Supply Chain Engineering MN 799 69 ? Understanding How Supply Chains Work ? The Value Principle and Network Stakeholders ? Mapping a Supply Chain Netwo