Upload
bertha-weaver
View
224
Download
2
Embed Size (px)
Citation preview
2
Forecasting for operations Why we should forecast with models The importance of forecasting Exponential smoothing in a nutshell Case studies
1. Customer service: U.S. Navy distribution system
2. Inventory investment: Mfg. of snack foods
3. Purchasing workload: Mfg. of water filtration systems
Recommendations: How to improve forecast accuracy
3
Paper folding forecast
A sheet of notebook paper is 1/100 of an inch thick.
I fold the paper 40 times.
How thick will it be after 40 folds?
4
Fold Inches MilesStart 0.01
1 0.02
5 0.32
10 10.24
20 10,485.76 0.17
25 335,544.32 5.30
30 10,737,418.24 169.47
35 343,597,383.68 5,422.94
40 10,995,116,277.76 173,534.03
5
The Importance of Forecasting
Forecasts determine: Master schedules Economic order quantities Safety stocks JIT requirements to both internal and external
suppliers
6
The Importance of Forecasting (cont.) Better forecast accuracy always cuts inventory
investment. Example:
Forecast accuracy is measured by the standard deviation of the forecast error
Safety stocks are usually set at 3 times the standard deviation
If the standard deviation is cut by $1, safety stocks are cut by $3
7
Exponential smoothing methods Forecasts are based on weighted moving
averages of Level Trend Seasonality
Averages give more weight to recent data
8
Origins of exponential smoothing Simple exponential smoothing –
The thermostat model Error = Actual data – forecast New forecast = Old Forecast + (Weight x Error)
Invented by Navy operations analyst Robert G. Brown in 1944
First application: Using sonar data to forecast the tracks of Japanese submarines
9
Exponential smoothing at work
“A depth charge has a magnificent laxative effect on a submariner.”
Lt. Sheldon H. Kinney, Commander, USS Bronstein (DE 189)
10
Forecast profiles from exponential smoothing
Additive Multiplicative
Nonseasonal Seasonality Seasonality
Constant Level
Linear Trend
Exponential
Trend
Damped Trend
11
26
27
28
29
30
31
32
33
34
35
36
Automatic Forecasting with the damped trend
In constant-level data, the forecasts emulate simple exponential smoothing:
12
20
25
30
35
40
45
50
55
60
In data with consistent growth and little noise, the forecasts usually follow a linear trend:
Automatic Forecasting with the damped trend
13
Automatic Forecasting with the damped trend
When the trend is erratic, the forecasts are damped:
20
25
30
35
40
45
50 Saturation level
14
Automatic Forecasting with the damped trend
The damping effect increases with noise in the data:
20
25
30
35
40
45
50
Saturation level
15
Case 1: U.S. Navy distribution system Scope
50,000 line items stocked at 11 supply centers 240,000 demand series $425 million inventory investment
Decision Rules Simple exponential smoothing Replenishment by economic order quantity Safety stocks set to minimize backorder delay time
16
Problems Customer pressure to reduce backorder delay No additional inventory budget available
Characteristics of demand series 90% nonseasonal Frequent outliers and jump shifts in level Trends, usually erratic, in most series
Solution Automatic forecasting with the damped trend
U.S. Navy distribution system (cont.)
17
U.S. Navy distribution system (cont.) Research design 1
Random sample (5,000 items) selected Models tested
Random walk benchmark Simple, linear-trend, and damped-trend smoothing
Error measure Mean absolute percentage error (MAPE)
Results 1 Damped trend gave the best MAPE Impact of backorder delay unknown
18
U.S. Navy distribution system (cont.) Research design 2
The mean absolute percentage error was discarded Monthly inventory values were computed:
EOQ Standard deviation of forecast error Safety stock Average backorder delay
Results 2 Damped trend gave the best backorder delay Management was not convinced
19
U.S. Navy distribution system (cont.) Research design 3
6-year simulation of inventory performance, using actual daily demand and lead time data
Stock levels updated after each transaction Forecasts updated monthly
Results 3 Again, damped trend was the clear winner Results very similar to steady-state predictions Backorder delay reduced by 6 days (19%) with no
additional inventory investment
20
Average delay in filling backordersU.S. Navy distribution system
Damped trend
Simple smoothing
Linear trend
Random walk
25
30
35
40
45
50
370 380 390 400 410 420 430
Inventory investment (millions)
Ba
ck
ord
er
da
ys
21
Case 2: Snack-food manufacturer Scope
82 snack foods Food stocks managed by commodity traders Packaging materials managed with subjective
forecasts and inventory levels
Problems Excess stocks of packaging materials Impossible to predict inventory on the balance sheet
22
11-Oz. corn chipsMonthly packaging inventory and usage
Actual Inventory from
subjective forecasts
Monthly Usage
Month
23
Snack-food manufacturer (cont.) Solutions
Automatic forecasting with the damped trend Replenishment by economic order quantity Safety stocks set to meet target probability of
shortage
24
Damped-trend performance11-oz. corn chips
$200,000
$250,000
$300,000
$350,000
$400,000
$450,000
$500,000
Actual
ForecastOutlier
25
Investment analysis: 11-oz. corn chipsForecast annual usage $4,138,770
Economic order quantity $318,367
Standard deviation of forecast errors $34,140
Nbr. shortages
per 1,000 Probability Safety Order Maximum
order cycles of shortage stock quantity investment
100.0000 0.1000 $43,758 $318,367 $362,12550.0000 0.0500 $56,167 $318,367 $374,5341.0000 0.0010 $105,510 $318,367 $423,8770.0100 0.0000 $145,601 $318,367 $463,9680.0001 0.0000 $177,496 $318,367 $495,863
26
Safety stocks vs. shortages11-oz. corn chips
$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
$140,000
$160,000
$180,000
$200,000
0 10 20 30 40 50 60 70 80 90 100
Shortages per 1,000 order cycles
Saf
ety
stoc
k
Target
27
Safety stocks vs. forecast errors11-oz. corn chips
($200,000)
($150,000)
($100,000)
($50,000)
$0
$50,000
$100,000
$150,000
$200,000Safety stock
Forecast errors
28
11-Oz. corn chipsTarget vs. actual packaging inventory
Actual Inventory from
subjective forecasts
Month
$0
$500,000
$1,000,000
$1,500,000
$2,000,000
$2,500,000
Target maximum inventory based on damped trend
Actual Inventory from
subjective forecasts
Monthly Usage
29
How to forecast regional demand Forecast total units with the damped trend Forecast regional percentages with simple
exponential smoothing
30
Damped-trend performance11-oz. corn chips
$200,000
$250,000
$300,000
$350,000
$400,000
$450,000
$500,000
Actual
ForecastOutlier
31
Regional sales percentages: Corn chips
0%
10%
20%
30%
40%
50%
Mar Jun Sep Dec Mar Jun Sep Dec
South
West
North
East
32
Case 3: Water filtration systems company Scope
Annual sales of $15 million Inventory of $5.8 million, with 24,000 stock records
Inventory system Reorder monthly to maintain 3 months of stock Numerous subjective adjustments
Forecasting system 6-month moving average No update to average if demand = 0 Numerous subjective adjustments
33
Problems Purchasing and receiving workload
70,000 orders per year
Forecasting Total forecasts on the stock records = $28 million
Annual sales = $15 million
Frequent stockouts due to forecast errors
34
Solutions Develop a decision rule for what to stock Implement the damped trend Use the forecasts to do an ABC classification Replace monthly orders with:
Class A JIT Class B EOQ/safety stock Class C Annual buys
35
What to stock?
Cost to stock Average inventory balance x holding rate +
Number of stock orders x transportation cost
Cost to not stock Number of customer orders x drop-ship transportation cost
Note: Transportation costs for not stocking may be bothin-and out bound, depending on whether we choose todrop-ship from the vendor
36
Water filtration company: Inventory status
4,202 with inadequate
demand to stock18%
2,928 substitute items13%
2,200 obsolete9%
7,526 with no hits in 12 months
33%
6,336 active items27%
37
ABC classification based ondamped-trend forecasts for the next yearClass Sales forecast System Items Dollars
A > $36,000 JIT 3% 75%
B $600 - $35,999 EOQ 49% 18%
C < $600 Annual buy 48% 7%
38
Inventory control system recommendations
Control SystemInventory
ClassProduction Schedule
Lead-time Behavior
JIT A, B Level Certain
MRP A, B Variable Reliable
EOQ / Safety stock A, B Variable Variable
Annual buy C Any Any
39
Annual purchasing workloadTotal savings = 58,000 orders (76%)
JIT
EOQ
JIT
EOQ
Annual buys
0
5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
A B C
Monthly orderingABC system
40
Inventory investmentTotal savings = $591,000 (15%)
JIT
EOQ
JIT
EOQ
Annual buys
0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
3,000,000
A B C
Monthly orderingABC system
41
Recommendations Benchmark the forecasts with a random walk Judge forecast accuracy in operational terms
Customer service measures Average backorder delay time Percent of time in stock Probability of stockout Average dollars backordered
Inventory investment on the balance sheet Purchasing workload or production setups