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By
Liu Paipai 305052644
Wang Nan 306076136
Feng Xi 305088637
PXNCase Study Case Study
– – Inventory PolicyInventory Policy
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PXNTable of ContentTable of Content
NN IntroductionNN Literature ReviewNN Data AnalysisNN Inventory PolicyNN Conclusion
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PXNIntroductionIntroduction
Case Description Companies NPX – Manufacturer of engine oil cooler for
automobile WLF – Germany Car Manufacturer
Products Four models of engine oil cooler A, B, C and D
MODEL PRICE (USD) DIMENSIONS (CM) WEIGHT (KG)
A 18.42 1020*720*820 2.34
B 29.28 1020*720*820 3.76
C 35.80 1020*760*820 4.6
D 56.10 1200*720*800 7.1
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PXNIntroductionIntroduction
Current Inventory Policy:
Forecast made by WLF :
Storage: warehouse in Germany, paid by WLF Service Level: 100% NPX responsible for delay; shipment at a cost of USD365 per 100kgs via air Lead Time: One month production One month shipment via sea
NN Forecasts were made very early, sometimes 8 months before.
NN Number of forecast during a month was not fixed.NN Amount in forecast has no rule.NN Last adjustment must be made to be accurate as the
actual demand at least one week before the expected pickup date.
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PXNIntroductionIntroduction
Problem Identify:
Demand: Uncertain Forecast: Fluctuating
Inventory Level: 100% service level lead to a very high
inventory level
Capital cost: High unit price result in a significant
capital cost whiling holding high level inventory.
Pick up: WLF seldom picked up the products on time
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PXNLiterature Literature
ReviewReview Inventory Control Methods
EOQ Lot Sizing
Min-max Order Point Order up to Level
Inventory Largely Unnecessary
Base Stock Newsvendor
Fixed Costs Significant
Fixed Costs Relatively Insignificant
Demand Largely Known Demand Unknown
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PXN
Question
Assume : (Retail Price) a > (Cost) b > (Return Price) c
Profit of selling one piece of newspaper: a-b
Loss of return on piece of newspaper: b-c
How much should be ordered per day to maximize profit
AnalysisOrder too much overstock loss profitOrder too little stockout loss profit
Demand per day is discrete
How to maximize Expected Profit per day ?
Profit per day is discrete
Optimal order Q ?
Classical Newsvendor Classical Newsvendor ModelModel
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PXN
uo
u
cc
cQF
*
oc
uc-- overage cost = loss
-- underage cost = profit
Critical Ratio:
The critical ratio = profit/(profit + loss)=50/(50+15) = 0.77
Each copy is purchased ---- 25 cents sold for ---- 75 cents paid ---- 10 cents (each unsold
copy)
Profit Cu: 75 25 = 50 cents Loss Co: 25 10 = 15 cents
Classical Newsvendor Classical Newsvendor ModelModel
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PXN
The critical ratio for this problem was 0.77, which corresponds to a value of between 14 and 15.
Q Qf QF Q Qf QF
0 1/52 1/52(0.0192) 12 4/52 30/52 (0.5769)
1 0 1/52(0.0192) 13 1/52 31/52 (0.5962)
2 0 1/52(0.0192) 14 5/52 36/52 (0.6923)
3 0 1/52(0.0192) 15 5/52 41/52 (0.7885)
4 3/52 4/52(0.0769) 16 1/52 42/52 (0.8077)
5 1/52 5/52(0.0962) 17 3/52 45/52 (0.8654)
6 2/52 7/52 (0.1346) 18 3/52 48/52 (0.9231)
7 2/52 9/52 (0.1731) 19 3/52 51/52 (0.9808)
8 4/52 13/52(0.2500) 20 0 51/52 (0.9808)
9 6/52 19/52 (0.3654) 21 0 51/52 (0.9808)
10 2/52 21/52 (0.4038) 22 1/52 52/52 (1.000)
11 5/52 26/52 (0.5000)
0.77
Since we round up, the optimal solution * 15Q
Classical Newsvendor Classical Newsvendor ModelModel
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PXNCurrent Inventory PolicyCurrent Inventory Policy
Data: 8 June, 2005 to 30 September, 2006
A B C D
Average Inventory 1294 1517 2770 426
Peak Demand 704 488 1728 504
NN Large amount of shipment to achieve Economic Scale.NN NPX seldom took inventory level into account while
deciding the amount to be transported.
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Emergent Solution for Shortage: 130% original production cost + air transport
Transportation Fee (USD/100kg):
Truck: 1.5; Sea: 20; Air: 365
Gross Profit Margin: 20%;
Net Profit Margin: 10%
Total Cost = Production Cost + Operation Cost + Transportation Cost
Current Inventory Policy Current Inventory Policy (Cont’d)(Cont’d)
reduce lead time to one week
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PXNCurrent Inventory Policy Current Inventory Policy
(Cont’d)(Cont’d)
(USD) A B C D
Production Cost 14.736 23.424 28.64 44.88
Operation Cost 1.3389 2.1196 2.591 4.0835
Trans Cost (Sea) 0.5031 0.8084 0.989 1.5265
Total Cost (Sea) 16.578 26.352 32.22 50.49
Trans Cost (Air) 8.5761 13.7804 16.859 26.0215
Total Cost (Air) 24.651 39.324 48.09 74.985
Net Profit Margin (Air) -33.83% -34.30% -34.33% -33.66%
Total Cost (E) 29.0718 46.3512 56.682 88.449
Net Profit Margin (E) -57.83% -58.30% -58.33% -57.66%
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PXNNewsvendor ModelNewsvendor Model
Overstock Cost: Capital Cost: 0.1% per day
Co= Price * Days * 0.1%
Stock Shortage Cost: Cu= Net Profit + Loss caused by air transportation = Price * 10% + Net Profit Margins Ratio * Price
(USD) A B C D
Shortage Loss 12.49 20.00 24.46 37.96
Overstock Cost 14.74*0.1%*T 23.42*0.1%*T 28.64*0.1%*T 44.88*0.1%*T
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PXNNewsvendor ModelNewsvendor Model (Cont’d)(Cont’d)
A
Demand 352 505 704
Probability 0.44 0.11 0.44
Cumulative P 0.44 0.56 1
B
Demand 0 224 244 448 468 488
Probability 0.13 0.25 0.13 0.25 0.13 0.13
Cumulative P 0.13 0.38 0.5 0.75 0.88 1
B Adj.
Demand 0 234 468
Probability 0.13 0.38 0.5
Cumulative P 0.13 0.5 1
C
Demand 0 576 960 1344 1536 1728
Probability 0.14 0.29 0.14 0.14 0.14 0.14
Cumulative P 0.14 0.43 0.57 0.71 0.86 1
D
Demand 0 126 252 504
Probability 0.22 0.44 0.11 0.22
Cumulative P 0.22 0.67 0.78 1
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PXNNewsvendor ModelNewsvendor Model
(Cont’d)(Cont’d)
In practice, longest time is two months.
Co is insignificant compared to Cu
Critic Ratio is always > 93.4%
More data is needed to get a more accurate cumulative probability to choose a optimized amount.
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PXNNew ForecastNew Forecast
NN WLF’s demand on cooler is driven by the demand of end customers in the supply chain.
NN It is assumed the demand of end customer is constant, thus WLF’s is constant.
NN Forecasts provided by WLF are not reliable. NN Making new forecast based on the
consumptions.
Foresting with Actual Demand Regardless
of Forecasts Provided by WLF
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PXNNew ForecastNew Forecast (Cont’d)(Cont’d)
Daily Demand: Historical Demand / Time Gap
Error in Pickup Date: Mean: 8.58 Standard Deviation: 5.05
A B C D
Mean 24.75 12.90 33.72 7.46
Std. 18.20 8.60 25.01 9.50
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PXNNew ForecastNew Forecast (Cont’d)(Cont’d)
Unreasonable forecast compared to historical actual demand.
Product A, 30 days time gap: Forecast Amount = 24.75 * (30 + 8.58 + 3.1 * 5.05) + 3.1 * SQRT[(30 + 8.58 + 3.1 * 5.05) * 18.202] ≈ 1758
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PXNUsing ForecastsUsing Forecasts
Two months lead time
Key Forecast: The last one provided two months before the expected pickup date (Fx)
Compare Fx with Actual Demand:
AFx 352 505 0 0 704 704 704 704 704
D 352 505 352 704 704 352 352 704 704
BFx 244 0 448 224 224 448 448 0
D 468 0 488 448 224 224 244 448
CFx 960 352 960 2688 2122 1920 1728
D 0 576 576 960 1536 1728 1344
DFx 252 252 252 252 252 126 0 252 504
D 126 0 126 126 126 504 0 252 504
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PXNUsing ForecastsUsing Forecasts (Cont’d)(Cont’d)
Differences between Fx and Demand:
A
Difference -704 -352 0 352
Times 1 1 5 2
Probability 11.11% 11.11% 55.56% 22.22%
B
Difference -448 -224 -40 0 204 224
Times 1 2 1 2 1 1
Probability 12.50% 25.00% 12.50% 25.00% 0.125 0.125
C
Difference -224 192 384 586 960 1728
Times 1 1 2 1 1 1
Probability 14.29% 14.29% 28.57% 14.29% 0.1429 0.1429
D
Difference -378 0 126 252
Times 1 3 4 1
Probability 11.11% 33.33% 44.44% 11.11%
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PXNUsing ForecastsUsing Forecasts (Cont’d)(Cont’d)
Expected Differences:
A: Expected Differences
= – 704 * 11.11% – 352 * 11.11% + 352 * 22.22% ≈ – 39 B: – 36; C: 573; D: 42
Planned Amount: = Fx + Expected Difference
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PXNUsing Forecasts Using Forecasts (Cont’d)(Cont’d)
Using ratios of differences over Fx due to
variation of Demand Size
A
Rd 0 0.5
Times 5 2
Probability 71.43% 28.57%
B
Rd -1 0 0.5
Times 2 2 2
Probability 33.33% 33.33% 33.33%
C
Rd -0.75 0 0.25 0.5 0.75 1
Times 1 1 2 1 1 1
Probability 14.29% 14.29% 28.57% 14.29% 0.1429 0.1429
D
Rd -3 0.5 1
Times 1 4 1
Probability 16.67% 66.67% 16.67%
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PXNUsing ForecastsUsing Forecasts (Cont’d)(Cont’d)
Expected Ratios: A: Expected Ratio = 0.5 * 28.57% ≈ 0.14
B: – 0.17; C: 0.29; D: 0
Planned Amount: = Fx * (1 + Expected Ratio)
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PXNConclusionConclusion
None of the models is good
One solution is better than none Data is not sufficient Keep improving them as time goes on
Current contract led NPX to difficulty
NN More accurate NN Less random
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Thank you!
PXN PXN