By Liu Paipai 305052644 Wang Nan 306076136 Feng Xi 305088637 PX N Case Study – Inventory Policy.

By

Liu Paipai 305052644

Wang Nan 306076136

Feng Xi 305088637

PXNCase Study Case Study

– – Inventory PolicyInventory Policy

TPTM6190– Logistics System TPTM6190– Logistics System Final Report Presentation--NPX Case Study Final Report Presentation--NPX Case Study

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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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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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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



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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



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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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PXN

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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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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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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PXN

Thank you!

PXN PXN

By Liu Paipai 305052644 Wang Nan 306076136 Feng Xi 305088637 PX N Case Study – Inventory Policy.

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