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

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 2 Table of Content Introduction Literature Review Data Analysis Inventory Policy Conclusion

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 3 Introduction 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 MODELPRICE (USD)DIMENSIONS (CM)WEIGHT (KG) A18.421020*720*8202.34 B29.281020*720*8203.76 C35.801020*760*8204.6 D56.101200*720*8007.1

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 4 Introduction 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 Forecasts were made very early, sometimes 8 months before. Number of forecast during a month was not fixed. Amount in forecast has no rule. 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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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 5 Introduction 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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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 6 Literature Review Inventory Control Methods

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 7 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 Analysis Order too much overstock loss profit Order 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 Model

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 8 -- 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 Model

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 9 The critical ratio for this problem was 0.77, which corresponds to a value of between 14 and 15. 0.77 Since we round up, the optimal solution Classical Newsvendor Model

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 10 Current Inventory Policy Data: 8 June, 2005 to 30 September, 2006 ABCD Average Inventory129415172770426 Peak Demand7044881728504 Large amount of shipment to achieve Economic Scale. NPX seldom took inventory level into account while deciding the amount to be transported.

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 11 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 (Cont’d) reduce lead time to one week

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 12 Current Inventory Policy (Cont’d) (USD)ABCD Production Cost14.73623.42428.6444.88 Operation Cost1.33892.11962.5914.0835 Trans Cost (Sea)0.50310.80840.9891.5265 Total Cost (Sea)16.57826.35232.2250.49 Trans Cost (Air)8.576113.780416.85926.0215 Total Cost (Air)24.65139.32448.0974.985 Net Profit Margin (Air)-33.83%-34.30%-34.33%-33.66% Total Cost (E)29.071846.351256.68288.449 Net Profit Margin (E)-57.83%-58.30%-58.33%-57.66%

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 13 Newsvendor Model Overstock Cost: Capital Cost: 0.1% per day C o = Price * Days * 0.1% Stock Shortage Cost: C u = Net Profit + Loss caused by air transportation = Price * 10% + Net Profit Margins Ratio * Price (USD)ABCD Shortage Loss12.4920.0024.4637.96 Overstock Cost14.74*0.1%*T23.42*0.1%*T28.64*0.1%*T44.88*0.1%*T

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 14 Newsvendor Model (Cont’d) A Demand352505704 Probability0.440.110.44 Cumulative P0.440.561 B Demand0224244448468488 Probability0.130.250.130.250.13 Cumulative P0.130.380.50.750.881 B Adj. Demand0234468 Probability0.130.380.5 Cumulative P0.130.51 C Demand0576960134415361728 Probability0.140.290.14 Cumulative P0.140.430.570.710.861 D Demand0126252504 Probability0.220.440.110.22 Cumulative P0.220.670.781

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 15 Newsvendor Model (Cont’d) In practice, longest time is two months. C o is insignificant compared to C u 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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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 16 New Forecast WLF’s demand on cooler is driven by the demand of end customers in the supply chain. It is assumed the demand of end customer is constant, thus WLF’s is constant. Forecasts provided by WLF are not reliable. Making new forecast based on the consumptions. Foresting with Actual Demand Regardless of Forecasts Provided by WLF

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 17 New Forecast (Cont’d) Daily Demand: Historical Demand / Time Gap Error in Pickup Date: Mean: 8.58 Standard Deviation: 5.05 ABCD Mean24.7512.9033.727.46 Std.18.208.6025.019.50

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 18 New Forecast (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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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 19 Using Forecasts Two months lead time Key Forecast: The last one provided two months before the expected pickup date (F x ) Compare F x with Actual Demand: A FxFx 35250500704 D352505352704 352 704 B FxFx 2440448224 448 0 D4680488448224 244448 C FxFx 9603529602688212219201728 D0576 960153617281344 D FxFx 252 1260252504 D1260 5040252504

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 20 Using Forecasts (Cont’d) Differences between F x and Demand: A Difference-704-3520352 Times1152 Probability11.11% 55.56%22.22% B Difference-448-224-400204224 Times121211 Probability12.50%25.00%12.50%25.00%0.125 C Difference-2241923845869601728 Times112111 Probability14.29% 28.57%14.29%0.1429 D Difference-3780126252 Times1341 Probability11.11%33.33%44.44%11.11%

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 21 Using Forecasts (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: = F x + Expected Difference

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 22 Using Forecasts (Cont’d) Using ratios of differences over F x due to variation of Demand Size A RdRd 00.5 Times52 Probability71.43%28.57% B RdRd 00.5 Times222 Probability33.33% C RdRd -0.7500.250.50.751 Times112111 Probability14.29% 28.57%14.29%0.1429 D RdRd -30.51 Times141 Probability16.67%66.67%16.67%

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 23 Using Forecasts (Cont’d) Expected Ratios: A: Expected Ratio = 0.5 * 28.57% ≈ 0.14 B: – 0.17; C: 0.29; D: 0 Planned Amount: = F x * (1 + Expected Ratio)

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 24 Conclusion 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 More accurate Less random

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PX N TPTM6190– Logistics System Final Report Presentation--NPX Case Study 25 Thank you!

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