Operations & Logistics Management in Air Transportation - - PowerPoint PPT Presentation

Operations & Logistics Management in Air Transportation

Professor David Gillen (University of British Columbia ) & Professor Benny Mantin (University of Waterloo)

Air Transportation Systems and Infrastructure Strategic Planning Module 9-10 : 13 June 2014 Istanbul Technical University Air Transportation Management M.Sc. Program

THE NEWSVENDOR AND APPLICATIONS

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Additional Slides June 12, 2014

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Newsvendor Solution: Explanation

Marginal Analysis: Suppose you stock S units

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Marginal Overage Cost with S

Probability of S being “over” P{D ≤ S} Marginal cost of

• ver-stocking

P{D ≤ S} * Co

Marginal Underage Cost with S

Probability of S being “under” 1 - P{D ≤ S} Marginal cost of under-stocking {1-P{D ≤ S}} * Cu

To find the optimal stocking level:

Marginal Cost of Over-Stocking Marginal Cost of Under-Stocking

P{D ≤ S} * Co {1-P{D ≤ S}} * Cu

P{D ≤ S} Cu / (Cu + Co)

Representing the Decision Problem Mathematically

• If D were known, the cost function would be

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C(S, D) = Cost (S, D) = Co ∙max{0, S-D} + Cu ∙ max{0, D-S} = Co ∙ [S-D]+ + Cu ∙ [D-S]+

Had too much stock Had too Little stock Total Cost (S-D) units There exists a fundamental economic tradeoff

Impact of Demand Variability

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Expected Cost Function

$0 $25 $50 $75 $100 $125 $150 $175 $200 $225 $250 $275 $300 10 20 30 40 50 60 70 80 90 100

Stock Level (units) Expected Cost ($)

Expected Cost Curve for Mean = 30, StdDev = 10, CV = 33% Expected Cost Curve for Mean = 30, StdDev = 20, CV = 67% Expected Cost Curve for Mean = 30, StdDev = 30, CV = 100% Deterministic

=

Normal Distribution Tutorial (1)

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• 0.0020

0.0040 0.0060 0.0080 0.0100 0.0120 0.0140 0.0160 0.0180 25 50 75 100 125 150 175 200 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018

• 100
• 75
• 50
• 25

25 50 75 100

0.00 0.05 0.1 0.1 5 0.20 0.25 0.30 0.35 0.40 0.45

• 4
• 3
• 2
• 1

1 2 3 4

Start with = 100, = 25. Q = 125 Center the distribution over 0 by subtracting the mean Rescale the vertical and horizontal axes by dividing by the standard deviation

) , ( ~

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  N D

1 25 100 125        Q z

) 1 , ( ~ N Z

P(D ≤ 125) P(Z ≤ 1)

z-Scale

Standard normal

• Let Q be the order quantity, and

(, ) the parameters of the normal demand distribution

• Prob{demand is Q or lower} =

Prob{the outcome of a standard normal is z or lower}, where

• Look up Prob{the outcome of a

standard normal is z or lower} in the Standard Normal Distribution Function Table, or Excel NORMSDIST function.

• r

Q z Q z         