Slides Added over Course 2 Normal Distribution Tutorial (1) Let Q - - PowerPoint PPT Presentation

Slides Added over Course

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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

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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         

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Product Process One of a kind Low volume Many products High volume Standard products Very high volume Commodity products Very low volume Project Job shop Batch Assembly line or Flow shop Continuous flow

Job shop Flow shop

Space shuttle Print shop Bakery Car assembly Petroleum refining

What is a Good Process?

Product-Process Matrix

Unit Variable Generally costs too High Utilization of Fixed Capital Generally Too Low

Drift

With a banked schedule, minimum connect times drive turnaround times – not ground operations

Ground Operations – Required Time for a Turnaround ( Carriers – 737-300)

41-46 min Extend jetway and

• pen door

(1 min) Deplane (10 min) (10-15 min) (13 min) Prearrival (2 min) Equipment Set Up (2 Min) Weight and Balance (2 min) Ramp (Outside) Inside

Cater

(15 min)

Clean cabin Boarding

33-43 min Ground power A/C bin door (3 min) Unload/load bags and cargo (20-30 min) Departure Dispatch (4 min) Close door and jetway (1 min) Close cargo door (1 min) Arrival Fuel (10-15 min)

Opportunities To Compress Ground Operations’ Turnaround Times

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Fuel (6-11 min)

But, with a continuous schedule, ground operations drives turnaround time, and thus airplane/crew utilization

21-31 min Extend jetway and

• pen door

(<1 min) Deplane (6 min) (2-5 min) (9-13 min) Prearrival (2-7 min) Equipment Set Up (1-2 Min) Weight and Balance (1-2 min) Ramp (Outside) Inside

Cater

(13-16 min) Cleaning

Boarding

23-32 min Ground power A/C bin door (<2 min) Unload/load bags and cargo (18-21 min) Departure Close door and jetway (<1 min) Close cargo door (<1 min) Arrival

The LCCs Have Engineered Rapid Turnaround Processes emulated on short haul routes by network carriers

Ground Operations – Required Time for a Turnaround ( Southwest – 737-300)

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What information do unit loads give us?

Now, suppose the work is redistributed among the four workers as follows:

• Unit Load (for each worker) = 5 min
• Capacity rate for each worker = 12 units/hour
• Capacity rate for the resource pool = 12 units/hour

Task A (5 min) Task B (5 min) Task C (5 min) Task D (5 min) Worker 1 Worker 2 Worker 3 Worker 4

Under the continuous assumption: The average inventory? “Area under the curve/3”

Average Inventory

Average inventory depends on whether inventory is assumed to change in discrete steps, or continuously

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200 400 I(t) 1 2 3 Week

Under the discrete assumption: The average inventory over weeks 0 to 3 is 300 Under the continuous assumption: The average inventory? ??????

Near-shoring affects airlines in several ways; domestic gains relative to international, yields go down as domestic markets are more competitive