1 1 Newsvendor Models & the Sport Obermeyer Case John H. Vande Vate Spring, 2012.
1 1 Milk Runs and Variability John H. Vande Vate Fall, 2002.
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Transcript of 1 1 Milk Runs and Variability John H. Vande Vate Fall, 2002.
11
Milk Runsand
Variability
John H. Vande VateFall, 2002
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What are Milkruns?
• Daily routes • Visit several suppliers• Allow frequent visits by sharing vehicle
capacity• Reduce inventory without increasing
transport• Same route every day
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Milkruns & Consolidation
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Building Milkruns
• Filter out any full truckload• Decide the number of routes (may take
several passes)• Using our Location/Allocation heuristic
– Treat the facilities as route “anchors”– The customers assigned to the “anchor” are
on the same milk run– Treat the sum of distances to the anchors as
a surrogate for the route length
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Example
Assembly Plant
Route Anchor
Route Anchor
Route AnchorRoute Anchor
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The Impact of Variability
Plan for variability by allowing routes to use only, say, 80% of vehicle capacity on average
When daily volume exceeds vehicle capacity, pay premium freight to expedite excess
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Total Cost
Build routes that minimize Total Cost• Cost of planned transportation• Cost of unplanned (expedited)
transportation
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Approximation• Daily Volume from supplier is normally
distributed• Mean • Variance 2 • Covariances ij
• Mean on the route r = sum of Means
• Variance on the route r
2 = sum of variances + 2*sum of covariances
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Probability of Expediting
• Depends on – how full we plan to load the vehicle– What the variance of demand on the route is
• Probability we have to expedite– 1 - N((c-r)/r) (Cumulative Std Normal)
• Doesn’t address the possibility of requiring more than one truck!
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Distribution
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 2 4 6 8 10 12
Expediting
• If we plan to fill the truck, 50% chance we expedite, regardless of the variance
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Distribution
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 2 4 6 8 10 12
Expediting
• The less we plan to fill the truck the less likely we are to expedite
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Nomal Distributions with Different Variances
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
-10 -8 -6 -4 -2 0 2 4 6 8 10
Expediting
• The greater the variance the less we should plan to fill the truck
C
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Tuesday• Aaron Marshall• Distribution Engineer• Peach State Integrated Technologies• Translating these kind of location models into
practice – case studies, challenges.