1 1 milk runs and variability john h. vande vate fall, 2002

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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

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Tuesday• Aaron Marshall• Distribution Engineer• Peach State Integrated Technologies• Translating these kind of location models into

practice – case studies, challenges.