11

Milk Runsand

Variability

John H. Vande VateFall, 2002

22

What are Milkruns?

• Daily routes • Visit several suppliers• Allow frequent visits by sharing vehicle

capacity• Reduce inventory without increasing

transport• Same route every day

33

Milkruns & Consolidation

44

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

55

Example

Assembly Plant

Route Anchor

Route Anchor

Route AnchorRoute Anchor

66

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

77

Total Cost

Build routes that minimize Total Cost• Cost of planned transportation• Cost of unplanned (expedited)

transportation

88

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

99

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!

1010

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

C

1111

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

C

1212

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

1313

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

practice – case studies, challenges.