Truck Shipment Example: Periodic 19. If the value of the product - - PowerPoint PPT Presentation

Truck Shipment Example: Periodic

• 19. If the value of the product increased to $85,000 per ton,

should the product be shipped TL or LTL?

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0.76 1.90 Shipment weight (tons)

(a) $25000 value per ton

28536 40066 TLCTL TLCLTL TCTL TCLTL IC 0.27 1.03 Shipment weight (tons)

(b) $85000 value per ton

47801 52618 TLCTL TLCLTL TCTL TCLTL IC

Truck Shipment Example: Periodic

• Better to pick from separate optimal TL and LTL because

independent charge has two local minima:

{ }

*

arg min ( ), ( ) =

TL LTL q

q TLC q TLC q

*

arg min ( ) α     =  + 

q

f q c q vhq q

!

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Truck Shipment Example: Periodic

• 20. What is optimal independent shipment size to ship 80 tons

per year of a Class 60 product valued at $5000 per ton, with the same inventory fraction and carrying rate, between Raleigh and Gainesville?

{ }

3 * * *

32.16 lb/ft arg min ( ), ( ) 8.5079 ton ( ) $25,523.60 / yr ( ) = = = = <

TL LTL q TL LTL

s q TLC q TLC q TLC q TLC q

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Truck Shipment Example: Periodic

• 21. What is the optimal shipment size if both shipments will

always be shipped together on the same truck (with same shipment interval)?

( )

( )

1 2 agg 1 2 agg 1 2 agg 1 2 agg 3 agg 3 1 2 1 2 1 2 agg 1 2 agg agg

, , 20 80 100 ton aggregate weight, in lb 100 14.31lb/ft 20 80 aggregate cube, in ft 4.44 32.16 20 80 85,000 5000 $21,000 / ton 100 100 d d h h h f f f f s f f s s f f v v v f f α α α = = = = = = + = + = = = = = + + = + = + =

agg * agg agg agg

100(2.5511)532 4.6414 ton (1)21000(0.3)

TL TL

f r d q v h α = = =

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Truck Shipment Example: Periodic

• Summary of results:

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Ex 6: FTL vs Interval Constraint

• On average, 200 tons of components are shipped 750 miles from your fabrication

plant to your assembly plant each year. The components are produced and consumed at a constant rate throughout the year. Currently, full truckloads of the material are shipped. What would be the impact on total annual logistics costs if TL shipments were made every two weeks? The revenue per loaded truck-mile is $2.00; a truck’s cubic and weight capacities are 3,000 ft3 and 24 tons, respectively; each ton

• f the material is valued at $5,000 and has a density of 10 lb per ft3; the material

loses 30% of its value after 18 months; and in-transit inventory costs can be ignored.

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• bs

max

1 1 200, 750, 1, 2, 3000, 24, 5000, 10 2 2 0.3 0.2 0.05 0.06 0.2 0.31, min , 15 1.5 2000

TL cu wt h cu FTL wt h

f d r K K v s x sK h h q q K t α = = = + = = = = = =   = = =  = + + = = = =    

max min 2wk 2wk min 2wk min

2 7 26.09, 7.67, 51,016 365.25

TL

f t n q TLC n r d vhq n α ⋅ =  = = = = + =

2wk

$7,766 per year increase with two-week interval constraint

FTL

TLC TLC TLC ∆ = − = 2-wk TL LTL not considered 13.33, 43,250,

FTL FTL FTL TL FTL FTL

f n TLC n r d vhq q α = = = +  =

Ex 7: FTL Location

• Where should a DC be located in order to minimize

transportation costs, given:

1. FTLs containing mix of products A and B shipped P2P from DC to customers in Winston-Salem, Durham, and Wilmington 2. Each customer receives 20, 30, and 50% of total demand 3. 100 tons/yr of A shipped FTL P2P to DC from supplier in Asheville 4. 380 tons/yr of B shipped FTL P2P to DC from Statesville 5. Each carton of A weighs 30 lb, and occupies 10 ft3 6. Each carton of B weighs 120 lb, and occupies 4 ft3 7. Revenue per loaded truck-mile is $2 8. Each truck’s cubic and weight capacity is 2,750 ft3 and 25 tons, respectively

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• 83
• 82
• 81
• 80
• 79
• 78

34 34.5 35 35.5 36 36.5

Asheville Statesville Winston-Salem Greensboro Durham Raleigh W i l m i n g t

• n

50 150 190 220 270 295 420 40

Ex 7: FTL Location

($/yr) ($/mi-yr) (mi) , ($/mi-yr) (TL/yr) ($/TL-mi) (ton/yr) ($/ton-mi) , ($/ton-mi) max max

,

i i i i FTL i i i FTL i

TC w d w f r n r r f r n q q = × = × = × = =



( )

in

• ut

in

• ut

in

• ut

(Montetary) Weight Losing: 79 67 39 33 Physically Weight Unchanging (DC): 480 480 w w n n f f Σ = > Σ = Σ = > Σ = Σ = = Σ =

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13 30 33

48

20 78 > 73 48 < 73

:

i

w

*

Asheville Durham Statesville Winston-Salem Wilmington

146, 73 2 W W = =

DC

4 3 5 1 2

3 2 max 2 2 2

120 30(2750) 30 lb/ft , min 25, 25 ton 4 2000 380 380, 15.2, 15.2(2) 30.4 25 s q f n w   = = = =     = = = = =

3 agg 3 3 4 agg 4 4 5 agg 5 5

96 0.20 96, 6.69, 6.69(2) 13.38 14.3478 144 0.30 144, 10.04, 10.04(2) 20.07 14.3478 240 0.50 240, 16.73, 16.73(2) 33.45 14.3478 f f n w f f n w f f n w = = = = = = = = = = = = = = = = = =

3 1 max 1 1 1

30 3(2750) 3 lb/ft , min 25, 4.125 ton 10 2000 100 100, 24.24, 24.24(2) 48.48 4.125 s q f n w   = = = =     = = = = =

agg 3 agg agg max

480 10.4348(2750 $2 / TL-mi, 100 380 480 ton/yr, 10.4348 lb/ft , 25, 14.3478 100 380 2000 3 30

A B A B A B

f r f f f s q f f s s   = = + = + = = = = = =     + +

Durham Winston- Salem Wilmington

DC

30% Asheville Statesville

Ex 7: FTL Location

• Include monthly outbound frequency constraint:

– Outbound shipments must occur at least once each month – Implicit means of including inventory costs in location decision

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{ } { } { } { }

max min max min 3 3 4 4 5 5

1 1 yr/TL 12 TL/yr 12 max , max 6.69,12 12, 12(2) 24 max 10.04,12 12, 12(2) 24 max 16.73,12 16.73, 16.73(2) 33.45

FTL

t n t TC n n rd n w n w n w =  = = ′ = = = = = = = = = = = = =

24 30 33

48

24 78 < 80 48 < 80

:

i

w

*

Asheville Durham Statesville Winston-Salem Wilmington

102 > 80

160, 80 2 W W = =

( )

in

• ut

in

• ut

in

• ut

(Montetary) Weight : 79 81 39 41 Physically Weight Unchanging (DC) Ga : 480 48 ining w w n n f f Σ = < Σ = Σ = < Σ = Σ = = Σ =

Location and Transport Costs

• Monetary weights w used for location are, in general, a

function of the location of a NF

– Distance d appears in optimal TL size formula – TC & IC functions of location  Need to minimize TLC instead of TC – FTL (since size is fixed at max payload) results in only constant weights for location  Need to only minimize TC since IC is constant in TLC

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1 1 1 1 max max max 1 1

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) con

m m i TL i i i i i i i i m m i i i i i i i i i i m m i FTL i i i FTL i i

f TLC w d vhq rd vhq q f f rd rd vh f rd vh vh f rd vh vh f TLC rd vhq w d vhq TC q α α α α α α α α α

= = = = = =

= + = +   = + = +       = + = + = +

     

x x x x x x x x x x x x x x x stant

Transshipment

• Direct: P2P shipments from Suppliers to Customers
• Transshipment: use DC to consolidate outbound

shipments

– Uncoordinated: determine separately each optimal inbound and outbound shipment  hold inventory at DC – (Perfect) Cross-dock: use single shipment interval for all inbound and outbound shipments  no inventory at DC

(usually only cross-dock a selected subset of shipments)

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Uncoordinated Inventory

• Average pipeline inventory level at DC:

1.55 2 ≈ q 1.11 2 ≈ q

Supplier 2 Supplier 1

1 , inbound 2 ,

• utbound

α α α α α = +   + =   + 

O D O D

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TLC with Transshipment

• Uncoordinated:
• Cross-docking:

( )

* * *

• f supplier/customer

arg min ( ) = = =

i i i q i i

TLC TLC i q TLC q TLC TLC q

( )

* * *

, shipment interval ( ) ( ) cf. ( ) ( ) ( ) independent transport charge as function of 0, inbound ,

• utbound

arg min ( )

i i O D i t i

q t f c t f TLC t vhft TLC q c q vhq t q c t t t TLC t TLC TLC t α α α α α =   = + = +     = +  =  +  = =

 

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