Logistics Management Transportation DecisionsThe transportation decision affects the cycle inventory, safety inventory, and in-transit inventory. The AM Railroad proposal requires

Logistics Management

Transportation Decisions

Özgür Kabak, Ph.D.

Typical Transport Decisions

Mode/Service selection

Freight consolidation

Trade-off between transportation cost and customer

responsiveness

Vehicle Routing

Seperate and Single Origin and Destination Points

Multiple Origin and Destination points

Routing with a Coincident Origin/Destination Point

Mode/Service Selection The problem

Define the available choices

Balance performance effects on inventory against the cost of transport

Methods for selection Indirectly through network configuration

Directly through channel simulation

Directly through a spreadsheet approach as follows

Alternatives: Air / Truck / Rail

Cost types Transportation

In-transit inventory

Source inventory

Destination inventory

Mode/Service Selection

Example

The CarryAll Luggage Company produces a line of luggage goods. The typical distribution plan is to produce finished goods inventories to be kept at the plant site. Goods are then shipped to company-owned field warehouses by way of common carriers.

Rail is currently used to ship between the East Coast plant and a West Coast warehouse. The average transit time for rail shipments is T = 21 days. At each stocking point, there is an average of 100,000 units of luggage having an average cost of C = $30 per unit. Inventory carrying cost is i = 30 percent per unit cost per year.

The company wishes to select the mode of transportation that will minimize the total costs. It is estimated that for every day that transit time can be reduced from the current 21 days, average inventory levels can be reduced by 1 percent.


Example

The demand is D = 700,000 units sold per year out

of the West Coast warehouse.

The company can use the following transportation

services:

Transport

Service

Rate($/unit)) Door-to-Door

Transit Time

(days)

Number of

shipment per

year

Rail 0.10 21 10

Piggyback (TOFC) 0.15 14 20

Truck 0.2 5 20

Air 1.4 2 40


Example

The four factors to be considered are:

Transport costs: If R denotes unit transport rate and D denotes annual demand, then RD gives an estimate of the annual transport cost

In-transit inventory: Each unit, valued at $C, spends T days in transit. If i is annual holding rate, each item costs ICT/365 in holding charges during transport time. Since D is annual demand, total in-transit inventory cost equals [ICT/365]*D.

Letting Q = shipment size, and assuming production occurs instantaneously at the plant, average annual inventory cost at the plant equals ICQ/2.(for rail Q/2=100 both at the plant and at the warehouse)

Letting C ’ = C + R, i.e., product value at the field warehouse, then average inventory cost at the field warehouse equals IC’ ‘Q/2, assuming constant lead time (All of these inventory cost estimates

assume constant and deterministic demand rate).


Example

Cost type Formule Rail TOFC Truck Air

Transp’n RXD (0.1)(700.000)

=70.000

(0.15)(700.000)

=105.000

(0.2)(700.000)

=140.000

(1.4)(700.000)

=980.000

In-transit Inv. ICDT/365 ((0.3)(30)

X(700

00)X(21))/365

=363.465

((0.3)(30)

X(700.000)

X(14))/365

=241.644

((0.3)(30)

X(700.000)X(5))/36

5

=86.301

((0.3)(30)

X(700.000)X(2))/3

65

=34.521

Plant

Inventory

ICQ/2 ((0.3)(30)

X(100.000))

=900.000

((0.3)(30)

X(50.000)(0.93)

=418.500

((0.3)(30)

(50.000)

(0.84))

=378.000

(0.3)(30)

X(25.000)

X(0.8)

=182.250

Warehouse

Inventory

IC’Q/2 ((0.3)(30.1)

X(100.000))

=903.000

((0.3)(30.15)

X(50.000)(0.93)

=420.593

((0.3)(30.2)

(50.000

X(0.84))

=380.520

((0.3)(30.4)

X(25000)

X(0.8))

=190.755

Total 2.235.465 1.185.737 984.821 1.387.526


Example

Characteristics of Transport Mode Selection

Based on Total Cost

Although assumptions in these ‘back of the envelope’ calculations seem restrictive, they generally lead to good decisions in transport mode (since costs of different modes can be significantly different) given that we do not invest in transportation equipment. Calculations do not consider costs of investing in trucks, planes, rail cars, or ships and assume that we decide mode through third-party carrier.

Calculations do not reflect costs of demand variability since they assume demand occurs at a constant, fixed rate. In distribution systems, variable demand can lead to significant ‘overage costs’ in periods when demand exhausts capacity. These costs become more significant after transport mode decision, when deciding fleet capacity for a particular mode.

Example 2 for the Choice of Transportation

Mode Based on Cost Trade-Offs

Eastern Electric (EE) purchases all the motors for its appliance from Westview.

EE currently purchases 120,000 motors each year from Westview at a price of $120 per motor. Demand has been relatively constant for several years and is expected to stay this way

Each motor averages about 10 kg and EE has traditionally purchased in lots of 3,000 motors

Westview ships each EE order within a day of receiving it

At its assembly plant, EE carries a safety inventory equal to 50 percent of the average demand for motors during the delivery lead time

The plant manager at EE has received several proposals for transportation and must decide on the one to accept



Carrier Range of Quantity

Shipped (100 kg)

Shipping Cost

($/100 kg)

AM Railroad 200 + 6.50

Northeastern

Trucking

100 + 7.50

Golden Freightways – 150 8.00

Golden Freightways 150 – 250 6.00

Golden Freightways 250 – 4.00

New Proposal:

Golden Freightways

400 – 3.00

The details of various proposals for Eastern Electric



Annual cost of holding inventory=25%

Annual holding cost is, therefore,

H= $120(price)*0.25=$30/motor

Shipments by rail requires 5 days

Shipments by truck requires 3 days



The transportation decision affects the cycle inventory, safety

inventory, and in-transit inventory.

The AM Railroad proposal requires a minimum shipment of

20,000 kg(20 tons) which corresponds to 2000 motors

The replenishment lead time = 5+1=6days

For Q=2000 motors, the plant manager obtains the following:

Cycle inventory = Q/2 = 2,000/2 = 1,000 motors

Safety inventory = L/2 days of demand (6/2)(120,000/365)

= 986 motors

In-transit Inventory = 120,000(5/365) = 1,644 motors

Total Average Inventory = 1,000 + 986 + 1,644 = 3,630 motors

Annual holding cost using AM Rail = 3,630 30 = $108,900



The transportation cost:

AM Rail charges $6.50 per 100 kg, resulting in a

transportation cost of $0.65 per motor because each

motor is about 10 kg.

Annual transportation cost using AM Rail

=120,000*0.65 = $78,000

The total annual cost using AM Rail

= inventory holding cost + transportation cost

= $108,900 + $78,000 = $186,900



Alternative Lot Size

(Motors)

Transporta

tion Cost

Cycle

Inventory

Safety

Inventory

In-transit

Inventory

Inventory

cost

Total Cost

AM Rail 2,000 $78,000 1,000 986 1,644 $108,900 $186,900

Northeaster

n Trucking

1,000

$90,000 500 658 986 $64,320 $154,320

Golden 500 $96,000 250 658 986 $56,820 $152,820

Golden 1,500 $96,000 750 658 986 $71,820 $167,820

Golden 2,500 $86,400 1,250 658 986 $86,820 $173,220

Golden 3,000 $78,000 1,500 658 986 $94,320 $172,320

Golden (old

proposal)

4,000

$72,000 2,000 658 986 $109,320 $181,320

Golden

(new

proposal)

4,000

$67,500 2,000 658 986 $109,320 $176,820

Key Points

When selecting a mode of transportation, managers

must account for inventory costs.

Modes with high transportation cost can be justified if

they result in significantly lower inventories

Trade-off between Transportation Cost and

Customer Responsiveness

Temporal aggregation is the process of combining

orders across time

Temporal aggregation reduces transportation cost

because it results in larger shipments and reduces

variation in shipment sizes

However, temporal aggregation reduces customer

responsiveness

Temporal aggregation

Example Alloy Steel is a steel service center.

All orders are shipped to customers using Carrier charges $100 for an order

an LTL shippments are charged 0.01x as variable cost

a TL (40,000 pounds) shipment charged $350 (additional)

x: number of pounds of steel shipped on the truck.

Currently Alloy Steel ships orders on the day they are received. Allowing for two days in transit, this policy allows Alloy to achieve a response time of two days.

What is the cost advantage of increasing the response time to three or four days?

Demands over two-week period:

Monday Tuesday Wednesday Thursday Friday Saturday Sunday

Week 1 19,790 17,470 11,316 26,192 20,263 8,381 25,377

Week 2 39,171 2,158 20,633 23,370 24,100 19,603 18,442

Temporal aggregation

Example

Two-day response Three-day

response Four-day

response

Day Demand Quantity

Shipped Cost ($)

Quantity

Shipped Cost ($)

Quantity

Shipped Cost ($)

1 19790 19790 297,90 0 0 0 0

2 17470 17470 274,70 37260 450,00 0 0

3 11316 11316 213,16 0 0 48576 535,76

4 26192 26192 361,92 37508 450,00 0 0

5 20263 20263 302,63 0 0 0 0

6 8381 8381 183,81 28644 386,44 54836 598,36

7 25377 25377 353,77 0 0 0 0

8 39171 39171 450,00 64548 695,48 0 0

9 2158 2158 121,58 0 0 66706 717,06

10 20633 20633 306,33 22791 327,91 0 0

11 23370 23370 333,70 0 0 0 0

12 24100 24100 341,00 47470 524,70 68103 731,03

13 19603 19603 296,03 0 0 0 0

14 18442 18442 284,42 38045 450,00 38045 450,00

Total Cost 4120,95 3284,53 3032,21

Vehicle Routing

Seperate and Single Origin and Destination Points

Multiple Origin and Destination points

Routing with a Coincident Origin/Destination Point

Seperate and Single O/D Points

Origin

Amarillo

Oklahoma

City

Destination

Fort Worth

A B E

I

C

D G

F

H

J

90 minutes 84 84

138

348

156

48

132

150

126

132 120 66

126

48

60

Note : All link times are in minutes

90

Determine the best path between origin and destination points over a

network of routes


Shortest route method is efficient for finding the minimal cost route

Consider a time network between Amarillo and Fort Worth. Find the minimum travel time.

The procedure can be paraphrased as:

Find the closest unsolved node to a solved node

Calculate the cost to the unsolved node by adding the accumulated cost to the solved node to the cost from the solved node to the unsolved node.

Select the unsolved node with the minimum time as the new solved node. Identify the link.

When the destination node is solved, the computations stop. The solution is found by backtracking through the connections made.


Multiple origin and destination points

Use Excel Solver to solve the problem!

Plant 1

Requirements = 600

Plant 2

Requirements = 500

Plant 3

Requirements = 300

Supplier A

Supply 400

Supplier C

Supply 500

Supplier B

Supply 700

4 a

7

6

5

5

5

9

5

8

a The transportation rate in $ per ton for an optimal routing between supplier A and plant 1 .

Multiple origin and destination points

Solving via Excel Solver

Routing with a Coincident

Origin/Destination Point

Typical of many single truck routing problems from a single depot

Mathematically, a complex problem to solve efficiently. However, good routes can be found by forming a route pattern where the paths do not cross -a "tear drop" pattern.

D D

Depot Depot

(a) Poor routing--

paths cross

(b) Good routing--

no paths cross

Single Route solved as a Travelling Sales

Person Problem

0 1 2 3 4 5 6 7 8

8

7

6

5

4

3

2

1

0

X coordinates

1

2

3

19

11

12

13

14

15

16

17

18

4

5

6

7

8

9

10

20

D

Y coordinates

0 1 2 3 4 5 6 7 8

8

7

6

5

4

3

2

1

0

X coordinates

1

2

3

19

11

12

13

14

15

16

17

18

4

5

6

7

8

9

10

20

D

Y coordinates

(a) Location of beverage accounts

and distribution center (D) with

grid overlay

(b) Suggested routing pattern

Multi-Vehicle Routing and Scheduling

A problem similar to the single-vehicle routing

problem except that a number of restrictions are

placed on the problem.

Chief among these are:

A mixture of vehicles with different capacities

Time windows on the stops

Pickups combined with deliveries

Total travel time for a vehicle

Practical Guidelines for Good Routing and

Scheduling

1. Load trucks with stop volumes that are in

closest proximity to each other

(a) Weak clustering

Depot

(b) Better clustering

D D

Depot

Stops

Guidelines (Cont’d)

2. Stops on different days should be arranged to

produce tight clusters

F

F

F

F

F

F

F

T

T T

T

T

T

T

D

Depot

F

F

F

F

F

T

T

T

F T

F

T

T

T

D

Depot

(a) Weak clustering-- routes cross

(b) Better clustering

Stop

May need to

coordinate with

sales to achieve

clusters

Guidelines (Cont’d)

3. Build routes beginning with the farthest stop from the

depot

4. The stop sequence on a route should form a teardrop

pattern (without time windows)

5. The most efficient routes are built using the largest

vehicles available first

6. Pickups should be mixed into delivery routes rather

than assigned to the end of the routes

7. A stop that is greatly removed from a route cluster is a

good candidate for an alternate means of delivery

8. Narrow stop time window restrictions should be

avoided (relaxed)

“Sweep” Method for VRP Example A trucking company has 10,000-unit vans for merchandise

pickup to be consolidated into larger loads for moving over long distances. A day’s pickups are shown in the figure below. How should the routes be designed for minimal total travel distance?

“Sweep” Method Solution Sweep direction

is arbitrary

Depot

1,000

2,000

3,000

2,000

4,000

2,000

3,000 3,000

1,000

2,000 2,000

2,000

Route #1

10,000 units

Route #2

9,000 units

Route #3 8,000 units

The “Savings” Method for VRP

Depot Depot

(a) Initial routing

Route distance = d 0,A +d A,0 +d 0,B + d B,0

(b) Combining two stops on a route

Route distance = d 0,A +d A,B +d B,0

A

B

d A,0

d 0,A d 0,B

d B,0

A

B d B,0

d 0,A

d A,B

Stop

Stop

0 0

“Savings” is better than “Sweep” method—

has lower average error

Savings Method Observation

The points that offer the greatest savings when

combined on the same route are those that are

farthest from the depot and that are closest to

each other.

This is a good principle

for constructing multiple-stop

routes

Next Class

Midterm Exam

The Exam will be held in the classroom

20 questions multiple choice

2 or 3 questions problem solving (notes/books are open)

Documents

Logistics Management Transportation DecisionsThe transportation decision affects the cycle inventory, safety inventory, and in-transit inventory. The AM Railroad proposal requires