Logistics Cost

Professor Goodchild

Spring 08

Follow the path of an item

• Carried from production area to storage area

• Held in temporary storage

• Loaded into transport vehicle

• Transported to the destination

• Unloaded, handled, and held for consumption

What incurs cost?

• Overcoming distance (motion): – transportation cost (over the road/rail) – handling cost (through a terminal, in and out of

vehicles)

• Overcoming time (holding): – holding cost:

• Rent (proportional to D’H)• Waiting (value*time*interest rate)

– In transit– pipeline

How you calculate the value depends on the analysis you are doing (cost or price)We will include all costs, regardless of who pays them (we are designing systems)

Cumulative Number of Items Diagram

time

cumulative number of items

Production (rate D’)

shipments

arrivals

Consumption (D’)

An item is a fixed quantity of infinitely divisible quantity (e.g. person, parcel, case of beer)

tm

H

Consider units on area

Queue Discipline

• FIFO: First In First Out

• LIFO: Last In First Out

• Others

If LIFO inventory cost is usually underestimated

Holding cost: Rent

• proportional to max. accumulation

• Independent of flow rate, D’

• Proportional to max. time between dispatches

Holding cost: Waiting

• Cost associated with delay to items

• ciHi+citm

• Stationary+pipeline inventory

• Determining ci is difficult

Transportation Cost

• Shipment cost has fixed and variable portions: cf+cvv (v is number of items)

– Fixed cost: driver wage– Variable cost: increased fuel consumption

• Cost for n shipments: cfn+cvV (V is total items across shipments, n is number of shipments)

Transportation cost

• Cost per item: cf/vavg+cv

– Economies of scale from sharing fixed cost

– Also cost per item is (cf/D’Havg)+cv

• Transportation cost decreases with average headway

• Holding cost increased with maximum headway• Therefore shipments should be spread so as to

minimize the maximum (all the same)

Transportation cost and distance

• cf is independent of v (items) but both cf and cv are typically functions of distance (d)

• cf=cs+cdd• cv=c’s+c’dd• Cost for n shipments: cfn+cvV

– csn+cddn+c’sV+c’ddV– Add cost of stopping:

cs(1+ns)n+cddn+c’sV+c’ddV

So small we neglect it

Transportation cost

• Cost per item (divide by nvavg):

– cs(1+ns)/vavg+cdd/vavg+c’s or

– cs(1+ns)/D’Havg+cdd/D’Havg+c’s

• If headways vary a lot so do shipment sizes, and therefore truck sizes, better to use consistent truck sizes (second reason to keep shipment sizes consistent)

shipment size

Trans. CostPer shipment

Capacity Restrictions

vmax – number of items that will fit in vehicle

cf

cv

Slope is total cost per item, lowestwhen truck full

shipment size

Trans. CostPer shipment

Relationship to sizeMagnitude of fixed and variable cost determine most economic choice as a function of shipment size.

As shipment size increases, favor lower variableand higher fixed costs.

Inventory Cost

• Captures time-value of holding product

• Perishability, theft, opportunity cost of cash, insurance, shrinkage, obsolescence

• Usually 10-15% for electronics

• Value of good*interest rate*time

Exercise

DC100 miles

100 miles

100 miles

60 miles

40 miles

50 miles

50 miles

Fuel economy: 10 mpgDriver wages: $15/hourIgnore depreciation of vehicle, insuranceSpeed of vehicle: 25 mphPrice of fuel: $2.50 per gallon

Value of goods in a truck: $100,000Interest rate: 6% per year

Time spent at DC: 3 daysHandling cost at DC: $50 per truckIgnore rent, operating cost of DC

Calculate one way transportation cost and one way inventory cost.

Cost ComparisonTransportation Inventory Handling Total

Direct 3($60+$25)

=$255

3($2.74)

=$8.22

$0 $263.22

DC (3 days)

($36+$15)+

2($30+$12.50)

+($24+$10)

=$170

$4.93+

2($1.37)+

$1.10+

3*($49.32)

=$156.73

$150 $476.73

DC (1 days)

($36+$15)+

2($30+$12.50)

+($24+$10)

=$170

$4.93+

2($1.37)+

$1.10+

$49.32

=$58.09

$150 $378.09

Hypothetical curves

Shipment frequency

cost

transportation

inventory

total

Minim cost shipment frequency

We will identify the optimal when we talk about distribution systems

Cumulative Number of Items Diagram

time

cumulative number of items

Production (rate D’)

shipments

arrivals

Consumption (D’)

An item is a fixed quantity of infinitely divisible quantity (e.g. person, parcel, case of beer)

tm

H

Consider units on area

Cumulative Number Diagram

• Good for one origin/one destination problems• Identify production and consumption rates• Items waiting to be shipped• Shipment times• Shipment sizes• Items waiting to be consumed• Total wait time from production to consumption (if FIFO)• Headway (H)• Travel time• Units• Storage space proportional to max accumulation is D’H

Network Structures

• Trade-off inventory cost and transportation cost

• Milk-run

• Hub and spoke (distribution center)

• Direct Shipping

•No DC cost•Reduce lead times•Higher transportation expense•Good if fully loaded trucks or timely goods

•Store goods to pool inventory risk•Trade-offs in size as more demand can be pooled, but then farther from destination

•Not stored for a significant length of time•Sorted, consolidated, shipped out directly•Use different containers•Requires high volume

warehouse crossdocks

Exercise

DC100 miles

100 miles

100 miles

60 miles

40 miles

50 miles

50 miles

Inventory Pooling

What is the inventory heldin the system without the distribution center?

What is the inventory held in the system with the distribution center?

Inventory Aggregation

Store 1 Store 2 Store 3

Average demand

10 units/day

20 units/day

30 units/day

Standard deviation of demand

2 units/day 4 units/day 6 units/day

Calculate number required on hand if held at 3 stores, central facility.Online retailers as well as traditional retailersTypically increases transportation cost (think outbound, but who pays?)

Inventory Management

• Improve service level

• Reduce logistics cost

• Cope with randomness and seasonality

• Speculate on price

• Overcoming inefficiencies in managing the logistics system