Logistics Cost Part II

Professor GoodchildSpring 11

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

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

Network Structures

• Trade-off inventory cost and transportation cost

• Best choice depends on qualities of product, customer demand, and network

• 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 3Average 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

Distribution Systems

Prof. Anne GoodchildSpring 2010

Distribution systems

• One to one• One to many• Many to one• Many to many

1-1 Distribution Examples

• Port to rail head drayage• Small in scale and/or scope

• Decisions: – Shipment frequency– Route (this is typically a function of the network

and travel times)– Shipment times

1-1 Distribution

• Constant demand• Trade-off inventory and transportation cost:

z=minv{(ch/D’)v+cf/v}, s.t. v<vmax

• cf: fixed transportation cost

• ch: holding cost

• v*=sqrt{cfD’/ch}

EOQ (economic order quantity)

• z=minv{Av+B/v+C}• v*=sqrt{B/A}• z*=2sqrt{AB}• If v*>vmax use v=vmax

• v* makes both of the terms in the objective function equal (motion cost = holding cost)

Lot Size problem with Variable Demand

• D(t) gives cumulative number of items demanded between 0 and t

• D’(t) is variable demand rate• Seek the set of times when shipments are to be

received and the shipment sizes that will minimize sum of motion plus holding costs over some time period

• With an infinite time horizon and constant demand this is the EOQ problem just discussed

When holding cost close to rent• Variable demand• Inventory cost negligible (big, cheap items)• Increases with maximum inventory accumulation• Recall motion cost independent of shipment sizes

and times (only dependent on total amount moved or average)

• Thus we want to choose times and sizes to minimize holding cost

• V*= D(tmax)/n, all equal minimizes cost• cost/time=crD(tmax)/n+cfn/tmax, find n by minimizing

When rent is negligible

• Small, expensive items• Simple expression cannot be obtained unless

D(t) varies slowly with t (CA method)• Use numerical solution (e.g. dynamic

programming)

One to Many Distribution• Movement of containers from the port to landside

destinations• Delivery systems

• Decisions:– Network structure– Fleet size (VRP and TSP)– Shipment frequency– Use of an intermediate facility (minimizing logistics cost)

Many to one distribution• Export containers being delivered to a marine port• Collection systems• The same analytical methods can be used as with

one to many distribution

• Decisions:– Network structure– Fleet size– Shipment frequency– Use of an intermediate facility

Many to Many Distribution

• Global distribution of marine containers• Collection and distribution systems

• Decisions:– Network structure– Coordination of inbound

and outbound shipments

Many to many distribution

• The problem can often, and should often, be broken down into pieces – Inbound logistics (many to one)– Outbound logistics (one to many)– Be mindful of who is responsible for cost within

the supply chain– Most supply chains are not operated by the same

entity– Use terminals to consolidate some of the flow

Transshipment

Transshipment

1

Reduce line-haul cost through consolidation

Transshipment

1

Introduce levels of transshipment terminalsThese can be used on the collection side or the distribution sideConsider the use of tiered airports in a hub and spoke system

2

2

Influence area

Influence Areas

total

outbound

inboundterminal

Cost

per

item

del

iver

ed

Size of influence area

Themes

• Scale – What part of the logistics system will you

consider?– Typically determined by ownership and operating

units but it depends on your goals• Consistency

– Logistics systems are more manageable