Logistics Cost Part II
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Transcript of Logistics Cost Part II
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