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
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