Inventory CostInventory Cost

Captures time-value of holding Captures time-value of holding productproduct

Perishability, theft, opportunity cost Perishability, theft, opportunity cost of cash, insurance, shrinkage, of cash, insurance, shrinkage, obsolescenceobsolescence

Usually 10-15% for electronicsUsually 10-15% for electronics

Value of good*interest rate*timeValue of good*interest rate*time

ExerciseExercise

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 ComparisonCost ComparisonTransportationTransportation InventoryInventory HandlingHandling TotalTotal

DirectDirect 3($60+$25)3($60+$25)

=$255=$2553($2.74)3($2.74)

=$8.22=$8.22$0$0 $263.22$263.22

DC (3 DC (3 days)days)

($36+$15)+($36+$15)+

2($30+$12.50)2($30+$12.50)

+($24+$10)+($24+$10)

=$170=$170

$4.93+$4.93+

2($1.37)+2($1.37)+

$1.10+$1.10+

3*($49.32)3*($49.32)

=$156.73=$156.73

$150$150 $476.73$476.73

DC (1 DC (1 days)days)

($36+$15)+($36+$15)+

2($30+$12.50)2($30+$12.50)

+($24+$10)+($24+$10)

=$170=$170

$4.93+$4.93+

2($1.37)+2($1.37)+

$1.10+$1.10+

$49.32$49.32

=$58.09=$58.09

$150$150 $378.09$378.09

Hypothetical curvesHypothetical 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 Cumulative Number of Items DiagramItems 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 Cumulative Number DiagramDiagram

Good for one origin/one destination problemsGood for one origin/one destination problems Identify production and consumption ratesIdentify production and consumption rates Items waiting to be shippedItems waiting to be shipped Shipment timesShipment times Shipment sizesShipment sizes Items waiting to be consumedItems waiting to be consumed Total wait time from production to consumption (if Total wait time from production to consumption (if

FIFO)FIFO) Headway (H)Headway (H) Travel timeTravel time UnitsUnits Storage space proportional to max accumulation is Storage space proportional to max accumulation is

D’HD’H

Network StructuresNetwork Structures

Trade-off inventory cost and Trade-off inventory cost and transportation costtransportation cost

Milk-runMilk-run Hub and spoke (distribution center)Hub and spoke (distribution center) Direct ShippingDirect 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

ExerciseExercise

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 AggregationInventory Aggregation

Store 1Store 1 Store 2Store 2 Store 3Store 3

Average Average demanddemand

10 10 units/dayunits/day

20 20 units/dayunits/day

30 30 units/dayunits/day

Standard Standard deviation deviation of of demanddemand

2 2 units/dayunits/day

4 4 units/dayunits/day

6 6 units/dayunits/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 ManagementInventory Management

Improve service levelImprove service level Reduce logistics costReduce logistics cost Cope with randomness and Cope with randomness and

seasonalityseasonality Speculate on priceSpeculate on price Overcoming inefficiencies in Overcoming inefficiencies in

managing the logistics systemmanaging the logistics system

Distribution Distribution SystemsSystems

Prof. Anne GoodchildProf. Anne Goodchild

Spring 2009Spring 2009

Distribution systemsDistribution systems

One to oneOne to one One to manyOne to many Many to oneMany to one Many to manyMany to many

1-1 Distribution 1-1 Distribution ExamplesExamples

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

Decisions: Decisions: Shipment frequencyShipment frequency Route (this is typically a function of the Route (this is typically a function of the

network and travel times)network and travel times) Shipment timesShipment times

1-1 Distribution1-1 Distribution

Constant demandConstant demand Trade-off inventory and Trade-off inventory and

transportation cost: transportation cost: z=minz=minvv{(c{(chh/D’)v+c/D’)v+cff/v}, s.t. v<v/v}, s.t. v<vmaxmax

ccff: fixed transportation cost: fixed transportation cost

cchh: holding cost: holding cost

v*=sqrt{cv*=sqrt{cffD’/cD’/chh}}

EOQ (economic order EOQ (economic order quantity)quantity)

z=minz=minvv{Av+B/v+C}{Av+B/v+C} v*=sqrt{B/A}v*=sqrt{B/A} z*=2sqrt{AB}z*=2sqrt{AB} If v*>vIf v*>vmaxmax use v=v use v=vmaxmax

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

Why should these be equal?Why should these be equal?

Lot Size problem with Lot Size problem with VariableVariable Demand Demand

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

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

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

With an With an infinite time horizon and constant infinite time horizon and constant demanddemand this is the EOQ problem just this is the EOQ problem just discusseddiscussed

When holding cost close When holding cost close to rentto rent

Variable demandVariable demand Inventory cost negligible (big, cheap items)Inventory cost negligible (big, cheap items) Increases with maximum inventory Increases with maximum inventory

accumulationaccumulation Recall motion cost independent of shipment Recall motion cost independent of shipment

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

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

V*= D(tV*= D(tmaxmax)/n, all equal minimizes cost)/n, all equal minimizes cost cost/time=ccost/time=crrD(tD(tmaxmax)/n+c)/n+cffn/tn/tmaxmax, find n by , find n by

minimizingminimizing

When rent is negligibleWhen rent is negligible

Small, expensive itemsSmall, expensive items Simple expression cannot be Simple expression cannot be

obtained unless D(t) varies slowly obtained unless D(t) varies slowly with t (CA method)with t (CA method)

Use numerical solution (e.g. dynamic Use numerical solution (e.g. dynamic programming)programming)

One to Many DistributionOne to Many Distribution Movement of containers from the port to Movement of containers from the port to

landside destinationslandside destinations Delivery systemsDelivery systems

Decisions:Decisions: Network structureNetwork structure Fleet size (VRP and TSP)Fleet size (VRP and TSP) Shipment frequencyShipment frequency Use of an intermediate facility (minimizing Use of an intermediate facility (minimizing

logistics cost)logistics cost)

Many to one distributionMany to one distribution Export containers being delivered to a Export containers being delivered to a

marine portmarine port Collection systemsCollection systems The same analytical methods can be used The same analytical methods can be used

as with one to many distributionas with one to many distribution

Decisions:Decisions: Network structureNetwork structure Fleet sizeFleet size Shipment frequencyShipment frequency Use of an intermediate facilityUse of an intermediate facility

Many to Many Many to Many DistributionDistribution

Global distribution of marine Global distribution of marine containerscontainers

Collection and distribution systemsCollection and distribution systems

Decisions:Decisions: Network structureNetwork structure Coordination of inboundCoordination of inbound

and outbound shipmentsand outbound shipments

Many to many Many to many distributiondistribution

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

cost within the supply chaincost within the supply chain Most supply chains are not operated by Most supply chains are not operated by

the same entitythe same entity Use terminals to consolidate some of Use terminals to consolidate some of

the flowthe flow

TransshipmentTransshipment

TransshipmentTransshipment

1

Reduce line-haul cost through consolidation

TransshipmentTransshipment

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 AreasInfluence Areas

total

outbound

inbound

terminal

Cost

per

item

deliv

ere

d

Size of influence area

ThemesThemes

Scale Scale What part of the logistics system will What part of the logistics system will

you consider?you consider? Typically determined by ownership and Typically determined by ownership and

operating units but it depends on your operating units but it depends on your goalsgoals

ConsistencyConsistency Logistics systems are more manageableLogistics systems are more manageable