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Chris Caplice ESD.260/15.770/1.260 Logistics Systems
Dec 2006
Transportation Management Network & Hubs
© Chris Caplice, MIT2MIT Center for Transportation & Logistics – ESD.260
Distribution System Approach
Distribution System Number and location of transshipment pointsRoutes and schedules of vehicles Routes and schedules of items flowing
Operational Tactical Strategic
Decisions made at different times Strategic – longer scope and less data available (yr+)Tactical – shorter scope w/ planning data (week to yr)Operational – very short scope real data (daily)
© Chris Caplice, MIT3MIT Center for Transportation & Logistics – ESD.260
The Network Design Problem
V VVVV V V V
PP P P P
W WW W W WW
C CC C C CC
C CC C C C CC
Treat each potential facility location as a node
© Chris Caplice, MIT4MIT Center for Transportation & Logistics – ESD.260
V VVVV V V V
PP P P P
W WW W W WW
C CC C C CC
C CC C C C CC
The Network Design Problem
Treat shipment flows as links or arcs
© Chris Caplice, MIT5MIT Center for Transportation & Logistics – ESD.260
The Network Design Problem
Network design is the selection of nodes and links that minimize total cost
V
The Network Design Problem
V V V
P P P
W WW W
C CC C C CC
C CC C C C CC
© Chris Caplice, MIT6MIT Center for Transportation & Logistics – ESD.260
Distribution Network Design
Three key questions for Distribution NDHow many DCs should there be?Where should the DCs be located?For each SKU and each customer:
which DC should serve the customer, and which plant should serve the DC?
Cost & Performance Trade-OffsTransportation Costs (Inbound versus Outbound)Facility Costs (Fixed versus Throughput)Inventory Costs (Cycle versus Safety Stock)Customer Service (Availability versus Order Cycle Time)
© Chris Caplice, MIT7MIT Center for Transportation & Logistics – ESD.260
Facility Location Cost Trade-Offs
0 2 4 6 8 10 12 14 16 18 20Number of Warehouses
Freight Cost Facility CostsInventory Cost Total Costs
© Chris Caplice, MIT8MIT Center for Transportation & Logistics – ESD.260
A “Simple” MILP Formulation
ijkl
k
il
Where:X Total annual volume of product i produced at plant j
and shipped through DC k on to customer zone lZ {0,1};1 if the DC at k is selected, else 0
D = annual demand for product i at custom
=
=
ij
k
k
ijkl
er zone lP = maximum annual capacity for product i at plant j
V = maximum annual throughput volume at DC at kF = The fixed annual operating cost of a DC at kC The variable cost to produce one =
ijkl ij ijk ik ikl
unit of product i at
plant j and ship it through DC k to cuC =C[mnfg] +
stomerTL +DCTHPT
zone lso +LTt Ltha
I J K L K
ijkl ijkl k ki=1 j=1 k=1 l=1 k=1
J K
ijkl ilj=1 k=1
K L
ijkl ijk=1 l=1
I J L
ijkl k ki=1 j=1 l=1
ijk
Minimize: C X F Z
Subject to:
X D ; for all I and L
X P ; for all I and J
X V Z ; for all K
X 0 , for all I, J, K
Z
+
≥
≤
≤
≥
∑ ∑ ∑ ∑ ∑
∑ ∑
∑ ∑
∑ ∑ ∑
k = {0,1} , for all K
How big is this formulation?
20 Plants, 30 Products/ Product Groups, 50 Potential DCs, and 400 Customers
Regions, there are:
12,000,000 possible flows!
© Chris Caplice, MIT9MIT Center for Transportation & Logistics – ESD.260
A “Better” MILP FormulationI J K I K L K
ijk ijk ikl ikl k ki=1 j=1 k=1 i=1 k=1 l=1 k=1
K
ikl ilk=1K
ijk ijk=1
I J
ijk k ki=1 j=1
J L
ijk iklj=1 l=1
Minimize: A X B Y F Z
Subject to:
Y D ; for all I and L
X P ; for all I and J
X V Z ; for all K
X Y ; for
+ +
≥
≤
≤
≥
∑∑∑ ∑∑∑ ∑
∑
∑
∑∑
∑ ∑
ijk
ikl
k
all I and K
X 0; for all I, J, K
Y 0; for all I, K, LZ = {0,1} , for all K
≥
≥
How big is this formulation?
20 Plants, 30 Products/ Product Groups, 50 Potential DCs, and 400 Customers
Regions, there are:
50,000 (30k IB & 20k OB) possible flows
ijk
k
ikl
X Total annual volume of product i produced at plant j and shipped through DC k
Y Total annual volume of product i shipped from DC k t
Where:
Z {0,1};1 if tho customer zo
e DC k is selne l
ected,
=
=
=
ijk
ikl
A The variable cost to produce one unit of product i at plant
j and ship it to the DC at kB The variable cost to move one unit of product i through the DC at k and ship it to the
c
el
us
se
r
0
tome
=
=
il
ij
k
k
D = annual demand for product i at customer zone lP = maximum annual capacity for product i at plant j
V = maximum annual throughput volume at DC at kF = The fixed annual oper
zone at l
ating cost of a DC at k
© Chris Caplice, MIT10MIT Center for Transportation & Logistics – ESD.260
Issues & Concerns
Data IssuesDemand Point AggregationDemand over Time PeriodsProfiling freight cost data Fixed Costs: Periodic versus One-TimeCost Estimating Functions
Global ExtensionsFreight Rate AvailabilityTransfer Prices and TaxesExchange RatesDuty and Duty Drawback
Missed QuestionsWhat about Inventory? What about Customer Service?Supply Chain Extensions
© Chris Caplice, MIT11MIT Center for Transportation & Logistics – ESD.260
Inventory Deployment
What safety stock should each DC have?
Why is this difficult?
ij ij
22 2ij ijij i D LSS K σ L σ D= +
Safety Stock Units for SKUi@ DCj
Std Dev of Demand
Average Supplier Lead Time
Std Dev of Supplier Lead time
Average Demand
ICCij = COGi x ICC%ij x SSij
Inventory Carrying Cost for SKUi @ DCj
Fill rate adjustment by SKU by Customer
Inventory Carrying Cost %
Cost of Goods Sold
© Chris Caplice, MIT12MIT Center for Transportation & Logistics – ESD.260
Transportation Networks
One to Many w/o TransshipmentOne to Many w/ Transshipment (why?)Many to Many
w/o TransshipmentDirectMulti-Stop
w/ Transshipment (Hub)DirectsMulti-Stops
© Chris Caplice, MIT13MIT Center for Transportation & Logistics – ESD.260
Many to Many Networks
W1
W2
W3
E2
E1
E3
W4 E4
W5 E5
How should I ship from 5 origins to 5 destinations?
Direct Network
© Chris Caplice, MIT14MIT Center for Transportation & Logistics – ESD.260
H
W1
W2
W3
E2
E1
E3
W4 E4
W5 E5
How should I ship from 5 origins to 5 destinations?
Hub & Spoke Network
Many to Many Networks
© Chris Caplice, MIT15MIT Center for Transportation & Logistics – ESD.260
Direct versus Hub
Which is better? How many trucks are needed?What is the cost? How can I increase frequency of service?
Example DetailsNeed to pick up every day from terminalsAverage distance between terminals = 500 milesAverage distance from terminals to hub = 350 milesCost for transportation = $200 shipment + 1 $/mile
distance
Cost
per
load
© Chris Caplice, MIT16MIT Center for Transportation & Logistics – ESD.260
Hub versus Direct
How does demand impact?Daily demand from terminal i to j is ~N(100, 30)Suppose break even for a TL move is 50 units.
Variability Direct Network
What is the:Average quantity per move?Standard deviation of load per move?Coefficient of Variation per move?
What is the frequency of moves that lose money?Hub Network
What is the:Average quantity per move?Standard deviation of load per move?Coefficient of Variation per move?
What is the frequency of moves that lose money?
© Chris Caplice, MIT17MIT Center for Transportation & Logistics – ESD.260
Hub Advantages
Hub consolidation reduces costsConsolidation increases conveyance utilizationTransportation has a fixed (per conveyance) cost
Fewer conveyances are requiredIs consolidation better . . .
when point to point demand is higher or lower?when variability of point to point demand is higher or lower?
Coefficient of variation as useful metricProvides better level of service with fewer resources
Non-stop vs. frequency of serviceNon-stop vs. geographical coverage
serving more / smaller cities
© Chris Caplice, MIT18MIT Center for Transportation & Logistics – ESD.260
Hub Disadvantages
Cost of operating the hubFacility costsHandling costs - unloading, sorting, loadingOpportunity for misrouting, damage, theft (shrinkage)
CircuityLonger total distance travelledMore vehicle-hours expended
Impact on service levelsAdded time in-transitLower reliability of transit
Productivity/utilization lossCycle/”bank” size
© Chris Caplice, MIT19MIT Center for Transportation & Logistics – ESD.260
Hub EconomicsRelative distances
Degree of circuityVehicle and shipment size
Smaller shipments → hub more economical
Demand patternMany destinations from each originMany origins into each destination
The hub locationSignificant business generation for passengers
Air – large cityTransit – CBD
Good access for freightHighways accessAway from population centers
© Chris Caplice, MIT20MIT Center for Transportation & Logistics – ESD.260
Terminal Bypass Operations
When would you want to bypass hub handling?Examples
Air - through flightUse heaviest pairMarketing; reliability; lower costs
LTL - “head loading”Rail - block placementParcel - pre-packaging
Packages physically travel to the hub, but are not touched or handled.
© Chris Caplice, MIT21MIT Center for Transportation & Logistics – ESD.260
Directs in a Hub-and-Spoke Network
H
W1
W2
W3
E2
E1
E3
W4 E4
W5 E5
Considerations in setting direct service:
Demand between E1 and W2Service E1-Hub and Hub-W2 Effect on the hub Effect on E1 activities
For freight services:Dynamic (“opportunistic”)Direct services (“surge move”)Planned (“multiple offerings”)
© Chris Caplice, MIT22MIT Center for Transportation & Logistics – ESD.260
Regional Terminals
H
W1
W2
W3
E2
E1
E3
W4 E4
W5 E5
What if there is demand between the W terminals?
© Chris Caplice, MIT23MIT Center for Transportation & Logistics – ESD.260
H
W1
W2
W3
E2
E1
E3
W4 E4
W5 E5
W
Regional Terminals
© Chris Caplice, MIT24MIT Center for Transportation & Logistics – ESD.260
Bypassing the Hub
H
W1
W2
W3
E2
E1
E3
W4 E4
W5 E5
W
© Chris Caplice, MIT25MIT Center for Transportation & Logistics – ESD.260
More Routing Alternatives
H
W1
W2
W3
E2
E1
E3
W4 E4
W5 E5
W E
© Chris Caplice, MIT26MIT Center for Transportation & Logistics – ESD.260
H
W1
W2
W3
E2
E1
E3
W4 E4
W5 E5
W E
Routings:• W5-W-E5• W5-H-E5• W5-E-E5• W5 – E5
More Routing Alternatives
Direct effects:•On each of the three alternatives
Indirect effects:•Congestion and spill-overs
© Chris Caplice, MIT27MIT Center for Transportation & Logistics – ESD.260
Strategic Network
Service Offerings from W5 to E5Central Hub RoutingRegional Terminal RoutingDirect Routing
E5W5
Central Hub: 3 days, $100
West/East Hub: 2 days, $120
Direct: 1 day, $200
© Chris Caplice, MIT28MIT Center for Transportation & Logistics – ESD.260
Location Pooling
SituationRegion has 3 sales/delivery teamsEach team has its own territoryEach team has its own inventory siteDaily demand ~N(15, 4) within each territoryLead time to each territory site = 2 daysCycle service level set at 99.9%
How much safety stock should be in each territory?What if they pool to a common site?
Assume same lead time and CSL
© Chris Caplice, MIT29MIT Center for Transportation & Logistics – ESD.260
Location Pooling
Note declining marginal benefit of poolingGoing from 1 to 3 – reduced SS by 42%Going from 7 to 9 – reduced SS by 12%
Good or bad?
Issues?Concerns?
-
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1 2 3 4 5 6 7 8 9 10
Number of Stocking Points
Days
of S
uppl
y
© Chris Caplice, MIT30MIT Center for Transportation & Logistics – ESD.260
Location Pooling
Recall the impact on cycle stock as well . . .Impact on replenishment to the DC locationOther impacts?
2*
* * 22
ADQvr
QIOH TRC DAvr
=
= =
1Q*3
12
q1*
q2*
q3*
*
*
1
2 2
*2 2
ii
n ii
Ad ADqvr vrn
q QIOH n=
= =
⎛ ⎞ ⎛ ⎞= =⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠
∑* 2TRC nDAvr=
versus
© Chris Caplice, MIT31MIT Center for Transportation & Logistics – ESD.260
Lead Time Pooling
Types of Uncertainty FacedTotal demand uncertaintyAllocation demand uncertaintyProduct mix uncertainty
Consolidated DistributionKeep inventory near customersHedge against allocation uncertainty
Adapted from Cachon & Terwiesch 2005
© Chris Caplice, MIT32MIT Center for Transportation & Logistics – ESD.260
Lead Time Pooling
SituationVendor direct shipments to 100 retail stores4 week replenishment lead time4 week review period at storeStores use (R,S) policy for inventoryWeekly demand in each store is iid ~N(75, 20)IFR = 99.5%
Vendor
Store 1
Store 2
Store 3
Store 100
What is the safety stock on hand in the system?Other concerns?
© Chris Caplice, MIT33MIT Center for Transportation & Logistics – ESD.260
Lead Time Pooling
Proposed SituationVendor direct shipments to 100 retail stores4 week replenishment lead time Vendor to RDC1 week replenishment lead time RDC to StoresStores & RDC use (R,S) policy for inventory4 week review period at RDC (4 or 1 week R at stores)Weekly demand in each store is iid ~N(75, 20)IFR = 99.5% at RDC and Stores
RDC
Store 1
Store 2
Store 3
Store 100
What is the safety stock on hand in the system?What would happen if R=1 for stores?Who owns the pipeline inventory?
Vendor
© Chris Caplice, MIT34MIT Center for Transportation & Logistics – ESD.260
Flow Strategies / Profiles
Multiple Patterns to Flow ProductDirect Vendor to Customer Direct Vendor to Store (DSD)Vendor to RDC to Store
Which pattern is ‘the best’?
Should I only have one flow pattern?
© Chris Caplice, MIT35MIT Center for Transportation & Logistics – ESD.260
Network Structure Tradeoffs
Structure Pros Cons
Direct Shipping No intermediate DCsSimple to coordinate
Large lot sizes (high inventory levels)
Large receiving expense
Direct w/ Milk Runs Lower transport costs for smaller shipments
Lower inventory levels
Increased coordination complexity
Direct w/Central DC (holding inventory)
Lower IB transport costs (consolidation)
Increased inventory costsIncreased handling at DC
Direct w/ Central DC (X-dock)
Very low inventory requirementsLower IB transport costs
(consolidation)
Increased coordination complexity
DC w/ Milk Runs Lower OB transport costs for smaller shipments
Further increase in complexity
Hybrid System Best fit of structure for businessCustomized for product, customer
mix
Exceptionally high level of complexity for planning and execution
Source: Chopra & Meindl 2004
© Chris Caplice, MIT36MIT Center for Transportation & Logistics – ESD.260
Network Structure Drivers
High Value Product Low Value Product
High Demand
Disaggregate cycle inventoryAggregate safety stockInexpensive transport for cycle replenishmentFast transport for safety stock
Aggregate all inventoryFast transport for customer orders
Disaggregate all inventoryInexpensive transport for replenishment
Low Demand
Aggregate only safety stockInexpensive transport for replenishment
Source: Chopra & Meindl 2004
Short Distance Medium Distance Long Distance
High Density Pvt fleet with milk runs
Third Party Milk Runs
Third Party Milk Runs or LTL Carrier
X-dock with milk runs X-dock with milk runs
Medium Density
LTL Carrier LTL or Package Carrier
Low Density LTL or Package Carrier Package Carrier
Customer density versus Length of Haul
Demand versus Product Value
Questions, Comments?