Ted GiffordDirector – Research GroupSchneider National Inc

Facility Location ProblemsAt Schneider Logistics

General Background

• Subsidiary of Schneider National– Largest truckload carrier in North America,

2001 Revenue $2.4 B, 14,000 tractors/drivers, 42,000 trailers

• SLI operates in 38 countries, employs 1,200 associates

• Freight Management Services– Global, Multi-Modal Transportation - Manage $2.5 B purchased transportation

• Engineering Services– Network and Route Design– Facility Location– Supply Chain Engineering

• Payment Services & Bid Management – Pay $7.5 billion third party invoices– Combined Value Auctions

Facility Location Design at SLI

• 12-15 distinct problems / year• 8 – 10 engineers participate, 30 engineers total• Problem size Average Max

– Mfg facilities 2-10 20– DC sites 15-30 50– Customers 200-300 500– Products 5-10

25• Major Industries/Clients

– Consumer Products – KC (US & Europe)– Manufacturing – Otis Elevator (US & Europe)– Automotive - Ford (US & Europe) & GM– Paper products – Polyone– Home Delivery (food) – Schwan’s

Problem Types

PLANTSUPPLIER DC CUSTOMER

P-median / coverage

DC Location:Fixed ChargeMultiple CommoditiesSourcing

Indirect CostsSupplier SourcingTransportation impact

Warehouse: Transportation Cost DC fixed Cost DC Variable Cost

Plant: Union Taxes Wages / Education Transportation Cost Variable Cost

Operational Issues

• Most problems are one-off -- A specific client request which often has unique complications or side constraints.

• Time & budget constraints often argue against sophistication or pursuit of a mathematically elegant solution.

• Limited availability or poor quality of data is often the main challenge and greatest consumer of effort.

• Realistic cost models are often either complex or ill-defined. Estimates of actual costs are highly variable.

• Service requirements are often ambiguous. Cost/service tradeoffs are unclearly specified.

• Forecasts of expected demand exhibit considerable uncertainty.

Current Process

• Access Database / Excel with VB Add-ins– Basic user interface– Navigation per problem taxonomy– Data import & maintenance

• AMPL w/ CPLEX– MIP models

• Set Covering• P-center• Fixed Charge• P-median• Special algorithms

What is the underlyingdistance network?

Spatial(planar or rectilinear

distances)

Single ormultiple

locations?

Rectilineardistances orstraight line?

Single

Rectilinear

Rectilinearlocationproblem(easy)

Fermat-Weberproblem

(numericalmethods -

Excel solver)

Straight Line

Multi-sourceWeber

problem(randomized

search)

Multiple

Graphical(arcs and nodes)

ServiceCoverage or Cost

Objective?Service Cost

Fixedcoveragedistance?

Set CoveringProblem(AMPL,

reductionmethods)

Yes

Minimize maximum distance

Number ofeschelons

Single Multiple

Fixed chargeson locations?Cover all

demands?

Yes Not necessary

MaximumCoveringProblem(AMPL,

LagrangianRelaxation )

P-CenterVertex

Problem(Special

algorithms)

Solutionon nodes?

Nodesonly

Arcs andNodes

AbsoluteP-CenterProblem(Special

algorithms)

Number ofcommodities

Capacitieson locations?

Yes

No

CapacitatedFixed ChgProblem(CAPS,AMPL)

Yes No

UncapacitatedFixed ChgProblem

(AMPL w/Addins)

P-MedianProblem

(AMPL w/Addins)

Single

HierarchicalLocationProblems(AMPL,iterative

menthods)

Multiple

GeneralSupply Chain

Design(All methods)

Given a set of customers with different demands:Choose a set of locations to serve those demands based

on the answers to the following questions

SLI has applied, formulated, and solved models addressing all of these problems

Easy for mostpractical problems

ModeratelyDifficult

Possibly VeryDifficult

Problem Taxonomy - 1

underlying distancenetwork?

Graphical(arcs & nodes)

Service Coverage or CostObjective?Service

Cost

Fixedcoveragedistance?

Set CoveringProblem(AMPL,

reductionmethods)

Yes Min Max distance

Number ofeschelons

Single

Fixedcharges

on locations?

Cover alldemands?

Yes Not necessary

MaximumCoveringProblem(AMPL,

LagrangianRelaxation )

P-CenterVertex

Problem(Special

algorithms)

Solutionon nodes?

Nodesonly

Arcs andNodes

AbsoluteP-CenterProblem(Special

algorithms)

Capacitieson

locations?

Yes

CapacitatedFixed ChgProblem

(CAPS, AMPL)

Yes No

UncapacitatedFixed Chg

Problem (AMPLw/

Addins)

(Emergency Service) (depends on tightness)

Problem Taxonomy - 2Underlyingdistancenetwork?

Spatial(planar or rectilinear

distances)

Single ormultiple

locations?

Rectilinear orstraight linedistance?

Single

Rectilinear

Rectilinearlocationproblem(easy)

Fermat-Weber

(numericalmethods -

Excelsolver)

Straight Line

Multi-sourceWeber

(random-ized

search)

Multiple

Cost

Number ofeschelons

Single Multiple

Fixed chargeson locations?

Number ofcommodities

No

P-MedianProblem

(AMPL w/Addins)

Single

HierarchicalLocationProblems(AMPL,iterative

menthods)

Multiple

GeneralSupplyChainDesign

(Allmethods)

Service Coverage orCost Objective?

Graphicalnodes & arcs

(relaxation close)

(10 %) (90 %)

(agricultural centroid)

Use of off-the-shelf software

• Some experience with CAPS Logic Tools, SLIM 2000, I2 Strategist

• Common difficulties– Underlying model and MIP Formulation not

visible to user– Limited flexibility – rigid parameter options – Often necessary to “trick” the system for

some simple problems– Poor performance for problem structures not

anticipated by the model• Example - CAPS several hours• Excel add-in 15

seconds• High cost per use – not general enough to

handle all problem types

Factors which tend to complicate problems

• Ill-defined criteria • Inconsistent or missing data• Large number of candidate facilities• Single sourcing requirements• Disjunctive constraints• Reverse logistics – container flow back• Echelon skipping• Minimum flow constraints• Piecewise linear (or worse) cost functions

Current Development Activities

• Monte Carlo Simulation – Risk Analysis– Probability Distributions for Cost & Demand

• Constraint Programming– ILOG Solver / Dispatcher /OPL– Local Search Heuristics– Constraint Propagation / Domain Reduction– Index variables over enumerated sets– Special Purpose Algorithms for Global

Constraints• Conversion of AMPL to OPL

– Convert Excel Solver routines– Utilize global & set constraints– Hybrid optimization – Cooperative Solvers