SOLVING BUSINESS PROBLEMS WITH SAS ANALYTICS AND … · SASANALYTICS INTRODUCTION BACKGROUNDONSAS...

SOLVING BUSINESS PROBLEMS WITH SAS ANALYTICS AND OPTMODEL

Ed Hughes, Rob Pratt, Yan Xu, and Pelin Çay

OUTLINE

1 SAS Analytics Introduction2 p−Median Problem (MILP)3 Portfolio Optimization (QP, NLP, LSO)4 Car Painting Problem (CLP)5 Traveling Salesman Problem (network)6 p−Median Problem (Benders)7 Optimization for Machine Learning (Autotune)8 Boston Public Schools9 Sample Consulting Engagements

Copyright 2017, SAS Institute Inc. All rights reserved. 2

SAS ANALYTICSINTRODUCTION BACKGROUND ON SAS

Founded in 1976World’s largest privately heldsoftware companyOffices in 58 countriesOver 1350 alliance partners globallyOver 83,000 customer sitesin 149 countriesSAS customers: 94 of the top 100companies in the 2016 FortuneGlobal 500User groups worldwide


SAS ANALYTICSINTRODUCTION SAS DATA SETS, LANGUAGE, TERMINOLOGY

SAS data set: tabular data fileI Rows are “observations”I Columns are “variables”I Created with SAS DATA step and/or SQLI Read from / write to all major data formats

SAS programming language base: data handling and exploration, elementarystatistics, wide range of functions

Software modules are procedures, abbreviated “PROC”


SAS ANALYTICSINTRODUCTION SAMPLE SAS DATA SET


SAS ANALYTICSINTRODUCTION SAS DATA SETS AND EXTERNAL DATA FORMATS

SAS has several ways (programmatic, point and click)to convert any data in tabular form into a SAS data set

I DATA step functionalityI PROC IMPORTI Enterprise Guide

Through SAS ACCESS engines, can create SAS viewsto any commonly used database

I Data appears as SAS data sets to SAS, but remains in thenative database format

I SAS can write results back to the native database format


SAS ANALYTICSINTRODUCTION OVERVIEW OF SAS FUNCTIONS

Mathematical, Arithmetic, TruncationArrayCharacterDate and TimeFinancialProbability DistributionsTrigonometric, HyperbolicRandom Number GenerationSample Statistics, Quantiles


SAS ANALYTICSINTRODUCTION SAS PRODUCTS AND SOLUTIONS

SAS products: breadth and depthI Data Management: access, integration, preparation, governanceI Business Intelligence: query, reporting, visualization, collaborationI Analytics: statistics, forecasting, data mining, text analytics, quality control,optimization, simulation, scheduling

SAS solutionsI Cross-Industry: Advanced Analytics, Cloud Analytics,Customer Intelligence, Risk Management, Supply Chain Intelligence,Fraud and Security Intelligence, Business Intelligence, IoT Solutions

I Industry-Specific: Retail, Oil and Gas, Automotive, Manufacturing, Utilities,Banking, Capital Markets, Insurance, Health Care, Life Sciences, Defense &Security, Government, P-12 & Higher Education, Communications, Media,Hotels, Casinos, Sports, Travel & Transportation, Consumer Goods


SAS ANALYTICSINTRODUCTION

SAS-RELATED PRESENTATIONSAT INFORMS HOUSTON

SB78B Tuning a Bayesian Framework for B2B PricingFang Liang, Maarten Oosten (Vistex)

SD70 Time Series Classification Using Normalized SubsequencesIman Vasheghani Farahani, Alex Chien, Russell Edward King (North Carolina State University)

MA43 Internet of Things: Promises, Challenges and AnalyticsPatricia Neri, Ann Olecka (Honeywell), Bill Groves (Honeywell)

MB77 The SAS MILP Solver: Current Status and Future DevelopmentsImre Pólik, Menal Güzelsoy, Amar Kumar Narisetty, Philipp M. Christophel

TC83 Robust Operational Decisions for Multi Period Industrial Gas Pipeline Networksunder UncertaintyPelin Çay, Camilo Mancilla (Air Products and Chemicals), Robert H. Storer (Lehigh University),Luis F. Zuluaga (Lehigh University)



SAS-RELATED PRESENTATIONSAT INFORMS HOUSTON

TD70 Robust Principal Component Analysis in Cloud-based Run-time EnvironmentKyungduck Cha, Seunghyun Kong, Zohreh Asgharzadeh, Arin Chaudhuri

TD71 Building and Solving Optimization Models with SASEd Hughes, Rob Pratt

TD71 JMP Pro: Top Features That Make You Say “Wow!”Mia L. Stephens

WA23 Pricing Advance Purchase ProductsMatthew Maxwell, Jennie Hu

WB58 Effective Methods for Solving the Bicriteria P-center P-dispersion ProblemGolbarg Kazemi Tutunchi, Yahya Fathi (North Carolina State University)

WC83 Warmstart of Interior Point Methods for Second Order Cone Optimization via RoundingOver Optimal Jordan FramesSertalp Bilal Çay, Imre Pólik, Tamas Terlaky (Lehigh University)


SAS ANALYTICSINTRODUCTION “OPERATIONS RESEARCH WITH SAS” BLOG

http://blogs.sas.com/content/operations/


http://blogs.sas.com/content/operations/

SAS ANALYTICSINTRODUCTION SAS SUPPORT COMMUNITIES

https://communities.sas.com/


https://communities.sas.com/

SAS ANALYTICSINTRODUCTION THE SCOPE OF SAS/OR®

1 Mathematical optimization

2 Discrete-event simulation

3 Project and resource scheduling


SAS ANALYTICSINTRODUCTION BROAD RANGE OF OPTIMIZATION SOLVERS

Linear Programming:I Primal, Dual, Network Simplex; Interior Point*I Concurrent*

Mixed Integer Linear Programming:I Branch and Cut* with heuristics, conflict search, option tuningI Decomposition algorithm* (MILP and LP)

Quadratic Programming:I Interior Point*

Nonlinear Programming:I Active Set, Interior Point*I Multistart*, Concurrent*

Network AlgorithmsConstraint Logic ProgrammingLocal Search* *parallel computation


SAS ANALYTICSINTRODUCTION DECOMPOSITION ALGORITHM

Accessible in OPTMODEL, OPTLP, OPTMILP proceduresUser conveys block structure via .block constraint suffixsolve with LP|MILP / decomp=(method=user);Master and subproblems generated and solved automatically and in parallelFor block-angular problems, dramatic performance improvements overbranch-and-cut algorithmAutomatically detects identical subproblems and uses Ryan-Foster branchingif applicable


SAS ANALYTICSINTRODUCTION DECOMP: METHOD= OPTION

USER: User defines subproblems via .block constraint suffixNETWORK: Heuristically finds embedded network [Bixby88] and uses weaklyconnected components as subproblem blocksCONCOMP: Uses connected components algorithm to search for block-diagonalstructure (no linking constraints)AUTO: Searches for block-angular structureSET: Searches for set-partitioning or set-covering structure as linkingconstraints, with weakly connected components of remaining matrix assubproblem blocks


SAS ANALYTICSINTRODUCTION NETWORK ALGORITHMS

PROC OPTNET: specialized procedurePROC OPTMODEL access using:

I SUBMIT blockI SOLVE WITH NETWORK

Connected componentsBiconnected components andarticulation pointsMaximal cliquesCyclesTransitive closure

Linear assignment problemShortest path problemMinimum-cost network flow problemMinimum spanning tree problemMinimum cut problemTraveling salesman problem


SAS ANALYTICSINTRODUCTION CONSTRAINT PROGRAMMING SOLVER

PROC CLP: specialized procedurePROC OPTMODEL access using:

I SUBMIT blockI SOLVE WITH CLP

Supported features and predicatesI Multiple solutionsI Strict inequalities (<, >) and disequality ( ̸=)I ALLDIFFI ELEMENTI GCCI LEXICOI PACKI REIFY


SAS ANALYTICSINTRODUCTION LOCAL SEARCH OPTIMIZATION

PROC OPTLSOFor black-box objectivesContinuous and discrete variablesLinear and nonlinear constraintsParallel execution of:

I Local search methodsI Global GA-type heuristicsI Pattern search

Objective can be an aggregation over an external predistributed data setMultiobjective optimizationArray-structured input data



OTHER RECENT ENHANCEMENTSIN OPTIMIZATION WITH SAS/OR

Performance improvements: LP, MILP, QP, NLP, and network solvers;DECOMP algorithmParallel MILP algorithmMILP symmetry detectionNLP, QP, and LP infeasibility diagnosticsConcurrent FOR (COFOR) loop in PROC OPTMODELAccess to constraint programming and network optimization algorithmsfrom PROC OPTMODELCrossover enhancements for LP interior point algorithmProfiler in PROC OPTMODEL


SAS ANALYTICSINTRODUCTION SAS OPTIMIZATION-BASED SOLUTIONS

SAS® Marketing OptimizationSAS® Launch Revenue OptimizationSAS® Revenue Optimization SuiteSAS® Pack OptimizationSAS® Credit Scoring

SAS® Risk Management for BankingSAS® Customer Link AnalyticsSAS® Inventory OptimizationWorkbenchSAS® Fraud Framework



SAS® OPTIMIZATION 8.1, A SAS® VIYATM

PRODUCT

Procedures carry over from SAS/ORActions corresponding to general and network optimization solversare accessible from SAS, Python, Lua, Java, and RModeling is done in PROC OPTMODEL on the SAS clientDistributed computation features:

I Solving independent optimization scenarios: COFOR loopI Multistart option for nonlinear (NLP) solverI Decomposition algorithm (LP and MILP)I Distributed network algorithms: connected components and shortest pathI Distributed BY-group processing in network algorithms



COMING IN SAS OPTIMIZATION 8.2(DECEMBER 2017)

Improved performance (MILP solver and DECOMP algorithm)and numerical stabilityMILP solver enhancements

I Adds distributed branch-and-cut algorithmI Can return multiple solutions

Network solver: new path enumeration algorithmLocal search optimization (LSO) solver accessible from PROC OPTMODELPROC CLP addedTwo new optimization actions to convert an .mps file to a CAS table


SAS ANALYTICSINTRODUCTION PROC OPTMODEL: MAJOR FEATURES

Algebraic modeling language with optimization-oriented syntax:I Variables, constraints, bounds, objectivesI Algebraic expression of functionsI Parameters, arrays, index sets

Close integration with SAS programming environmentFlexible input/output: read from and create data setsSeparation between model structure and instance dataInteractive environmentDirect access to LP, MILP, QP, NLP, CLP, and network solversSupport for customized algorithmsStandard and user-defined functions



PROC OPTMODEL PROGRAMMING STATEMENTS(1)

Control and Looping:I DO, IF, and so onI DO iterative, DO UNTIL, DO WHILE, and so onI FOR, COFOR

GeneralI CALLI SUBMIT/ENDSUBMITI PROFILE



PROC OPTMODEL PROGRAMMING STATEMENTS(2)

Input/Output:I READ DATA, CREATE DATA: working with SAS data setsI SAVE MPS, SAVE QPSI FILE, PRINT, PUT

Model Management:I SOLVEI PROBLEM/USE PROBLEM (named models)I DROP/RESTORE (constraints)I FIX/UNFIX (variables)I EXPAND (selective or overall)


SAS ANALYTICSINTRODUCTION PROC OPTMODEL EXPRESSIONS OVERVIEW

Aggregation operators (evaluate an expression or a set expression over anindex set):

I SUM, PROD, MAX, MINI INTER aggregation, UNION aggregationI SETOF, AND aggregation, OR aggregation

Set operators:I IN, WITHINI INTER, UNION, SYMDIFF, DIFFI CROSS, SLICE

Logical:I Conditional: IF-THEN-ELSEI Boolean: AND, OR

Scalar and set expressions


p−MEDIAN PROBLEM DESCRIPTION

Uncapacitated facility location problem variantGiven customer locations, weights, and positive integer pSelect p customers as facilitiesMinimize total weighted distance to closest facility


p−MEDIAN CUSTOMER LOCATIONS


p−MEDIAN OPTIMAL SOLUTION FOR p = 5


p−MEDIAN MILP FORMULATION

xj =

{1 if customer j is selected as facility0 otherwise

yij =

{1 if customer i is assigned to facility j0 otherwise



minimize∑i∈C

∑j∈C

widijyij

subject to∑j∈C

xj = p

∑j∈C

yij = 1 i ∈ C

yij ≤ xj i ∈ C, j ∈ Cxj ∈ {0, 1} j ∈ Cyij ∈ {0, 1} i ∈ C, j ∈ C


p−MEDIAN LIVE DEMO

CodepMedianData.sas

CodepMedianMILP.sas


p−MEDIAN LAGRANGIAN RELAXATION

Relax complicating constraints by moving to objective with Lagrangemultipliers λ

For fixed λ, resulting problem is easyLower bounds from Lagrangian objective, upper bounds from feasiblesolutionsUse subgradient algorithm to find best values for λ



minimize∑i∈C

∑j∈C

widijyij

subject to∑j∈C

xj = p

∑j∈C

yij = 1 i ∈ C (λi)



p−MEDIAN LAGRANGIAN RELAXATION

minimize∑i∈C

∑j∈C

widijyij +∑i∈C

λi

1−∑j∈C

yij

subject to

∑j∈C

xj = p


For fixed λ, reduces to a trivial (sorting) problemProvides lower bound on optimal objective value


p−MEDIAN LOWER AND UPPER BOUNDS ON OPTIMALOBJECTIVE VALUE



CodepMedianLagRel.sas


PORTFOLIOOPTIMIZATION PROBLEM DESCRIPTION

Given assets and historical returnsDetermine fraction of budget to invest in eachMinimize risk subject to lower bound on returnMaximize return subject to upper bound on risk


PORTFOLIOOPTIMIZATION QUADRATIC PROGRAMMING FORMULATION

minimize∑i∈A

∑j∈A

cijxixj

subject to∑i∈A

xi = 1∑i∈A

rixi ≥ ℓ

xi ≥ 0 i ∈ A


PORTFOLIOOPTIMIZATION NONLINEAR PROGRAMMING FORMULATION

maximize∑i∈A

rixi

subject to∑i∈A

xi = 1∑i∈A

∑j∈A

cijxixj ≤ u

xi ≥ 0 i ∈ A


PORTFOLIOOPTIMIZATION EFFICIENT FRONTIER


PORTFOLIOOPTIMIZATION COFOR LOOP

Uses multiple threads to execute SOLVE statements in parallel acrossiterations of loopCan also run distributed across multiple machines

Serial FOR loop:

for {i in ISET} do;...solve ...;...

end;

Parallel COFOR loop:

cofor {i in ISET} do;...solve ...;...

end;


PORTFOLIOOPTIMIZATION LIVE DEMO

CodePortfolio.sas


PORTFOLIOOPTIMIZATION MULTIOBJECTIVE FORMULATION

minimize∑i∈A

∑j∈A

cijxixj and maximize∑i∈A

rixi

subject to∑i∈A

xi = 1

xi ≥ 0 i ∈ A


PORTFOLIOOPTIMIZATION LIVE DEMO

CodePortfolioLSO.sas


CAR PAINTING PROBLEM DESCRIPTION

Cars arrive in some sequence to be paintedPaint color for each car specified in inputCostly purge if subsequent cars painted different colorsPermute cars to minimize number of purgesEach car must appear within three positions of originalRBGYRBGYRB has 9 purgesRRGYBBGYRB has 7 purges


CAR PAINTING SOLUTION APPROACH

Use CLP solverPredicates: ALLDIFF, ELEMENT, and REIFYFind all optimal solutionsPROC GANTT to display solutions


CAR PAINTING LIVE DEMO

CodeCarPainting.sas


TRAVELINGSALESMANPROBLEM

PROBLEM DESCRIPTION

Given cities and pairwise distances between themFind tour that visits each city exactly onceMinimize total distance traveled



LOCATIONS



OPTIMAL SOLUTION



THREE WAYS TO ACCESS SOLVER

SAS/OR OPTNET procedureSAS/OR OPTMODEL procedureSAS Viya tsp action



LIVE DEMO

CodeTSPCapitalCities.sas



SAS VIYA (NEW CLOUD-BASED PLATFORM)



SAS OPTIMIZATION ON SAS VIYA

Optimization action set Network Optimization action setsolveLp biconnectedComponents minSpanTreesolveMilp clique readGraphsolveQp connectedComponents shortestPathtuner cycle summary

linearAssignment transitiveClosureminCostFlow tspminCut



LIVE DEMO

CodeTSPCapitalCities.ipynb


p−MEDIAN BENDERS DECOMPOSITION

If complicating variables are fixed, resulting problem is easyBenders (1962): take integer variables as complicatingMILP master problem recommends values for complicating variablesLP subproblem generates optimality and feasibility cuts from dual variablesIterate between master and subproblem until optimality gap is small enoughDual of Dantzig-Wolfe decomposition



minimize∑i∈C

∑j∈C

widijyij

subject to∑j∈C

xj = p

∑j∈C

yij = 1 i ∈ C

yij ≤ xj i ∈ C, j ∈ Cxj ∈ {0, 1} j ∈ Cyij ≥ 0 i ∈ C, j ∈ C


p−MEDIAN MILP MASTER PROBLEM

minimize η

subject to∑j∈C

xj = p

η ≥ ak0 +

∑j∈C

akj xj k ∈ O

xj ∈ {0, 1} j ∈ C


p−MEDIAN LP SUBPROBLEM

minimize∑i∈C

∑j∈C

widijyij

subject to∑j∈C

yij = 1 i ∈ C

yij ≤ x̂j i ∈ C, j ∈ Cyij ≥ 0 i ∈ C, j ∈ C



CodepMedianBenders.sas


p−MEDIAN MULTIPLE SUBPROBLEMS

Often, LP subproblem decomposes into disjoint subproblemsCan solve independently and in parallelCan generate tighter cuts for master problem


p−MEDIAN MILP MASTER PROBLEM

minimize∑i∈C

ηi

subject to∑j∈C

xj = p

ηi ≥ aki0 +

∑j∈C

akij xj i ∈ C, ki ∈ Oi

xj ∈ {0, 1} j ∈ C


p−MEDIAN LP SUBPROBLEM FOR EACH i

minimize∑j∈C

widijyij

subject to∑j∈C

yij = 1

yij ≤ x̂j j ∈ Cyij ≥ 0 j ∈ C


p−MEDIAN LP SUBPROBLEM FOR EACH i

minimize∑j∈C

widijyj

subject to∑j∈C

yj = 1

yj ≤ x̂j j ∈ Cyj ≥ 0 j ∈ C



CodepMedianBendersMultiple.sas

CodepMedianBendersMultipleCofor.sas

CodepMedianBendersMultipleCoforShared.sas


OPTIMIZATION FORMACHINELEARNING

MACHINE LEARNING MODELS

Transformation of data to high-quality descriptive and predictive modelsThere are several challenges. For instance, for neural networks:

I How to determine model configuration?I How to determine weights, activation functions?



MODEL TRAINING: OPTIMIZATION PROBLEM

Objective function

f(w) = 1

n

n∑i=1

L(w, xi, yi) + λ1∥w∥1 +λ2

2∥w∥22

Stochastic Gradient Descent (SGD)I A variant of Gradient Descent: wk+1 = wk − η∇f(wk)I Approximate ∇f(wk) with gradient of mini-batch sample: {xki, yki}



SGD PARAMETERS



HYPERPARAMETER TUNING

The goal of tuning is to find better models



LOCAL SEARCH OPTIMIZATION



AUTOTUNE IN SAS PROCEDURES

PROCs with autotune feature include TREESPLIT, FOREST, GRADBOOST,NNET, SVMACHINE, and FACTMAC



HYPERPARAMETERS



OUTPUT TABLES



TUNING EFFECTIVENESS



PARALLEL EFFICIENCY

Model training: 4 workers; model tuning: n concurrently



TUNE GRADBOOST FOR MNIST DIGITS DATA

Model training: 4 workers; model tuning: 32 concurrentlyMaximum iterations: 20; population size: 129Tuning sequentially takes 1 month, but tuning in parallel takes 1 day


BOSTON PUBLICSCHOOLS BUSINESS PROBLEM

How can optimization improvetransportation for Boston PublicSchools?

A SAS and DataKind pro bono projectJuly 2016–March 2017

http://www.sas.com/en_us/data-for-good.html




BOSTON PUBLICSCHOOLS BUSINESS PROBLEM

Boston Public Schools (BPS)

>200 schools

>29,000 students

>600 school buses

>3,200 routes daily


BOSTON PUBLICSCHOOLS MOTIVATION

• 1 bus costs: $100,000/year

• Total transportation cost: >$100M

• Bus operations 65–70% of transportation cost

• 10% of the total school budget

• The national average is 3–5%


BOSTON PUBLICSCHOOLS AREAS FOR IMPROVEMENT

SAS Technologies UsedSAS/OR: OPTMODEL and MILP solver

SAS Visual Analytics

Bus stop consolidation

Bus routing Fleet scheduling Bell time assignment


BOSTON PUBLICSCHOOLS

BUS STOP CONSOLIDATION:CURRENT SYSTEM



BUS STOP CONSOLIDATION:SOLUTION APPROACH

For all morning school bell times (7:30, 8:30, and 9:30) solve four problems:1 Minimize total number of schools shared by each bus stop2 Minimize total number of school-bus stop combinations

⋆ Primary objective of BPS3 Minimize unique bus stops

⋆ Operational benefits to BPS4 Minimize total walking distance for each school

⋆ Additional benefit to students

Constraints:1 Each student must be assigned to one bus stop2 The number of students at a given stop cannot exceed the set maximum3 The number of schools that share a stop cannot exceed the maximum



BUS STOP CONSOLIDATION:RESULTS

Scenario summary - One of fiveOnly focus corner stop students: 21,000 studentsOnly consider corner stops: 1,249 stops (25% of all stops)3rd Grade & Above 0.5 mile max walking distance: Current BPS max2nd Grade & Below 0.3 mile max walking distance: Additional constraintMaximum students at a stop: 75

27% Reduction in Total Stops Made



BUS STOP CONSOLIDATION:CURRENT SYSTEM VS OPTIMAL SOLUTION



BUS ROUTING:CURRENT SYSTEM



FLEET SCHEDULING:MOTIVATION

Potential for improvements by rescheduling busesObjective: assign minimum number of buses to cover all morning andafternoon buses



FLEET SCHEDULING:SOLUTION APPROACH

1 Define specific time zone, bus type, and bus yard2 Data preparation to generate columns3 Solve IP problem



FLEET SCHEDULING:ROUTE COMBINATION LOGIC



FLEET SCHEDULING:MODEL FORMULATION

minimize∑

k ∈ BUSES

yk

subject to∑

k ∈ BUSES:(k,r)∈Syk = 1 r ∈ ROUTES

yk ∈ {0, 1} k ∈ BUSES



FLEET SCHEDULING:NUMERICAL RESULTS

schedule current total # bus optimal total # bus

morning 647 611

afternoon 657 555

bus type yard current # bus optimal # bus

FB Frpt 48 40

FB Ctwn 83 63

FB Read 108 83

MS Was 133 103

HS Frpt 96 91

HS Ctwn 36 35

HS Read 106 99

WB Frpt 47 41

Morning schedule Afternoon schedule

bus type yard current # bus optimal # bus

FB Frpt 45 44

FB Ctwn 81 74

FB Read 103 93

MS Was 133 122

HS Frpt 96 93

HS Ctwn 36 36

HS Read 106 104

WB Frpt 47 45



BELL TIME ASSIGNMENT:CURRENT STATUS



BELL TIME ASSIGNMENT:SOLUTION APPROACH

Bell Time Assignment Objectives:1 Minimize the maximum number of buses across all times2 Minimize the maximum number of buses across afternoon times3 Minimize number of changes in the schedule



BELL TIME ASSIGNMENT:AFTER FIRST SOLVE

Minimize the maximum number of buses across all times



BELL TIME ASSIGNMENT:AFTER SECOND SOLVE

Minimize the maximum number of buses across afternoon times



BELL TIME ASSIGNMENT:AFTER FINAL SOLVE

Minimize number of changes in the schedule



BELL TIME ASSIGNMENT:COMPARISON RESULTS


BOSTON PUBLICSCHOOLS BUSINESS BENEFITS

30–100 fewer buses: potential for $3–10M savings

>1,000 fewer bus stopsI Potential for fewer routesI Fewer hours on roadI Less trafficI Better on-time performance

Pilot studies on bus stop consolidation for selected schools in progress


SAMPLECONSULTING

ENGAGEMENTSOVERVIEW

Advanced Analytics and Optimization ServicesI Part of Advanced Analytics Division in R&DI Ph.D.-level developers/consultants

Areas of FocusI Generic Optimization Details

I Simulation Details

I Revenue Management Details

I Inventory Optimization Details


SAMPLECONSULTING

ENGAGEMENTSGENERIC OPTIMIZATION

Television advertising optimization Details

Chemical mixture optimization Details

Optimal ATM replenishment Details

Investment portfolio optimization Details

Water management Details

Casino floor mix optimization Details

Optimal loan assignment Details


SAMPLECONSULTING

ENGAGEMENTSSIMULATION

Hospital room assignment simulation Details

Prison population simulation Details

Neonatal intensive care unit simulation Details

Digital parts distribution Details


SAMPLECONSULTING

ENGAGEMENTSREVENUE MANAGEMENT (RM) AND PRICING

Price optimization for railroad Details

RM framework for car rental Details

RM framework for cruise line Details

Show ticket RM Details

Pricing and inventory optimization Details

SKU profitability Details


SAMPLECONSULTING

ENGAGEMENTSINVENTORY OPTIMIZATION (IO)

Multi-echelon inventory optimization Details

Retail inventory replenishment Details

IO for machine parts Details

IO for construction equipment Details

IO for automotive Details


SAMPLECONSULTING

ENGAGEMENTSTELEVISION ADVERTISING OPTIMIZATION

Customer: TV networkGoals: Schedule advertisement spots based on priorities

I Limited inventory of advertising spotsI Estimate the number of impressionsI Multiobjective model solved sequentially by priorities

SAS tools:I SAS/OR: OPTMODEL, MILP solver


SAMPLECONSULTING



SAMPLECONSULTING

ENGAGEMENTSMIXTURE OPTIMIZATION

Customer: Large US CPG companyOptimization of raw material portfolio for manufacturing

I Minimum cost portfolio problemI Nonlinear performance constraintsI Discrete: assignment constraints

MINLPSAS tools:

I SAS/OR: OPTMODEL, MILP solver, NLP solverI JMP

Completely custom algorithm


SAMPLECONSULTING

ENGAGEMENTSHOSPITAL ROOM ASSIGNMENT SIMULATION

Customer: Private hospitalHospital operates on an FCFS policy for inpatient roomsRooms are separated into wards by type of patient

I Orthopedics, cardiology, oncology, general medical are example typesI If the “primary service” room type is not available, patient will be assigned toanother ward

FCFS policy may leave shortages of key room types when they are needed


SAMPLECONSULTING


Hospital was not ready for full scheduling optimizationInitial fix is a room reservation policy

I Last x rooms of a ward must be occupied by patients of the primary “type”

Goal: Determine the best number of rooms to reserveSAS tools:

I SAS/OR: Simulation Studio


SAMPLECONSULTING


Simulation was used to test different policy valuesInitially running one ward, expanding to whole hospitalReserving beds by day of week reduced ortho displacementswith similar displacements to other wards


SAMPLECONSULTING

ENGAGEMENTSPRICE OPTIMIZATION FOR RAILROAD

Customer: US railroadRailroad publishes prices for services

I Updated periodically (annual, quarterly or monthly)I Sometimes build long-term contracts with key customersI Price at commodity/market (origin-destination)/service type/customer group


SAMPLECONSULTING


Railroad already had a demand service forecastSAS solution provides

I Market segmentation (for data sparsity)I Market price calculationI Estimation of price sensitivityI Optimize list prices

SAS tools:I Pricing Catalog with extensions


SAMPLECONSULTING


Additional business constraints are modeledI Car constraints/ratios (keep some premium cars)I Truck competition (pricing or availability)I Geographic “arbitrage”

Pilot study showed 1.2% lift in revenue, 3.7% lift in profitCurrently expanding the study to more commodities


SAMPLECONSULTING

ENGAGEMENTSINVENTORY OPTIMIZATION

Customer: Large appliance manufacturerMulti-echelon inventory optimization and replenishment

I 3,000+ SKUs, 30+ manufacturer distribution centers, and 30+ factories/vendorsI Mix of manufacturing locations and international vendorsI Lead times vary between vendors and over timeI Demand time-shifted for some customers

Goal: Improve service level with minimal increase in inventory holding cost


SAMPLECONSULTING


Demand forecast with promotional eventsWeekly inventory target calculated using specified SKU/location service levelReplenishment orders based on weekly inventory targetsMultiobjective MILP to tune optimization parametersSAS tools:

I SAS DDPO solution: PROC MIRP, demand forecastingI SAS/OR: OPTMODEL, MILP solverI SAS Visual Analytics (VA)


SAMPLECONSULTING


VA report: demand forecasts and projected inventory targets


SAMPLECONSULTING

ENGAGEMENTSATM CASH OPTIMIZATION OVERVIEW

Customer: Large Southeast Asian bankATM cash replenishment optimization

I Large number of ATMsI Side constraints (capacity and so on)

MILPSAS tools:

I SAS Forecast Studio: demand forecastingI SAS/OR: OPTMODEL, MILP solver

Reformulated for tractability


SAMPLECONSULTING

ENGAGEMENTSINVESTMENT PORTFOLIO OPTIMIZATION

Customer: Large US government agencyInvestment portfolio optimization

I Portfolio mix: T-Bills, T-Notes, CDsI Suggested investment strategy for five yearsI Discrete: minimum investment requirements

MILPSAS tools:

I SAS Forecast StudioI SAS/OR: OPTMODEL, MILP solver

Generalized network flow formulation


SAMPLECONSULTING

ENGAGEMENTSOPTIMAL LOAN ASSIGNMENT

Customer: Large US bankI Goal: assign new loans (foreclosures, short sales, and so on)I Minimize standard deviation between teamsI Resource pool: CRMs (Customer Relationship Managers) teamsand PS (Process Support) resources

I Constraints: maximum case loads, limits on case types, and so onI Eligibility rules: case type match, geographical (time zone), language, and so on

Difficult problem (MINLP):I Nonlinear objective (standard deviation)I Binary variables (assignment)

SAS tools:I SAS/OR: OPTMODEL, MILP solverI SAS/DI and SAS/BI for data integration and reporting


SAMPLECONSULTING

ENGAGEMENTSWATER MANAGEMENT

Customer: National utilities agencyWater flow scheduling and routing

I Demand forecast for public waterI Network of reservoirs and pumping stationsI Business rules for reserve capacity and flowI Multiobjective problem

SAS tools:I SAS/OR: OPTMODEL, MILP solverI SAS Forecast Server


SAMPLECONSULTING

ENGAGEMENTSCASINO FLOOR MIX OPTIMIZATION

Customer: Canadian casinoSlot machine floor mix optimization

I Machine categorizationI Forecasting revenue and utilizationI Optimizing revenue to determine slot machine mix on the floor(hard and soft constraints)

MILPSAS tools:

I SAS/OR: OPTMODEL, MILP solverI SAS Forecast StudioI SAS Enterprise Miner


SAMPLECONSULTING

ENGAGEMENTSPRISON POPULATION SIMULATION

Customer: State legislative agencyPrison planning and scenario analysis

I Mandated projections to plan for prison capacityI Numbers highly dependent on legislative policyI Must consider current population and future entriesI Need to account for revocations

SAS tools:I SAS/OR: Simulation Studio


SAMPLECONSULTING

ENGAGEMENTSNEONATAL INTENSIVE CARE UNIT SIMULATION

Customer: Private hospitalGoals: Determine appropriate nurse staffing levels

I Improve NICU safety and efficiencyI Accommodate variations in patient attributes, including acuity and length of stay

Randomly generate gestational age of each infantSimulate various NICU-specific morbidities and their temporal effects onpatient acuityEach model run simulates one year of activitySAS tools:



SAMPLECONSULTING

ENGAGEMENTSDIGITAL PARTS DISTRIBUTION SIMULATION

Customer: Digital parts distributorMulti-billion dollar business; more than one million SKUs per facilityGoal: Simulate distribution center and evaluate operational strategiesto decrease costsEach order to be shipped contains multiple itemsItems are picked (independently) and packed (collectively)Resource needs per item vary, depending on handlingEach model run simulates one operational daySAS tools:



SAMPLECONSULTING

ENGAGEMENTS

COMPUTER-ASSISTED TELEPHONEINTERVIEWING (CATI) SYSTEM

Customer: National statistical agencyGoal: Build a model of the CATI system to study:

I Effects of choosing different distributions of interviewers during the dayI Impact of enforcing a cap on calls per case during time slices

Cases flow through the system, are routed to interviewersEnglish- and French-speaking interviewersInterviewer capacity varies throughout the dayEach model run simulates 40 days of CATI system operationSAS tools:



SAMPLECONSULTING

ENGAGEMENTS

REVENUE MANAGEMENT FORCAR RENTAL

Customer: Large US car rental companyBusiness analytics framework developmentOptimizing for growth (market share)Automate RM processPricing and reservation system

I Data integrationI SegmentationI Forecasting: unconstrained demand by segment and length of rentI Optimization: automatic generation of step recommendations

Pricing Catalog


SAMPLECONSULTING

ENGAGEMENTS

REVENUE MANAGEMENT FORCRUISE LINE

Customer: Large US cruise lineBusiness analytics framework developmentAutomate pricing and availability management processAccount for multiple constraintsPricing and revenue management system

I Data integrationI SegmentationI Forecasting: unconstrained demand by segmentI Estimation: demand response to changes in pricing strategyI Optimization: automatic generation of pricing and availability recommendations

Pricing Catalog


SAMPLECONSULTING

ENGAGEMENTSSHOW TICKET REVENUE MANAGEMENT

Customer: Large US resortAttendance forecastShow ticket availability optimizationDemand channel managementSAS tools:

I Pricing CatalogI SAS/OR: OPTMODEL, QP solver


SAMPLECONSULTING

ENGAGEMENTSPRICING AND INVENTORY OPTIMIZATION

Customer: Large US retailerProduct promotion optimization

I Retail pricing and inventory networkI Nonconvex NLPI Discrete side constraints

Multiobjective NLPSAS tools:

I SAS/OR: OPTMODEL, NLP and MILP solvers

Customized heuristics


SAMPLECONSULTING

ENGAGEMENTS

SKU PROFITABILITY & HISTORICAL DEMANDANALYSIS

Customer: Large appliance retailerSKU profitability

I 3000+ SKUs, 9000+ customersI Forecast of cost breakdown by SKUI Excel-based tool powered by SAS Office AnalyticsI Scenario analysis

Historical demand analysisI Historical invoice & retail sales dataI Waterfall analysis of historical cost breakdownI Retail sensitivity analysis

SAS tools:I SAS/OR: OPTMODEL, MILP solverI SAS Office AnalyticsI SAS Visual Analytics


SAMPLECONSULTING

ENGAGEMENTSRETAIL INVENTORY REPLENISHMENT

Customer: Large retail companyRetail inventory replenishment

I Large number of SKUs, locations, and vendorsI Demand forecastI Reorder point to satisfy service levelI Order decisions

Stochastic optimization at storesMILP optimization at depotsSAS tools:

I SAS/OR: OPTMODEL, MILP solverI SAS Forecast Studio: demand forecasting


SAMPLECONSULTING

ENGAGEMENTS

SPARE MACHINE PARTS INVENTORYOPTIMIZATION

Customer: Injection molding systemsInventory replenishment

I Large number of SKUsI Three warehouses in America, Europe, and AsiaI Demand forecastI Reorder point to satisfy service levelI Order decisions

Stochastic optimization at warehousesInventory balancing across warehousesSAS tools:

I SAS Forecast Studio: demand forecastingI PROC MIRP

Decomposed for tractability


SAMPLECONSULTING

ENGAGEMENTSMANUFACTURING INVENTORY PLANNING

Customer: Large construction equipment manufacturerManufacturing inventory planning

I Supply chain networks with plants and warehousesI Dozens of product linesI Hundreds of critical componentsI Long order-to-delivery (OTD) timeI Inventory decisions for components to meet OTD constraints

SAS tools:I SAS Inventory Optimization Workbench


SAMPLECONSULTING

ENGAGEMENTSMANUFACTURING INVENTORY PLANNING

Customer: Large automakerManufacturing inventory planning

I Large supply chain networks with plants, warehouses, and dealersI Approximately 1,000 packages (cars with options)I 10,000+ service partsI A few hundred outsourcing parts for manufacturingI Inventory decisions for finished goods, service parts, and manufacturing parts

SAS tools:I SAS Inventory Replenishment PlanningI SAS/OR: OPTMODEL, MILP solverI SAS Forecast Server: demand forecasting


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Solving Business Problems with SAS Analytics and OPTMODEL

SOLVING BUSINESS PROBLEMS WITH SAS ANALYTICS AND … · SASANALYTICS INTRODUCTION BACKGROUNDONSAS...

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