SOLVING BUSINESS PROBLEMS WITH SAS ANALYTICS AND … · SASANALYTICS INTRODUCTION BACKGROUNDONSAS...
Transcript of 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
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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
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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”
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SAS ANALYTICSINTRODUCTION SAMPLE SAS DATA SET
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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
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SAS ANALYTICSINTRODUCTION OVERVIEW OF SAS FUNCTIONS
Mathematical, Arithmetic, TruncationArrayCharacterDate and TimeFinancialProbability DistributionsTrigonometric, HyperbolicRandom Number GenerationSample Statistics, Quantiles
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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
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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
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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)
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SAS ANALYTICSINTRODUCTION
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)
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SAS ANALYTICSINTRODUCTION “OPERATIONS RESEARCH WITH SAS” BLOG
http://blogs.sas.com/content/operations/
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SAS ANALYTICSINTRODUCTION SAS SUPPORT COMMUNITIES
https://communities.sas.com/
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SAS ANALYTICSINTRODUCTION THE SCOPE OF SAS/OR®
1 Mathematical optimization
2 Discrete-event simulation
3 Project and resource scheduling
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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
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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
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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
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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
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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
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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
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SAS ANALYTICSINTRODUCTION
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
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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
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SAS ANALYTICSINTRODUCTION
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
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SAS ANALYTICSINTRODUCTION
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
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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
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SAS ANALYTICSINTRODUCTION
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
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SAS ANALYTICSINTRODUCTION
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)
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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
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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
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p−MEDIAN CUSTOMER LOCATIONS
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p−MEDIAN OPTIMAL SOLUTION FOR p = 5
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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
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p−MEDIAN MILP FORMULATION
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
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p−MEDIAN LIVE DEMO
CodepMedianData.sas
CodepMedianMILP.sas
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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
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p−MEDIAN MILP FORMULATION
minimize∑i∈C
∑j∈C
widijyij
subject to∑j∈C
xj = p
∑j∈C
yij = 1 i ∈ C (λi)
yij ≤ xj i ∈ C, j ∈ Cxj ∈ {0, 1} j ∈ Cyij ∈ {0, 1} i ∈ C, j ∈ C
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p−MEDIAN LAGRANGIAN RELAXATION
minimize∑i∈C
∑j∈C
widijyij +∑i∈C
λi
1−∑j∈C
yij
subject to
∑j∈C
xj = p
yij ≤ xj i ∈ C, j ∈ Cxj ∈ {0, 1} j ∈ Cyij ∈ {0, 1} i ∈ C, j ∈ C
For fixed λ, reduces to a trivial (sorting) problemProvides lower bound on optimal objective value
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p−MEDIAN LOWER AND UPPER BOUNDS ON OPTIMALOBJECTIVE VALUE
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p−MEDIAN LIVE DEMO
CodepMedianLagRel.sas
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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
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PORTFOLIOOPTIMIZATION QUADRATIC PROGRAMMING FORMULATION
minimize∑i∈A
∑j∈A
cijxixj
subject to∑i∈A
xi = 1∑i∈A
rixi ≥ ℓ
xi ≥ 0 i ∈ A
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PORTFOLIOOPTIMIZATION NONLINEAR PROGRAMMING FORMULATION
maximize∑i∈A
rixi
subject to∑i∈A
xi = 1∑i∈A
∑j∈A
cijxixj ≤ u
xi ≥ 0 i ∈ A
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PORTFOLIOOPTIMIZATION EFFICIENT FRONTIER
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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;
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PORTFOLIOOPTIMIZATION LIVE DEMO
CodePortfolio.sas
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PORTFOLIOOPTIMIZATION MULTIOBJECTIVE FORMULATION
minimize∑i∈A
∑j∈A
cijxixj and maximize∑i∈A
rixi
subject to∑i∈A
xi = 1
xi ≥ 0 i ∈ A
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PORTFOLIOOPTIMIZATION LIVE DEMO
CodePortfolioLSO.sas
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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
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CAR PAINTING SOLUTION APPROACH
Use CLP solverPredicates: ALLDIFF, ELEMENT, and REIFYFind all optimal solutionsPROC GANTT to display solutions
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CAR PAINTING LIVE DEMO
CodeCarPainting.sas
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TRAVELINGSALESMANPROBLEM
PROBLEM DESCRIPTION
Given cities and pairwise distances between themFind tour that visits each city exactly onceMinimize total distance traveled
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TRAVELINGSALESMANPROBLEM
LOCATIONS
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TRAVELINGSALESMANPROBLEM
OPTIMAL SOLUTION
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TRAVELINGSALESMANPROBLEM
THREE WAYS TO ACCESS SOLVER
SAS/OR OPTNET procedureSAS/OR OPTMODEL procedureSAS Viya tsp action
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TRAVELINGSALESMANPROBLEM
LIVE DEMO
CodeTSPCapitalCities.sas
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TRAVELINGSALESMANPROBLEM
SAS VIYA (NEW CLOUD-BASED PLATFORM)
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TRAVELINGSALESMANPROBLEM
SAS OPTIMIZATION ON SAS VIYA
Optimization action set Network Optimization action setsolveLp biconnectedComponents minSpanTreesolveMilp clique readGraphsolveQp connectedComponents shortestPathtuner cycle summary
linearAssignment transitiveClosureminCostFlow tspminCut
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TRAVELINGSALESMANPROBLEM
LIVE DEMO
CodeTSPCapitalCities.ipynb
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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
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p−MEDIAN MILP FORMULATION
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
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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
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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
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p−MEDIAN LIVE DEMO
CodepMedianBenders.sas
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p−MEDIAN MULTIPLE SUBPROBLEMS
Often, LP subproblem decomposes into disjoint subproblemsCan solve independently and in parallelCan generate tighter cuts for master problem
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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
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p−MEDIAN LP SUBPROBLEM FOR EACH i
minimize∑j∈C
widijyij
subject to∑j∈C
yij = 1
yij ≤ x̂j j ∈ Cyij ≥ 0 j ∈ C
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p−MEDIAN LP SUBPROBLEM FOR EACH i
minimize∑j∈C
widijyj
subject to∑j∈C
yj = 1
yj ≤ x̂j j ∈ Cyj ≥ 0 j ∈ C
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p−MEDIAN LIVE DEMO
CodepMedianBendersMultiple.sas
CodepMedianBendersMultipleCofor.sas
CodepMedianBendersMultipleCoforShared.sas
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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?
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OPTIMIZATION FORMACHINELEARNING
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}
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OPTIMIZATION FORMACHINELEARNING
SGD PARAMETERS
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OPTIMIZATION FORMACHINELEARNING
HYPERPARAMETER TUNING
The goal of tuning is to find better models
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OPTIMIZATION FORMACHINELEARNING
LOCAL SEARCH OPTIMIZATION
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OPTIMIZATION FORMACHINELEARNING
AUTOTUNE IN SAS PROCEDURES
PROCs with autotune feature include TREESPLIT, FOREST, GRADBOOST,NNET, SVMACHINE, and FACTMAC
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OPTIMIZATION FORMACHINELEARNING
HYPERPARAMETERS
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OPTIMIZATION FORMACHINELEARNING
OUTPUT TABLES
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OPTIMIZATION FORMACHINELEARNING
TUNING EFFECTIVENESS
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OPTIMIZATION FORMACHINELEARNING
PARALLEL EFFICIENCY
Model training: 4 workers; model tuning: n concurrently
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OPTIMIZATION FORMACHINELEARNING
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
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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
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BOSTON PUBLICSCHOOLS BUSINESS PROBLEM
Boston Public Schools (BPS)
>200 schools
>29,000 students
>600 school buses
>3,200 routes daily
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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%
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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
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BOSTON PUBLICSCHOOLS
BUS STOP CONSOLIDATION:CURRENT SYSTEM
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BOSTON PUBLICSCHOOLS
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
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BOSTON PUBLICSCHOOLS
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
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BOSTON PUBLICSCHOOLS
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
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BOSTON PUBLICSCHOOLS
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
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BOSTON PUBLICSCHOOLS
BUS STOP CONSOLIDATION:CURRENT SYSTEM VS OPTIMAL SOLUTION
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BOSTON PUBLICSCHOOLS
BUS ROUTING:CURRENT SYSTEM
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BOSTON PUBLICSCHOOLS
FLEET SCHEDULING:MOTIVATION
Potential for improvements by rescheduling busesObjective: assign minimum number of buses to cover all morning andafternoon buses
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BOSTON PUBLICSCHOOLS
FLEET SCHEDULING:SOLUTION APPROACH
1 Define specific time zone, bus type, and bus yard2 Data preparation to generate columns3 Solve IP problem
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BOSTON PUBLICSCHOOLS
FLEET SCHEDULING:ROUTE COMBINATION LOGIC
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BOSTON PUBLICSCHOOLS
FLEET SCHEDULING:MODEL FORMULATION
minimize∑
k ∈ BUSES
yk
subject to∑
k ∈ BUSES:(k,r)∈Syk = 1 r ∈ ROUTES
yk ∈ {0, 1} k ∈ BUSES
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BOSTON PUBLICSCHOOLS
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
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BOSTON PUBLICSCHOOLS
BELL TIME ASSIGNMENT:CURRENT STATUS
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BOSTON PUBLICSCHOOLS
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
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BOSTON PUBLICSCHOOLS
BELL TIME ASSIGNMENT:AFTER FIRST SOLVE
Minimize the maximum number of buses across all times
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BOSTON PUBLICSCHOOLS
BELL TIME ASSIGNMENT:AFTER SECOND SOLVE
Minimize the maximum number of buses across afternoon times
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BOSTON PUBLICSCHOOLS
BELL TIME ASSIGNMENT:AFTER FINAL SOLVE
Minimize number of changes in the schedule
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BOSTON PUBLICSCHOOLS
BELL TIME ASSIGNMENT:COMPARISON RESULTS
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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
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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
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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
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SAMPLECONSULTING
ENGAGEMENTSSIMULATION
Hospital room assignment simulation Details
Prison population simulation Details
Neonatal intensive care unit simulation Details
Digital parts distribution Details
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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
Copyright 2017, SAS Institute Inc. All rights reserved. 103
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
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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
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SAMPLECONSULTING
ENGAGEMENTSTELEVISION ADVERTISING OPTIMIZATION
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SAMPLECONSULTING
ENGAGEMENTSTELEVISION ADVERTISING OPTIMIZATION
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SAMPLECONSULTING
ENGAGEMENTSTELEVISION ADVERTISING OPTIMIZATION
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SAMPLECONSULTING
ENGAGEMENTSTELEVISION ADVERTISING OPTIMIZATION
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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
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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
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SAMPLECONSULTING
ENGAGEMENTSHOSPITAL ROOM ASSIGNMENT SIMULATION
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
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SAMPLECONSULTING
ENGAGEMENTSHOSPITAL ROOM ASSIGNMENT SIMULATION
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
Copyright 2017, SAS Institute Inc. All rights reserved. 113
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
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SAMPLECONSULTING
ENGAGEMENTSPRICE OPTIMIZATION FOR RAILROAD
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
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SAMPLECONSULTING
ENGAGEMENTSPRICE OPTIMIZATION FOR RAILROAD
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
Copyright 2017, SAS Institute Inc. All rights reserved. 116
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
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SAMPLECONSULTING
ENGAGEMENTSINVENTORY OPTIMIZATION
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)
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SAMPLECONSULTING
ENGAGEMENTSINVENTORY OPTIMIZATION
VA report: demand forecasts and projected inventory targets
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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
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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
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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
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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
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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
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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
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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:
I SAS/OR: Simulation Studio
Copyright 2017, SAS Institute Inc. All rights reserved. 126
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:
I SAS/OR: Simulation Studio
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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:
I SAS/OR: Simulation Studio
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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
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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
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SAMPLECONSULTING
ENGAGEMENTSSHOW TICKET REVENUE MANAGEMENT
Customer: Large US resortAttendance forecastShow ticket availability optimizationDemand channel managementSAS tools:
I Pricing CatalogI SAS/OR: OPTMODEL, QP solver
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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
Copyright 2017, SAS Institute Inc. All rights reserved. 132
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
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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
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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
Copyright 2017, SAS Institute Inc. All rights reserved. 135
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
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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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