Solving Business Problems with SAS Analytics and OPTMODEL

Copyright c©2013, SAS Institute Inc. All rights reserved.

Solving Business Problemswith SAS Analyticsand OPTMODEL

Pre-Conference WorkshopINFORMS Annual MeetingMinneapolis, MN

SAS Institute Inc.

October 5, 2013

Outline

1 SAS/OR Introduction

2 Multicommodity Flow Problem

3 Network Algorithms

4 COFOR Loop

5 SUBMIT Block

6 Graph Partitioning with Connectivity Constraints

7 Customer Case Study: Insurance Claim Assignment

8 Sample Consulting Engagements


Background on SAS

Founded in 1976World’s largest privatelyheld software companyOver 400 offices worldwideOver 800 alliances globallyOver 65,000 customersites in 135 countriesSAS customers, affiliates:90 of top 100 companies in2012 Fortune Global 500Hundreds of local usergroups


SAS Data Sets, Language, Terminology

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

SAS programming language base: data handling andexploration, elementary statistics, wide range of functions

Software modules are procedures, abbreviated “PROC”


Sample SAS Data Set


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

» DATA step functionality» PROC IMPORT» Enterprise Guide

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

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

» SAS can write results back to the native database format


Overview of SAS Functions

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


SAS Products and Solutions

SAS products: breadth and depth» Data Integration: access, cleansing, metadata creation» Business Intelligence: query, reporting, visualization» Analytics: statistics, forecasting, data mining, text mining,

quality control, optimization, scheduling, simulation

SAS solutions» Cross-Industry: Customer Intelligence, Supply Chain

Intelligence, Predictive Asset Maintenance, RiskManagement, Sustainability Management, SecurityIntelligence, Visual Analytics

» Industry-Specific: Retail, Oil and Gas, Manufacturing,Energy & Utilities, Financial Services, Health Care, LifeSciences, Insurance, Communications, Media, Hotels,Casinos, Travel & Transportation, Government, Education,Defense & Aerospace


SAS-Related Presentations at INFORMS

SA04 New Approaches to Mixed Integer Programming HeuristicsMenal Güzelsoy, Philipp Christophel, Imre Pólik

SB29 JMP Software from SASJian Cao

MA08 Recent Improvements in SAS/OR Optimization SolversImre Pólik, Philipp Christophel, Menal Güzelsoy, Yan Xu, Amar Narisetty

MA29 SAS Global Academic Program: High-Performance Data Mining withSAS Enterprise MinerAndré de Waal

MB34 ARD: An Automated Replication-Deletion Method for SimulationAnalysisEmily Lada, Anup Mokashi, James Wilson

MC08 New Features in OPTMODEL: Parallel Coroutines and SemanticModelingLeo Lopes


SAS-Related Presentations at INFORMS(cont.)

MC23 The Value of the Price EnvelopeBahadir Aral

MC23 Revenue Management as a Strategic ToolMaarten Oosten

MD08 Dip and DipPy: A Decomposition-based Modeling System and Solverco-author Matthew Galati

MD10 Managing Successful Careers in O.R. Practice - A Panel Discussionincluding Radhika Kulkarni

MD29 Building and Solving Optimization Models with SASEd Hughes, Rob Pratt


SAS-Related Presentations at INFORMS(cont.)

TA04 A Generalized Benders’ Algorithm for the Two-stage Stochastic MixedInteger Linear Problemco-author Menal Güzelsoy

TC65 Social Media Intelligence for Regional InstabilityTom Sabo, Sr.

WB06 P-median and P-dispersion Problems: A Bi-criteria AnalysisGolbarg Tutunchi, Fatemeh Sayyady

WB19 FlowBalancer Supports Strategic and Tactical Planning Problems byusing Analytical Queueing ModelsNico Vandaele, Kris Lieckens (KU Leuven)

WB30 Two-stage Stochastic View Selection for Data-analysis Queries:Properties and AlgorithmsRong Huang

WD23 Multicriteria Model for Price and Promotion OptimizationNatalia Viktorovna, Maarten Oosten


The Scope of SAS/OR

1. Mathematical optimization

2. Discrete event simulation

3. Constraint programming

4. Global and local search

5. Project and resource scheduling


Broad Range of Optimization SolversLinear Programming:

» Primal, Dual, Network Simplex» Interior Point» Concurrent

Mixed Integer Linear Programming:» Branch and Bound with heuristics, cuts, conflict search» Decomposition algorithm (MILP and LP)

Network Algorithms

Quadratic Programming:» Interior Point

Nonlinear Programming:» Active Set» Interior Point» Multistart, Concurrent


DECOMP (Decomposition) Algorithm

New in SAS/OR 12.1Accessible in PROC OPTMODELUser conveys block structure via .block constraint suffixsolve with LP|MILP / decomp=(method=user);

Master and subproblems generated and solvedautomatically and in parallelFor block-angular problems, dramatic performanceimprovements over direct solverIn SAS/OR 13.1, automatically detects identicalsubproblems and uses Ryan-Foster branching if applicable


Network Algorithms

PROC OPTNET (new in SAS/OR 12.1)PROC OPTMODEL:

» SUBMIT block (new in SAS/OR 12.1)» SOLVE WITH NETWORK (new in SAS/OR 13.1)

Connected componentsBiconnected componentsand articulation pointsMaximal cliquesCyclesTransitive closureLinear assignmentproblem

Shortest path problemMinimum-cost network flowproblemMinimum spanning treeproblemMinimum cut problemTraveling salesmanproblem


Global and Local Search Optimization

PROC OPTLSO (new in SAS/OR 12.3)For black-box objectivesContinuous and discrete variablesLinear and nonlinear constraintsParallel execution of:

» Local search methods» Global GA-type heuristics» Pattern search

Objective can be an aggregation over an externalpre-distributed data setArray-structured input data supported


Other Recent and Upcoming Enhancementsin SAS/OR 12.1 through 13.1

Concurrent LP and NLP solversParallel MILP option tunerParallel NLP multistartSAS code block (SUBMIT/ENDSUBMIT) in OPTMODELParallel FOR loop (COFOR) in OPTMODELNetwork algorithms access from OPTMODELCutting plane strategy and conflict search for MILPParallel MILP algorithmCrossover enhancements for LP interior point algorithm


SAS Optimization-Based Solutions

SAS MarketingOptimizationSAS Service PartsOptimizationSAS Contact CenterPlanning and OptimizationSAS Revenue OptimizationSuiteSAS Size OptimizationSAS Credit Scoring forBanking

SAS Risk Management forBanking, for InsuranceSAS Social NetworkAnalysisSAS InventoryOptimizationSAS Enterprise DecisionManagementSAS RevenueManagement and PriceOptimization Analytics


OPTMODEL: Major Features

Algebraic modeling language with optimization-orientedsyntax:

» Variables, constraints, bounds, objective» Algebraic expression of functions» Parameters, variables, arrays, index sets

Tight integration with SAS programming environmentFlexible input/output: read from and create data setsInteractive environmentDirect access to LP, MILP, Network, QP, NLP solversSupport for customized algorithms


OPTMODEL Programming Statements

Control and Looping:» DO, IF, etc.» DO iterative, DO UNTIL, DO WHILE, etc.» FOR, COFOR

General» CALL» SUBMIT/ENDSUBMIT

Input/Output:» READ DATA, CREATE DATA: working with SAS data sets» SAVE MPS, SAVE QPS» FILE, PRINT, PUT

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


OPTMODEL Expressions Overview

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

» SUM, PROD, MAX, MIN» INTER aggregation, UNION aggregation» SETOF, AND aggregation, OR aggregation

Set operators:» IN, WITHIN» INTER, UNION, SYMDIFF, DIFF» CROSS, SLICE

Logical:» Conditional: IF-THEN-ELSE» Boolean: AND, OR

Scalar and set expressions


Basics of the SAS Macro Language

Macros: parameterized blocks of SAS codeMacro variables:

» Assigning a value: %let varname=<value>;» Using: &varname

Declaring a macro:%macro macroname (param1, param2);<SAS code>

%mend macroname;

Invoking a macro:%macroname (<value1>, <value2>);Special code within macros:

» %if &varname=<value> %then %do; ...%end;» %do n=1 %to &number;...%end;


Outline




4 COFOR Loop

5 SUBMIT Block





Multicommodity Flow Problem

Given directed network (N,A) and commodities K

Each node i ∈ N has supply bki for commodity k ∈ K

Each arc (i, j) ∈ A has:» cost cij per unit of flow» capacity uij that limits sum of flows of commodities

Satisfy all supplies and demands at minimum cost, whilerespecting arc capacitiesTwo approaches:

» Direct LP» Dantzig-Wolfe Decomposition


Example Network with Two Commodities

110 2 −10

3 4

520 6 −20

(c = 1, u = 5)

(5, 30)

(1, 10)

(5, 30)

(1, 30)(1, 30)

(5, 30)


Optimal Solution

110 2 −10

3 4

520 6 −20

(c = 1, u = 5)

(5, 30)

(1, 10)

(5, 30)

(1, 30)(1, 30)

(5, 30)

5

5

5 5

5

55

15


Linear Programming Formulation

minimize∑

(i,j)∈A

∑k∈K

cijxkij

subject to∑k∈K

xkij ≤ uij (i, j) ∈ A∑

(i,j)∈A

xkij −

∑(j,i)∈A

xkji = bk

i i ∈ N, k ∈ K

xkij ≥ 0 (i, j) ∈ A, k ∈ K

var Flow {ARCS, COMMODITIES} >= 0;min TotalCost =

sum {<i,j> in ARCS, k in COMMODITIES} cost[i,j] * Flow[i,j,k];con Linking {<i,j> in ARCS}:

sum {k in COMMODITIES} Flow[i,j,k] <= capacity[i,j];con Balance {i in NODES, k in COMMODITIES}:

sum {<(i),j> in ARCS} Flow[i,j,k]- sum {<j,(i)> in ARCS} Flow[j,i,k] = supply[i,k];


Multicommodity Flow Problem: Direct LP

OPTMODEL codeMulticommodityFlow.sas


Constraint Matrix for Example Network

1 11 1

1 11 1

1 11 1

1 11 1−1 −1

−1 −1 1−1 1 1

1 1−1 −1

1 1−1 −1

−1 −1 1−1 1 1

1 1−1 −1


Block-Angular Structure

A1 A2 · · · A|K|B1

B2. . .

B|K|


Linear Programming Formulation

minimize∑

(i,j)∈A

∑k∈K

ckijx

kij

subject to∑k∈K

xkij ≤ uij (i, j) ∈ A (1)∑

(i,j)∈A

xkij −

∑(j,i)∈A

xkji = bk

i i ∈ N, k ∈ K (2)

xkij ≥ 0 (i, j) ∈ A, k ∈ K (3)

Dantzig-Wolfe DecompositionMaster: (1)Subproblem: (2)-(3)


DECOMP (Decomposition) Algorithm

New in SAS/OR 12.1Accessible in PROC OPTMODELUser conveys block structure via .block constraint suffixsolve with LP|MILP / decomp=(method=user);

Master and subproblems generated and solvedautomatically and in parallelFor block-angular problems, dramatic performanceimprovements over direct solverIn SAS/OR 13.1, automatically detects identicalsubproblems and uses Ryan-Foster branching if applicable


DECOMP: METHOD= Option

USER: User defines the subproblems using constraint suffix.block

NETWORK: Finds an embedded network [Bixby88] and usesthe weakly connected components as subproblem blocksAUTO: Searches for disjoint blocks (no master constraints)after presolve


Multicommodity Flow Problem:Decomposition Algorithm

OPTMODEL codeMulticommodityFlowDecomp.sas


Outline




4 COFOR Loop

5 SUBMIT Block





Network Algorithms in SAS/OR

Connected componentsBiconnected components and articulation pointsMaximal cliquesCyclesTransitive closureLinear assignment problemShortest path problemMinimum-cost network flow problemMinimum spanning tree problemMinimum cut problemTraveling salesman problem


Network Algorithm for Shortest Path

PROC OPTNET can be called directly:» Reads arc data set via DATA_LINKS= option» By default, SHORTPATH statement invokes all-pairs

shortest paths solver» Can specify SOURCE= and SINK= to solve s-t shortest

path problem

PROC OPTNET can also be called from within PROCOPTMODEL via SUBMIT/ENDSUBMITIn SAS/OR 13.1, network algorithms accessible usingSOLVE WITH NETWORK statement in PROC OPTMODEL


Network Algorithm

OPTMODEL codeShortestPathOPTNET.sas


Outline




4 COFOR Loop

5 SUBMIT Block





COFOR LoopUses multiple threads to execute SOLVE statements inparallel across iterations of loopSyntax for serial FOR loop:

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

end;

Syntax for parallel COFOR loop:cofor {i in ISET} do;

...solve ...;...

end;


Milk Collection: Periodic VRPH.P. Williams, Model Building in MathematicalProgramming (2013)SAS/OR R© 12.3 User’s Guide: Mathematical ProgrammingExamples (2013)Scheduling and routing milk collection trucks

» Truck collects milk from dairy farms» Each farm’s collection frequency is daily or every other day

1

2

3

4

5

6

7

8

9

10

11

1213

14

15

16

17

18

19

2021

-6 -4 -2 0 2 4 6

-5

0

5

10

12frequency

day = 1

1

2

3

4

5

6

7

8

9

10

11

1213

14

15

16

17

18

19

2021

-6 -4 -2 0 2 4 6

-5

0

5

10

12frequency

day = 2


Benders Decomposition

Combinatorial Benders Decomposition with a TSPsubproblem oracleMaster problem decides which nodes (farms) to visit eachday and enforces:

» capacity, frequency, and symmetry breaking» optimality cuts (generated by subproblem)

Subproblem is a TSP for each day» generates optimality cuts for the master» uses specialized TSP solver» subset of nodes changes at each iteration


Milk Collection Problem: BendersDecomposition using SOLVE WITHNETWORK and COFOR loop (both new inSAS/OR 13.1)

OPTMODEL codeMilkCollectionBendersNetworkCofor.sas


Outline




4 COFOR Loop

5 SUBMIT Block





SUBMIT Block

Access the full SAS system without exiting OPTMODELBuild novel dynamic algorithms using statistics, matrixmanipulation, visualization, interaction, etc.Syntax:

proc optmodel;...submit [arguments] [/ options];

[arbitrary SAS code]endsubmit;...

quit;


Cardinality Constrained Regression: WhichRegressors Produce the Best Fit?

Multivariate linear regression

Y = Xβ + β0e + ε,

whereY ∈ Rm, X ∈ Rm×n are datae ∈ Rm is vector of onesβ ∈ Rn, β0 ∈ R, ε ∈ Rm are decision variables

Letz ∈ {0, 1}n: indicator variables for βk: user input number of regressors to allow

Minimize the SSE over all models with k or fewer regressors.


Benders Decomposition

Master is selection problem (over z)Can include any rule expressible as a MILP (e.g., subsetcardinality, clique constraints)Optimality cut for each regressor subset and all its subsetsSubproblem is just linear regression (β, ε), so can usePROC REG


Cardinality Constrained Regression:Benders Decomposition using SUBMIT tocall PROC REG

OPTMODEL codeRegressionBendersSubmit.sas


Outline




4 COFOR Loop

5 SUBMIT Block





Problem Statement

Given undirected graph, node weights, positive integer k,target t ∈ [`, u]

Partition node set into k subsets, each with total weightwithin [`, u]

Usual objective: minimize sum of edge weights betweenparts of partitionOur objective: find most “balanced” partition

» Minimize total absolute deviation of subset weight fromtarget (L1 norm)

» Minimize maximum absolute deviation of subset weightfrom target (L∞ norm)

Connectivity constraints: each of the k resulting inducedsubgraphs must be connected


Motivation

Dennis E. Shasha, Doctor Ecco’s Cyberpuzzles (2002)» Political districting

AAOS consulting engagement» Assigning service workers to customer regions

INFORMS OR Exchange posting (Jan. 2013)http://www.or-exchange.com/questions/7248/

graph-partitioning-with-connectivity-constraints

» Forestry


http://www.or-exchange.com/questions/7248/graph-partitioning-with-connectivity-constraints

http://www.or-exchange.com/questions/7248/graph-partitioning-with-connectivity-constraints

Map from Shasha (2002)


Map Represented as Graph


Node Weights (Populations)


Solution for k = 14, t = 12000, [`, u] = t ± 100


Solution Approaches

Compact MILP formulation with IsCapital[i] binaryvariables and nonnegative flow variablesRow generation, dynamically excluding disconnectedsubsetsColumn generation, dynamically generating connectedsubsetsColumn generation, statically generating all possibleconnected subsets


Static Column Generation: Main Steps

1. Generate all possible connected subsets with weightsclose enough to target1.1 Relax connectivity and find all possible subsets1.2 Postprocess to filter out disconnected subsets

2. Solve cardinality constrained set partitioning problem


Static Column Generation: Features Used inPROC OPTMODEL

MILP solver to compute maximum subset size for eachnode (COFOR loop)SOLVE WITH NETWORK (all-pairs shortest path) togenerate valid cuts that encourage connectivityFILE and PUT statements to generate PROC CLP codeSUBMIT block to call PROC CLP (later, SOLVE WITHCLP)SOLVE WITH NETWORK (connected components) tocheck connectivity (COFOR loop)MILP solver to solve set partitioning problem


Column Generation Subproblem

Given node populations pi and target population range [`, u]

Find all connected node subsets close to target populationBinary variable xi to indicate whether node i appears insubset` ≤

∑i∈N

pixi ≤ u

Connectivity hard to impose directly, so relax (but do notignore)


Valid Subproblem Cuts to EncourageConnectivity: Nodes Too Far Apart

mi: max # nodes among feasible subsets containing node iIf shortest path distance dij ≥ min(mi,mj) then xi + xj ≤ 1


Valid Subproblem Cuts to EncourageConnectivity: Isolated Nodes

If xi = 1 and pi < ` then xj = 1 for some neighbor j of ixi ≤

∑j∈Ni

xj


Valid Subproblem Cuts to EncourageConnectivity: Isolated Edges

If xi = xj = 1 and pi + pj < ` then xk = 1 for some neighbor kxi + xj − 1 ≤

∑k∈(Ni∪Nj)\{i,j} xk


Valid Subproblem Cuts to EncourageConnectivity: Isolated Edges (Stronger Cuts)

If (xi = 1 or xj = 1) and pi + pj < ` then xk = 1 for someneighbor k in moat around {i, j}xi ≤

∑k∈(Ni∪Nj)\{i,j}

xk

xj ≤∑

k∈(Ni∪Nj)\{i,j}xk


Valid Subproblem Cuts to EncourageConnectivity: Sets with Small Population

More generally, if xi = 1 for some i ∈ S ⊂ N such that∑j∈S

pj < ` then xk = 1 for some neighbor k in moat around S

xi ≤∑

k∈(∪j∈SNj)\Sxk

Known as “ring inequalities” in the literature


Graph Partitioning with ConnectivityConstraints

OPTMODEL codeGraphPartitioningConnectivity.sas


Outline




4 COFOR Loop

5 SUBMIT Block





Business Problem

Given daily insurance claims and availability of adjustersObjective:

» Increase efficiency of claim processing» Provide user capability to visualize current state of workload

Optimization problem: Distribute claims evenly amongadjusters while considering eligibility and capacityconstraints


Mathematical Model

Objective» Minimize workload deviation among adjusters

Decision» Which claims assigned to which adjuster

Assignment eligibility» Skill level (hard constraints)» Location (soft constraints)

Capacity requirements based on skill level of adjuster» Limit on total weighted load» Limit on number of newly assigned claims


Insurance Claim Assignment Optimization

Planning horizon: 5 monthsClaims

» Average number of claims per day: 80» Type: auto, home

Adjusters» Number of adjusters: 20» Job grade: 1,2,3

Skills: Construction, auto body, paralegal, software, . . .Geographical regions in Florida: North, Central, South


Insurance Claim Assignment Optimization

Interface written in Adobe Flash/FlexCalls PROC OPTMODEL code as stored processCommunication via SAS data sets and SAS macrolanguage

Launch Insurance Claim Assignment Optimization Demo


http://coevm01.na.sas.com:8080/InsuranceDemo/InsuranceDemo.html

Outline




4 COFOR Loop

5 SUBMIT Block





Sample Consulting Engagements

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

Areas of Focus» Generic Optimization Details

» Simulation Details

» Revenue Management Details

» Inventory Optimization Details


Sample Consulting Engagements:Generic Optimization

Investment portfolio optimization Details

Optimal ATM replenishment Details

Optimal loan assignment Details

Chemical mixture optimization Details

Water management Details

Casino floor mix optimization Details


Sample Consulting Engagements:Simulation

Simulation for discovery oncology Details

Prison population simulation Details


Sample Consulting Engagements:Revenue Management (RM) and Pricing

RM framework for car rental Details

RM framework for cruise line Details

Show ticket RM Details

Pricing and inventory optimization Details


Sample Consulting Engagements:Inventory Optimization (IO)

Retail inventory replenishment Details

IO for spare parts Details

IO for automotive Details

IO for construction equipment Details


Investment Portfolio Optimization

Customer: Large US Government AgencyInvestment portfolio optimization

» Portfolio mix: T-Bills, T-Notes, CDs» Suggested investment strategy for 5 years» Discrete: minimum investment requirements

MILPSAS tools:

» SAS Forecast Studio» SAS/OR: OPTMODEL, MILP solver

Generalized network flow formulation


Simulation for Discovery Oncology

Customer: Large Global PharmaceuticalDiscrete Event Simulation for Oncology Drug Discovery

» Synthesizing and testing drug compounds is very expensive» Goal is to find a candidate compound for clinical trials:

» Faster—reduce time to market» Cheaper—reduce cost of assay testing» More reliably—increase chance of success in trials

» Major strategies to evaluate via simulation:» Which compound to synthesize next?» Which compounds to send to which assays?» When to stop testing a compound?» How to identify a good clinical candidate?

SAS Simulation Studio


ATM Cash Optimization Overview

Customer: Large South-East Asian BankATM cash replenishment optimization

» Large number of ATMs» Side constraints (capacity, etc)

MILPSAS tools:

» SAS Forecast Studio: demand forecasting» SAS/OR: OPTMODEL, MILP solver

Reformulated for tractability


Retail Inventory Replenishment

Customer: Large Retail CompanyRetail Inventory Replenishment

» Large number of SKUs, locations, and vendors» Demand forecast» Reorder point to satisfy service level» Order decisions

Stochastic optimization at storesMILP optimization at depotsSAS tools:

» SAS/OR: OPTMODEL, MILP solver» SAS Forecast Studio: demand forecasting


Optimal Loan Assignment

Customer: Large US BankLoan Assignment Optimization

» Goal: assign new loans (foreclosures, short sales, etc)» Minimize standard deviation between teams» Resource pool: CRMs (Customer Relationship Managers)

teams and PS (Process Support) resources» Constraints: maximum case loads, limits on case types, etc.» Eligibility rules: case type match, geographical (time zone),

language, etc.Difficult problem (MINLP):

» Nonlinear objective (standard deviation)» Binary variables (assignment)

SAS tools:» SAS/OR: OPTMODEL, MILP solver» SAS/DI and SAS/BI for data integration and reporting


Mixture Optimization

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

» Minimum cost portfolio problem» Nonlinear performance constraints» Discrete: assignment constraints

MINLPSAS tools:

» SAS/OR: OPTMODEL, MILP solver, NLP solver» JMP» (Future) SAS/Grid Manager: parallel computations

Completely custom algorithm


Revenue Management for Car Rental

Customer: Large US Car Rental CompanyBusiness Analytics Framework developmentOptimizing for growth (market share)Automate RM processPricing and reservation system

» Data integration» Segmentation» Forecasting: unconstrained demand by segment and length

of rent» Optimization: automatic generation of step

recommendations

RMPO with extensions


Show Ticket Revenue Management

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

» RMPO with extensions» SAS/OR: OPTMODEL, QP solver


Revenue Management for Cruise Line

Customer: Large US Entertainment CompanyBusiness Analytics Framework developmentAutomate pricing and availability management processAccount for multiple constraintsPricing and revenue management system

» Data integration» Segmentation» Forecasting: unconstrained demand by segment» Estimation: demand response to changes in pricing

strategy» Optimization: automatic generation of pricing and

availability recommendations

RMPO with extensions


Pricing and Inventory Optimization

Customer: Large US RetailerProduct promotion optimization

» Retail pricing and inventory network» Non-convex NLP» Discrete side constraints

Multi-objective NLPSAS tools:

» SAS/OR: OPTMODEL, NLP and MILP solvers

Customized heuristics


Spare Parts Inventory Optimization

Customer: Injection Molding SystemsInventory Replenishment

» Large number of SKUs» Three warehouses in America, Europe, and Asia» Demand forecast» Reorder point to satisfy service level» Order decisions

Stochastic optimization at warehousesInventory balancing across warehousesSAS tools:

» SAS Forecast Studio: demand forecasting» PROC MIRP

Decomposed for tractability


Manufacturing Inventory Planning

Customer: Large AutomakerManufacturing Inventory Planning

» Large supply chain networks with plants, warehouses, anddealers

» Close to one thousand packages (cars with options)» More than ten thousand service parts» A few hundred outsourcing parts for manufacturing» Inventory decisions for finished goods, service parts, and

manufacturing partsSAS tools:

» SAS Inventory Replenishment Planning» SAS/OR: OPTMODEL, MILP solver» SAS Forecast Server: demand forecasting


Manufacturing Inventory Planning

Customer: Large Construction Equipment ManufacturerManufacturing Inventory Planning

» Supply chain networks with plants, and warehouses» Dozens of product lines» Hundreds of critical components» Long order-to-delivery (OTD) time» Inventory decisions for components to meet OTD

constraintsSAS tools:

» SAS Inventory Replenishment Planning


Prison Population Simulation

Customer: State Legislative AgencyPrison Planning and Scenario Analysis

» Mandated projections to plan for prison capacity» Numbers highly dependent on legislative policy» Must consider current population and future entries» Need to account for revocations

SAS tools:» SAS/OR: Simulation Studio


Water Management

Customer: National Utilities AgencyWater flow scheduling and routing

» Demand forecast for public water» Network of reservoirs and pumping stations» Business rules for reserve capacity and flow» Multi-objective problem

SAS tools:» SAS/OR: OPTMODEL, MILP solver» SAS Forecast Server


Casino Floor Mix Optimization

Customer: Canadian CasinoSlot Machine Floor Mix Optimization

» Machine categorization» Forecasting Revenue and Utilization» Optimizing Revenue to determine slot machine mix on the

floor (hard and soft constraints)

MILPSAS tools:

» SAS/OR: OPTMODEL, MILP solver» SAS Forecast Studio» SAS Enterprise Miner


Solving Business Problems with SAS Analytics and OPTMODEL

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