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

Solving Business Problemswith SAS Analyticsand OPTMODEL

Technology WorkshopINFORMS Conference on BusinessAnalytics and Operations ResearchSan Antonio, TX

SAS Institute Inc.

April 7, 2013

Outline

1 SAS/OR Introduction

2 Shortest Path Problem

3 Multicommodity Flow Problem

4 Network Algorithms

5 SUBMIT Block

6 Customer Case Study: Insurance Claim Assignment

7 Sample Consulting Engagements


Background on SAS

Founded in 1976World’s largest privatelyheld software companyOver 400 offices worldwideOver 60,000 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

T11 Building and Solving Optimization Models with SASEd Hughes, Aysegul PekerMonday, 10:30am

T8 Win-Win in Inventory ManagementUsing Advanced Analytics TechniquesAysegul PekerMonday, 3:40pm

T13 Effective Use of Business AnalyticsKathy LangeTuesday, 9:10am

T23 High-Performance Data Mining with SAS Enterprise MinerAndré de WaalTuesday, 9:10am

T17 Process Control Approaches in Business ForecastingMichael GillilandTuesday, 11:30am


The Scope of SAS/OR

1. Mathematical optimization

2. Discrete event simulation

3. Constraint programming

4. Genetic algorithms

5. Project and resource scheduling


Broad Range of Optimization Solvers

Linear Programming:» Primal Simplex» Dual Simplex» Interior Point» Network Simplex

Mixed Integer Linear Programming:» Branch and Bound with heuristics, cuts, conflict search

Quadratic Programming:» Interior Point

Nonlinear Programming:» Active Set» Interior Point» Multistart


DECOMP: New in SAS/OR 12.1

Decomposition algorithm accessible 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 solver


Network Algorithms: New in SAS/OR 12.1

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


Other Enhancements in SAS/OR 12.1

Concurrent LP and NLP solversParallel MILP option tunerParallel NLP multistartSAS code block (SUBMIT/ENDSUBMIT) in OPTMODELConflict search for MILP


SAS Optimization-Based Solutions

SAS Marketing OptimizationSAS Service Parts OptimizationSAS Contact Center Planning and OptimizationSAS Revenue Optimization SuiteSAS Size OptimizationSAS Credit Scoring for BankingSAS Risk Management for BankingSAS Risk Management for InsuranceSAS Social Network Analysis


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, QP, NLP solversSupport for customized algorithms


OPTMODEL Programming Statements

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

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





5 SUBMIT Block




Shortest Path Problem

Given directed network (N,A) with source s and sink t

Each arc (i, j) ∈ A has cost cij

Find shortest path from s to t

Minimum cost network flow problem, sending one unit offlow from s to tSeveral approaches:

» LP» MILP» QP» NLP» Multiple objectives» Dynamic programming» Network algorithm


Example Network

2 4

1 6

3 5

1

10

1

2

1

5

12

10

1

2


Optimal Solution

1

2 4

6

2 4

1 6

3 5

1

10

1

2

1

5

12

10

1

2


Shortest Path Data and Setup

OPTMODEL codeShortestPath.sas


Linear Programming

minimize∑

(i,j)∈A

cijxij

subject to∑

(i,j)∈A

xij −∑

(j,i)∈A

xji = bi i ∈ N

xij ≥ 0 (i, j) ∈ A

where bs = 1, bt = −1, and bi = 0 for i ∈ N \ {s, t}


Linear Programming

minimize∑

(i,j)∈A

cijxij

subject to∑

(i,j)∈A

xij −∑

(j,i)∈A

xji =

1 if i = s− 1 if i = t0 if i ∈ N \ {s, t}

i ∈ N

xij ≥ 0 (i, j) ∈ A

var Flow {ARCS} >= 0;min TotalCost = sum {<i,j> in ARCS} cost[i,j] * Flow[i,j];con Balance {i in NODES}:

sum {<(i),j> in ARCS} Flow[i,j]- sum {<j,(i)> in ARCS} Flow[j,i]= (if i = source then 1 else if i = sink then -1 else 0);


Linear Programming

OPTMODEL codeShortestPathLP.sas


Mixed Integer Linear Programming

Given directed network (N,A) with source s and sink t

Each arc (i, j) ∈ A has cost cij and traversal time tijFind shortest s-t path with side constraint on total timeConstraint matrix not totally unimodularNeed to impose integrality on flow variables



minimize∑

(i,j)∈A

cijxij

subject to∑

(i,j)∈A

xij −∑

(j,i)∈A

xji =

1 if i = s−1 if i = t0 if i ∈ N \ {s, t}

i ∈ N

∑(i,j)∈A

tijxij ≤ T

xij ∈ {0, 1} (i, j) ∈ A


Example Network

2 4

1 6

3 5

(1, 10)

(10, 3)

(c = 1, t = 1)

(2, 3)

(1, 2)

(5, 7)

(12, 3)

(10, 1)

(1, 7)

(2, 2)


Optimal Solution for T = 14

1

3

2 4

6

2 4

1 6

3 5

(1, 10)

(10, 3)

(c = 1, t = 1)

(2, 3)

(1, 2)

(5, 7)

(12, 3)

(10, 1)

(1, 7)

(2, 2)



OPTMODEL codeConstrainedShortestPathMILP.sas


Outline





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 ck

ij per unit of flow of commodity k ∈ K» capacity uk

ij for commodity k ∈ K» 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∑k∈K

∑(i,j)∈A

ckijx

kij

subject to∑k∈K

xkij ≤ uij (i, j) ∈ A∑

(i,j)∈A

xkij −

∑(j,i)∈A

xkji = bk

i i ∈ N, k ∈ K

0 ≤ xkij ≤ uk

ij (i, j) ∈ A, k ∈ 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∑k∈K

∑(i,j)∈A

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)

0 ≤ xkij ≤ uk

ij (i, j) ∈ A, k ∈ K (3)

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


DECOMP: New in SAS/OR 12.1

Decomposition algorithm accessible 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 solver


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





5 SUBMIT Block




Network Algorithms: New in SAS/OR 12.1

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 a future release, network algorithms accessible usingSOLVE WITH NETWORK statement in PROC OPTMODEL


Network Algorithm

OPTMODEL codeShortestPathOPTNET.sas


Outline





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;


Milk Collection: Periodic VRPH.P. Williams, Model Building in MathematicalProgramming (1999)SAS/OR R© 12.1 User’s Guide: Mathematical ProgrammingExamples (2012)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 SUBMIT to call PROCOPTNET

OPTMODEL codeMilkCollectionBendersSubmit.sas


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





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» Location

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





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

Stochastic deal optimization Details

Optimal binning for credit risk Details

Student assignment optimization Details

Water management Details

Casino floor mix optimization Details

Census simulation optimization Details


Sample Consulting Engagements:Simulation

Simulation for discovery oncology Details

Mortgage loan simulation 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 a (e.g.) 1-month period» Discrete: minimum investment requirements

MILPSAS tools:

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

Generalized network flow formulation


Census Simulation Optimization Overview

Customer: Large US Government AgencyCensus simulation optimization for budget planning

» Minimize the deviation of the population change overdifferent census categories

» Census targets such as income, unemployment, healthinsurance

» Covers the whole US population

LPSAS tools:

» SAS/OR: OPTMODEL, LP solver


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 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» Discrete cashout constraints» Side constraints (budget, etc)

MILPSAS tools:

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

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

Decomposed for tractability


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


Mortgage Loan Simulation

Customer: Large US BankMortgage Loan SimulationGoal: to study how loans evolve from state to state overtime

» States include current, 30-days delinquent, bankruptcy, etc.» At end of each simulated month, compute the number of

loans in each state: used for capacity-planning purposes

Next phase of the model will attempt to determine optimalstaffing allocations to address the huge portfolio of loansLarge-scale model: Simulation Studio resource entityfeature is key to making the model efficientSAS tools:

» SAS/OR: SAS Simulation Studio


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» Optimization: automatic generation of step

recommendations

RMPO with extensions


Show Ticket Revenue Management

Customer: Large US ResortOccupancy forecastShow ticket price/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


Stochastic Deal Optimization Overview

Customer: Large US Airplane Engine ManufacturerPricing service contracts of engines ($50B portfolio)

» Find minimum yearly price stream to achieve financialmetrics

» Specify price intervals and bounds and maximum numberof price changes

» Replaces current business rule process

MILPSAS tools:

» SAS/OR: OPTMODEL, MILP solver» Embedded in SAS/FM application» Potential for Monte-Carlo simulations from SAS/ETS

Completely custom (replacing homegrown Excelspreadsheets)


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


Optimal Binning for Credit Scoring

Customer: Enterprise Miner (SAS Internal)Rigorous binning with constraints

» Monotonicity constraints» Nonlinear measures of risk» Discrete binning requirements

MINLPSAS tools

» SAS/OR: OPTMODEL, MILP solver, OPTNET» SAS Enterprise Miner

Reformulation or DP heuristic


Student Assignment Optimization

Customer: Wake County Public SchoolsYearly assignment of Elementary, Middle, and High Schoolstudents to schools

» > 100,000 students, 159 schools» Optimize: 3-year assignment planning period» Minimize overcrowding, travel distance, demographic

imbalances, reassignments» Required “what-if” analysis capability

MINLPSAS tools:

» SAS/OR: OPTMODEL, MILP solver» SAS Grid Manager» JMP

Completely custom solution


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:

» PROC MIRP» SAS Forecast Studio: demand forecasting

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 Enteprise Miner


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