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• Statistics & Operations Research
  • SAS/ETS
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SAS/OR^® Examples

Operations Research Categories

• Mathematical Programming
• Mathematical Programming Examples
• Mathematical Programming: Legacy Procedures
• Network Optimization Algorithms
• Project Management
• Bills of Material Processing
• Local Search Optimization
• Constraint Programming
• SAS Simulation Studio

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Mathematical Programming

The OPTMODEL Procedure

• An Unconstrained Optimization Example
• The Rosenbrock Problem
• A Transportation Problem

• Example 5.1: Matrix Square Root
• Example 5.2: Reading From and Creating a Data Set
• Example 5.3: Model Construction
• Example 5.4: Set Manipulation
• Example 5.5: Multiple Subproblems
• Example 5.6: Traveling Salesman Problem
• Example 5.7: Sparse Modeling
• Example 5.8: Chemical Equilibrium

The Linear Programming (LP) Solver

• Getting Started: LP Solver

• Example 7.1: Diet Problem
• Example 7.2: Reoptimizing the Diet Problem Using BASIS=WARMSTART
• Example 7.3: Two-Person Zero-Sum Game
• Example 7.4: Finding an Irreducible Infeasible Set
• Example 7.5: Using the Network Simplex Algorithm
• Example 7.6: Migration to OPTMODEL: Generalized Networks
• Example 7.7: Migration to OPTMODEL: Maximum Flow
• Example 7.8: Migration to OPTMODEL: Production, Inventory, Distribution
• Example 7.9: Migration to OPTMODEL: Shortest Path

The Mixed Integer Linear Programming (MILP) Solver

• Getting Started: MILP Solver

• Example 9.1: Scheduling
• Example 9.2: Multicommodity Transshipment Problem with Fixed Charges
• Example 9.3: Facility Location
• Example 9.4: Traveling Salesman Problem

The Nonlinear Programming (NLP) Solver

• A Simple Problem
• A Least Squares Problem
• A Larger Optimization Problem
• An Optimization Problem with Many Local Minima
• A Least Squares Estimation Problem for a Regression Model

• Example 11.1: Solving Highly Nonlinear Optimization Problems
• Example 11.2: Solving Unconstrained and Bound-Constrained Optimization Problems
• Example 11.3: Solving Equality-Constrained Problems
• Example 11.4: Solving NLP Problems with Range Constraints
• Example 11.5: Solving Large-Scale NLP Problems
• Example 11.6: Solving NLP Problems That Have Several Local Minima
• Example 11.7: Maximum Likelihood Weibull Estimation
• Example 11.8: Finding an Irreducible Infeasible Set

The Quadratic Programming Solver

• Getting Started: QP Solver

• Example 12.1: Linear Least Squares Problem
• Example 12.2: Portfolio Optimization
• Example 12.3: Portfolio Selection with Transactions

The OPTLP Procedure

• Getting Started: OPTLP Procedure

• Example 13.1: Oil Refinery Problem
• Example 13.2: Using the Interior Point Algorithm
• Example 13.3: The Diet Problem
• Example 13.4: Reoptimizing after Modifying the Objective Function
• Example 13.5: Reoptimizing after Modifying the Right-Hand Side
• Example 13.6: Reoptimizing after Adding a New Constraint
• Example 13.7: Finding an Irreducible Infeasible Set
• Example 13.8: Using the Network Simplex Algorithm

The OPTMILP Procedure

• Getting Started: OPTMILP Procedure

• Example 14.1: Simple Integer Linear Program
• Example 14.2: MIPLIB Benchmark Instance
• Example 14.3: Facility Location
• Example 14.4: Scheduling

The OPTQP Procedure

• Getting Started: OPTQP Procedure

• Example 15.1: Linear Least Squares Problem
• Example 15.2: Portfolio Optimization
• Example 15.3: Portfolio Selection with Transactions

The Decomposition Algorithm

• Solving a MILP with DECOMP and PROC OPTMODEL
• Solving a MILP with DECOMP and PROC OPTMILP

• Example 16.1: Multicommodity Flow Problem and METHOD=NETWORK
• Example 16.2: Generalized Assignment Problem
• Example 16.3: Block-Diagonal Structure and METHOD=CONCOMP
• Example 16.4: Block-Angular Structure
• Example 16.5: Bin Packing Problem
• Example 16.6: Resource Allocation Problem
• Example 16.7: Vehicle Routing Problem
• Example 16.8: ATM Cash Management
• Example 16.9: Kidney Donor Exchange and METHOD=SET

The OPTMILP Option Tuner

• Getting Started: The OPTMILP Option Tuner

• Example 17.1: Tuning the Default Set of Options for a Single Problem
• Example 17.2: Tuning a Defined Set of Options for Multiple Problems

The MPS-Format SAS Data Set

• Example 18.1: MPS-Format Data Set for a Product Mix Problem
• Example 18.2: Fixed-MPS-Format File
• Example 18.3: Free-MPS-Format File
• Example 18.4: Using the %MPS2SASD Macro

Mathematical Programming Examples

• Food Manufacture 1: When to Buy and How to Blend
• Food Manufacture 2: Limiting the Number of Ingredients and Adding Extra Conditions
• Factory Planning 1: What to Make, On What Machines, and When
• Factory Planning 2: When Should Machines Be Down for Maintenance
• Manpower Planning: How to Recruit, Retrain, Make Redundant, or Overman
• Refinery Optimization: How to Run an Oil Refinery
• Mining: Which Pits to Work and When to Close Them Down
• Farm Planning: How Much to Grow and Rear
• Economic Planning: How Should an Economy Grow
• Decentralization: How to Disperse Offices from the Capital
• Curve Fitting: Fitting a Curve to a Set of Data Points
• Logical Design: Constructing an Electronic System with a Minimum Number of Components
• Market Sharing: Assigning Retailers to Company Divisions
• Opencast Mining: How Much to Excavate
• Tariff Rates (Power Generation): How to Determine Tariff Rates for the Sale of Electricity
• Hydro Power: How to Generate and Combine Hydro and Thermal Electricity Generation
• Three-Dimensional Noughts and Crosses: A Combinatorial Problem
• Optimizing a Constraint: Reconstructing an Integer Programming Constraint More Simply
• Distribution 1: Which Factories and Depots to Supply Which Customers
• Depot Location (Distribution 2): Where Should New Depots Be Built
• Agricultural Pricing: What Prices to Charge for Dairy Products
• Efficiency Analysis: How to Use Data Envelopment Analysis to Compare Efficiencies of Garages
• Milk Collection: How to Route and Assign Milk Collection Lorries to Farms
• Yield Management: What Quantities of Airline Tickets to Sell at What Prices and What Times
• Car Rental 1
• Car Rental 2
• Lost Baggage Distribution
• Protein Folding
• Protein Comparison

Mathematical Programming: Legacy Procedures

The INTPOINT Procedure

• NPSC Problems
• LP Problems
• Typical PROC INTPOINT Run

• Example 3.1: Production, Inventory, Distribution Problem
• Example 3.2: Altering Arc Data
• Example 3.3: Adding Side Constraints
• Example 3.4: Using Constraints and More Alteration to Arc Data
• Example 3.5: Nonarc Variables in the Side Constraints
• Example 3.6: Solving an LP Problem with Data in MPS Format
• Example 3.7: Converting to an MPS-Format SAS Data Set
• Example 3.8: Migration to OPTMODEL: Production, Inventory, Distribution

The LP Procedure

• An Introductory Example
• An Integer Programming Example
• An MPS Format to Sparse Format Conversion Example

• Example 4.1: An Oil Blending Problem
• Example 4.2: A Sparse View of the Oil Blending Problem
• Example 4.3: Sensitivity Analysis: Changes in Objective Coefficients
• Example 4.4: Additional Sensitivity Analysis
• Example 4.5: Price Parametric Programming for the Oil Blending Problem
• Example 4.6: Special Ordered Sets and the Oil Blending Problem
• Example 4.7: Goal-Programming a Product Mix Problem
• Example 4.8: A Simple Integer Program
• Example 4.9: An Infeasible Problem
• Example 4.10: Restarting an Integer Program
• Example 4.11: Alternative Search of the Branch-and-Bound Tree
• Example 4.12: An Assignment Problem
• Example 4.13: A Scheduling Problem
• Example 4.14: A Multicommodity Transshipment Problem with Fixed Charges
• Example 4.15: Converting to an MPS-Format SAS Data Set
• Example 4.16: Migration to OPTMODEL: Assignment
• Example 4.17: Migration to OPTMODEL: Multicommodity Transshipment

The NETFLOW Procedure

• Introductory Example

• Example 5.1: Shortest Path Problem
• Example 5.2: Minimum Cost Flow Problem
• Example 5.3: Using a Warm Start
• Example 5.4: Production, Inventory, Distribution Problem
• Example 5.5: Using an Unconstrained Solution Warm Start
• Example 5.6: Adding Side Constraints, Using a Warm Start
• Example 5.7: Using a Constrained Solution Warm Start
• Example 5.8: Nonarc Variables in the Side Constraints
• Example 5.9: Pure Networks: Using the EXCESS= Option
• Example 5.10: Maximum Flow Problem
• Example 5.11: Generalized Networks: Using the EXCESS= Option
• Example 5.12: Generalized Networks: Maximum Flow Problem
• Example 5.13: Machine Loading Problem
• Example 5.14: Generalized Networks: Distribution Problem
• Example 5.15: Converting to an MPS-Format SAS Data Set
• Example 5.16: Migration to OPTMODEL: Generalized Networks
• Example 5.17: Migration to OPTMODEL: Maximum Flow
• Example 5.18: Migration to OPTMODEL: Production, Inventory, Distribution
• Example 5.19: Migration to OPTMODEL: Shortest Path

The NLP Procedure

• Introductory Examples

• Example 6.1: Using the DATA= Option
• Example 6.2: Using the INQUAD= Option
• Example 6.3: Using the INEST=Option
• Example 6.4: Restarting an Optimization
• Example 6.5: Approximate Standard Errors
• Example 6.6: Maximum Likelihood Weibull Estimation
• Example 6.7: Simple Pooling Problem
• Example 6.8: Chemical Equilibrium
• Example 6.9: Minimize Total Delay in a Network

Network Optimization Algorithms

The OPTNET Procedure

• Road Network Shortest Path

• Example 2.1: Articulation Points in a Terrorist Network
• Example 2.2: Cycle Detection for Kidney Donor Exchange
• Example 2.3: Linear Assignment Problem for Minimizing Swim Times
• Example 2.4: Linear Assignment Problem, Sparse Format versus Dense Format
• Example 2.5: Minimum Spanning Tree for Computer Network Topology
• Example 2.6: Transitive Closure for Identification of Circular Dependencies in a Bug Tracking System
• Example 2.7: Traveling Salesman Tour through US Capital Cities

Project Management

The CPM Procedure

• Getting Started: CPM Procedure

• Example 4.1: Activity-on-Node Representation
• Example 4.2: Activity-on-Arc Representation
• Example 4.3: Meeting Project Deadlines
• Example 4.4: Displaying the Schedule on a Calendar
• Example 4.5: Precedence Gantt Chart
• Example 4.6: Changing Duration Units
• Example 4.7: Controlling the Project Calendar
• Example 4.8: Scheduling around Holidays
• Example 4.9: CALEDATA and WORKDATA Data Sets
• Example 4.10: Multiple Calendars
• Example 4.11: Nonstandard Relationships
• Example 4.12: Activity Time Constraints
• Example 4.13: Progress Update and Target Schedules
• Example 4.14: Summarizing Resource Utilization
• Example 4.15: Resource Allocation
• Example 4.16: Using Supplementary Resources
• Example 4.17: INFEASDIAGNOSTIC Option and Aggregate Resource Type
• Example 4.18: Variable Activity Delay
• Example 4.19: Activity Splitting
• Example 4.20: Alternate Resources
• Example 4.21: PERT Assumptions and Calculations
• Example 4.22: Scheduling Course - Teacher Combinations
• Example 4.23: Multiproject Scheduling
• Example 4.24: Resource-Driven Durations and Resource Calendars
• Example 4.25: Resource-Driven Durations and Alternate Resources
• Example 4.26: Multiple Alternate Resources
• Example 4.27: Auxiliary Resources and Alternate Resources
• Example 4.28: Use of the SETFINISHMILESTONE Option
• Example 4.29: Negative Resource Requirements
• Example 4.30: Auxiliary Resources and Negative Requirements
• Example 4.31: Resource-Driven Durations and Negative Requirements
• Example : Statement and Option Cross-Reference Tables

The PM Procedure

• Getting Started: PM Procedure

• Example 5.1: Defining a New Project
• Example 5.2: Adding Subtasks to a Project
• Example 5.3: Saving and Comparing Baseline Schedules
• Example 5.4: Effect of Calendars
• Example 5.5: Defining Resources
• Example 5.6: Editing Progress

The Microsoft Project Conversion Macros

• Example 6.1: Simple %MSPTOSAS Conversion
• Example 6.2: Importing Activity Attributes
• Example 6.3: Importing Multiple Projects
• Example 6.4: Importing XML Files
• Example 6.5: Simple %SASTOMSP Conversion
• Example 6.6: Exporting Data Set and Variable Names
• Example 6.7: Exporting Calendars and Holidays
• Example 6.8: Exporting Resource-Constrained Schedules
• Example 6.9: Round Trip between a SAS Program and Microsoft Project

The DTREE Procedure

• Introductory Example
• Attitudes toward Risk
• Sensitivity Analysis and Value of Perfect Information
• Value of Perfect Control
• Oil Wildcatter’s Problem with Sounding Test

• Example 7.1: Oil Wildcatter’s Problem with Insurance
• Example 7.2: Oil Wildcatter’s Problem in Risk-Averse Setting
• Example 7.3: Contract Bidding Problem
• Example 7.4: Research and Development Decision Problem
• Example 7.5: Loan Grant Decision Problem
• Example 7.6: Petroleum Distributor’s Decision Problem
• Example : Statement and Option Cross-Reference Tables

The GANTT Procedure

• Getting Started: GANTT Procedure

• Example : Line-Printer Examples
• Example 8.1: Printing a Gantt Chart
• Example 8.2: Customizing the Gantt Chart
• Example : Graphics Examples
• Example 8.3: Marking Holidays
• Example 8.4: Marking Milestones and Special Dates
• Example 8.5: Using the COMPRESS Option
• Example 8.6: Using the MININTERVAL= and SCALE= Options
• Example 8.7: Using the MINDATE= and MAXDATE= Options
• Example 8.8: Variable-Length Holidays
• Example 8.9: Multiple Calendars
• Example 8.10: Plotting the Actual Schedule
• Example 8.11: Comparing Progress Against a Baseline Schedule
• Example 8.12: Using the COMBINE Option
• Example 8.13: Plotting the Resource-Constrained Schedule
• Example 8.14: Specifying the Schedule Data Directly
• Example 8.15: BY Processing
• Example 8.16: Gantt Charts by Persons
• Example 8.17: Using the HEIGHT= and HTOFF= Options
• Example 8.18: Drawing a Logic Gantt Chart Using AON Representation
• Example 8.19: Specifying the Logic Control Options
• Example 8.20: Nonstandard Precedence Relationships
• Example 8.21: Using the SAS/GRAPH ANNOTATE= Option
• Example 8.22: Using the Automatic Text Annotation Feature
• Example 8.23: Multiproject Gantt Charts
• Example 8.24: Multisegment Gantt Charts
• Example 8.25: Zoned Gantt Charts
• Example 8.26: Web-Enabled Gantt Charts
• Example 8.27: Using the CHARTWIDTH= Option
• Example 8.28: Using the TIMEAXISFORMAT= Option
• Example : Statement and Option Cross-Reference Tables

The NETDRAW Procedure

• Getting Started: NETDRAW Procedure

• Example 9.1: Line-Printer Network Diagram
• Example 9.2: Graphics Version of PROC NETDRAW
• Example 9.3: Spanning Multiple Pages
• Example 9.4: The COMPRESS and PCOMPRESS Options
• Example 9.5: Controlling the Display Format
• Example 9.6: Nonstandard Precedence Relationships
• Example 9.7: Controlling the Arc-Routing Algorithm
• Example 9.8: PATTERN and SHOWSTATUS Options
• Example 9.9: Time-Scaled Network Diagram
• Example 9.10: Further Time-Scale Options
• Example 9.11: Zoned Network Diagram
• Example 9.12: Schematic Diagrams
• Example 9.13: Modifying Network Layout
• Example 9.14: Specifying Node Positions
• Example 9.15: Organizational Charts with PROC NETDRAW
• Example 9.16: Annotate Facility with PROC NETDRAW
• Example 9.17: AOA Network Using the Annotate Facility
• Example 9.18: Branch and Bound Trees
• Example : Statement and Option Cross-Reference Tables

The Earned Value Management Macros

• Analysis
• Charts

• Example 10.1: Integrated Assembly Project
• Example 10.2: Construction Project

Bills of Material Processing

The BOM Procedure

• Getting Started: BOM Procedure

• Example 3.1: Bill of Material with Single Input Data Set
• Example 3.2: Bill of Material with Lead Time Information
• Example 3.3: Bill of Material with Scrap Factor Information
• Example 3.4: Planning Bill of Material
• Example 3.5: Modular Bill of Material
• Example 3.6: Bill of Material with Repeated Relationships
• Example 3.7: Bill of Material Verification
• Example 3.8: Roll-Up Cost in Indented Bill of Material
• Example 3.9: Bill of Material Explosion
• Example 3.10: Aggregating Forecasts Using PROC BOM
• Example : Statement and Option Cross-Reference Tables

Local Search Optimization

The GA Procedure

• Initializing the Problem Data
• Choosing the Problem Encoding
• Setting the Objective Function
• Controlling the Selection Process
• Setting Crossover Parameters
• Setting Mutation Parameters
• Creating the Initial Generation
• Monitoring Progress and Reporting Results
• A Simple Example

• Example 4.1: Traveling Salesman Problem with Local Optimization
• Example 4.2: Nonlinear Objective with Constraints Using Repair Mechanism
• Example 4.3: Quadratic Objective with Linear Constraints, Using Bicriteria Approach

The OPTLSO Procedure

• Introductory Examples

• Example 3.1: Using Dense Format
• Example 3.2: Using MPS Format
• Example 3.3: Using QPS Format
• Example 3.4: Combining MPS and FCMP Function Definitions
• Example 3.5: Linear Constraints and a Nonlinear Objective
• Example 3.6: Using Nonlinear Constraints
• Example 3.7: Using External Data Sets
• Example 3.8: Johnson’s Systems of Distributions
• Example 3.9: Discontinuous Function with a Lookup Table
• Example 3.10: Multiobjective Optimization

Constraint Programming

The CLP Procedure

• Send More Money
• Eight Queens

• Example 3.1: Logic-Based Puzzles
• Example 3.2: Alphabet Blocks Problem
• Example 3.3: Work-Shift Scheduling Problem
• Example 3.4: A Nonlinear Optimization Problem
• Example 3.5: Car Painting Problem
• Example 3.6: Scene Allocation Problem
• Example 3.7: Car Sequencing Problem
• Example 3.8: Round-Robin Problem
• Example 3.9: Resource-Constrained Scheduling with Nonstandard Temporal Constraints
• Example 3.10: Scheduling with Alternate Resources
• Example 3.11: 10×10 Job Shop Scheduling Problem
• Example 3.12: Scheduling a Major Basketball Conference
• Example 3.13: Balanced Incomplete Block Design
• Example 3.14: Progressive Party Problem
• Example 3.15: Resource-Constrained Project Scheduling Problem with Time Windows
• Example 3.16: Resource-Constrained Scheduling Problem with Nonstandard Temporal Constraints
• Example : Statement and Option Cross-Reference Table

SAS^® Simulation Studio

• A Simple M/M/1 Queueing Model
• Using the Stats Collector Block for Output Analysis
• Routing to Shortest Queue
• Reneging from a Queue
• Repair Shop Model
• PERT Network Model
• Modeling the Banking System by Using Mobile Resources
• The Banking System Model with Resource Scheduling
• Priority-Based Preemption of Service
• A Model of an Incoming Call Center
• Modeling Assembly Operation and Parts Inventory System
• Using the SAS Program Block to Analyze Simulation Results
• Machining Center Model
• Using the Observation Source Block to Set Entity Attributes
• Using the Dataset Writer Block to Save Data during a Run
• Using the Steady State Block for Output Analysis
• Updating an Input Distribution
• Extended Queueing Options