MSE 606A Engineering Operations Research Dr. Ahmad R. Sarfaraz Manufacturing Systems Engineering and Management California State University, Northridge

Agenda Overview of Operations Research (OR) Course syllabus and administration

Overview of Operations Research (OR) What is Operations Research? History of OR Terminology Who is leading? Journals Problem Domains of OR Topics Covered Nature of the OR Models Some OR Applications Phases of OR

What is Operations Research? Systematic representation of real world systems by mathematical model(s) to help managers and engineers make better decisions Can be used in a variety of organizations to solve many different types of problems Problem Domains of OR Business, Natural resources, Public administration, Military, Engineering, Telecommunications, Transportation, Nutrition, Public health, Network design

History of OR Initiated in UK during WWII Used mathematical models to make decisions regarding the best utilization of war material The term “Operational Research” [Research into (military) operations” Established in the UK and USA by end of WWII Diffused to industry, business, Gov’t. Now, OR is a dominant decision-making tool

Terminology The British/European refers to “operational Research” The Americans refer to “Operations Research”, or “Management Science”, and sometimes combine the terms together as “OR/MS”

Who is leading? USA leads the world both in the practical application of OR and in advancing the theory The American OR Conference have 2500-2700 participants while the UK OR Conference has 300

Journals Operations Research Management Science European Journal of Operational Research Journal of Operational Research Society Mathematical Programming Networks Naval Research Logistics Interfaces The first seven are theoretical while the last one focuses on applications

OR Models Deterministic Models A given set of inputs or conditions repeatedly produce a fixed and completely predictable output. Stochastic Models More realistic situation wherein a given set of inputs or conditions produce random (or "probabilistic”) stochastic" outcomes.

OR Topics Deterministic Stochastic Linear “programming” Transportation models Assignment models Network models Project Management with CPM/PERT Integer programming Nonlinear programming Goal Programming Dynamic programming Inventory Control Stochastic Game theory Queuing theory Markov chains Decision analysis Simulation Inventory Control Forecasting

Topics Covered Deterministic Linear Programming Model Transportation and Assignment models Network models Project Management with CPM/PERT Integer programming Goal Programming Inventory Control

Nature of the OR Models Maximize area of a rectangular made of a wire of length L Width and height of the rectangular? Alternatives: w and h as continuous variables (infinite) Restriction: 2(w+h)=L W,h>0 Objective Criterion: Maximize Area=w*h

Nature of the OR Models Maximize profit (sales revenue) given production capacity, demand restrictions , and other resources Minimize total cost given minimum requirements

Format of the OR Models Maximize or Minimize Objective Function Subject to: Constraints

OR Application-Monsanto Corp. Nature of Application Optimize production operations in chemical plants to meet production targets Related Topics Integer Programming Annual Savings $2,000,000

OR Application-United Airlines Nature of Application Schedule shift work at reservation offices and airports to meet customer needs with minimum cost Related Topics LP, IP, Queuing Theory, and Forecasting Annual Savings $6,000,000

OR Application San Francisco Police Dept. Nature of Application schedule and deploy police patrol officers with a computerized system Related Topics LP, IP, and Forecasting Annual Savings $11,000,000

OR Application-Texaco, Inc. Nature of Application Optimize the mix of ingredients into gasoline to meet quality and sales requirements Related Topics LP and NLP Annual Savings $30,000,000

OR Application-Citgo Petroleum Corp. Nature of Application Optimize refinery operations and the supply, distribution, and marketing of products Related Topics LP, Network, and Forecasting Annual Savings $70,000,000

OR Application-Delta Airlines Nature of Application Maximize the profit from assigning airplane types to over 2500 domestic flights Related Topics IP Annual Savings $100,000,000

OR Application-Digital Equipment Corp. Nature of Application Restructure of global supply chain of suppliers, plants, distribution centers, potential sites, and market areas Related Topics IP Annual savings $800,000,000

OR Application New Haven Health Department Nature of Application Design an effective needle exchange program to combat the spread of HIV/AIDS Related Topics OR Modeling Annual Savings 33% less HIV/AIDS

Phases of OR Study Definition of the Problem Construction of the Model Solution of the Model Validation of the Model Implementation of the Final Results

Definition of the Problem Decision variables What we want to decide? Objective function How we will decide? Constraints What binds our decision? Parameters What data and facts do we have?

Construction of the Model What is a Model? No general technique due to the type and complexity of the mathematical models Select the most suitable model Common OR models LP, IP, DP, network programming, NLP Simulation and Queuing models Measures performance of the real systems

Validation of the Model A model is valid if it can give a reasonable prediction of the system’s performance Compare system’s performance with some past data for actual system

Implementation of the Final Results Depends upon the support of top management, operating management, and the OR team

Phases of OR Modeling Observation Problem Definition Feedback Model Techniques Model Construction Model Solution Validation and Implementation

Objectives Solid foundation in OR/MS Math used as tool to solve problems Applications oriented Apply OR tools in your job Foundation for further study

Organization First Session Second Secession Introduction and motivation of new material, mathematical development Second Secession Solutions procedures, sample problems, and applications

Next Session LP Modeling Graphical Solution of LP problems Objective functions Decision variables Constraints Graphical Solution of LP problems