456/556 Introduction to Operations Research

1. 456/556 Introduction to Operations Research Chapter 1: Introduction Chapter 2: Overview of the Operations Research Modeling Approach

2. Origins of Operations Research • Operations Research (OR) or Management Science can be defined as the use of quantitative methods to assist analysts and decision makers in designing, analyzing, and improving the performance or operations of systems. • OR is a branch of mathematics that grew out of the need during WWII to allocate scarce resources to various military operations in an effective manner.

3. Origins of Operations Research (cont.) • Examples include: • The development and use of radar for detecting and tracking aircraft. • Allocation of scarce resources (raw materials, parts, time, people) to problems such as: • Producing high octane fuel, • Developing systems for detection of submarines and aircraft, • Strategic and tactical planning in order to achieve military and industrial goals.

4. Origins of Operations Research (cont.) • After WWII, an industrial boom led to increasing complexity and specialization in organizations. • Typical problems that needed to be solved: • How to get various components of a company working at cross purposes to work together. • How to allocate limited resources in the most effective way.

5. Origins of Operations Research (cont.) • People who had worked on OR problems for the military realized that these new problems were basically the same as those faced by the military in a different context. • Two factors that have played a key role in the growth of OR are: • The development of powerful techniques for solving OR problems such as the simplex method developed by George Dantzig in 1947. • The digital computer - large scale OR problems are solvable and anyone with a personal computer can solve OR problems with software such as Excel.

6. The Nature of Operations Research • Operations research is applied to problems that deal with how to conduct and coordinate the operations (or activities) within an organization. • Some of the areas where OR has been applied: • Manufacturing • Transportation • Construction • Telecommunications • Financial Planning • Health care • Military • Public services • See Table 1.1 in our textbook for some actual problems solved by OR techniques! • Some specific examples follow!

7. Reengineering IBM’s Global Supply Chain • In 1994, IBM began to reengineer its global supply chain. • It wanted to achieve quick responsiveness to customers with minimal inventory. • To support this effort, an extended-enterprise supply-chain analysis tool, the Asset Management Tool (AMT) was developed. • AMT integrates graphical process modeling, analytical performance optimization, simulation, activity-based costing, and enterprise database connectivity into a system that allows quantitative analysis of extended supply chains. • IBM has used AMT to study such issues as inventory budgets, turnover objectives, customer-service targets, and new-product introductions. • It has been implemented at a number of IBM business units and their channel partners. • AMT benefits include over $750 million in material costs and price-protection expenses saved in 1998. • INTERFACES 30: 1 January–February 2000 (pp. 7–25)

8. Nuclear Weapons Dismantlement, Evaluation, and Maintenance • The end of the Cold War changed the missions of facilities in the US nuclear weapons complex. • They ceased production of new weapons and focused on dismantling old weapons and maintaining the safety, security, and reliability of those remaining. • The Pantex Plant, operated for the US Department of Energy (DOE) by the Mason and Hanger Corporation, is the sole assembly and disassembly facility for dismantlement, evaluation, and maintenance activities for the US nuclear stockpile. • A decision support tool, the Pantex Process Model (PPM), was developed to help Pantex plan capacity and deploy resources to meet its new requirements. • Using the PPM, Pantex has provided critical input to help the US form and defend positions during arms-control-treaty negotiations. • It has changed the way Pantex and the DOE evaluate resource requirements in planning future workloads. • It has also led to an innovative cooperative agreement among Pantex, the Transportation Safeguards Division of DOE, and the Department of Defense (DOD) that resulted in Pantex exceeding weapon dismantlement goals. • INTERFACES 30: 1 January–February 2000 (pp. 57–82)

9. Optimized Crew Scheduling at Air New Zealand • The aircrew-scheduling problem consists of two important subproblems: • The tours-of-duty planning problem to generate minimum-cost tours of duty (sequences of duty periods and rest periods) to cover all scheduled flights • The rostering problem to assign tours of duty to individual crew members. • Between 1986 and 1999, Air New Zealand staff and consultants in collaboration with the University of Auckland have developed eight application-specific optimization-based computer systems to solve all aspects of the tours-of-duty planning and rostering processes for Air New Zealand’s national and international operations. • These systems have saved NZ$15,655,000 per year while providing crew rosters that better respect crew members’ preferences. • INTERFACES 31: 1 January–February 2001 (pp. 30–56)

10. Characterization of Operations Research • The scientific method is used to investigate problems to be solved. • OR is concerned with practical management of an organization. • OR must provide positive, understandable conclusions to decision makers when they are needed! • OR takes a broad viewpoint • OR attempts to resolve conflicts of interest among components of an organization in a way that is best for the organization as a whole.

11. Characterization of Operations Research (cont.) • The goal of OR is to find a best (optimal) solution. • Usually, the problems in OR need to be solved with a team of people with a collective expertise in: • Mathematics • Statistics and probability theory • Economics • Business administration • Computer science • Physical sciences • Behavioral sciences • Special techniques of OR

12. Overview of the OR Modeling Approach • An OR study usually consists of the following (overlapping) phases: • 1. Define the problem of interest and gather relevant data. • 2. Formulate a mathematical model to represent the problem. • 3. Develop a computer-based procedure for deriving solutions to the problem from the model. • 4. Test the model and refine it as needed. • 5. Prepare for the ongoing application of the model as prescribed by management. • 6. Implement.

13. Modeling Process in General Real World Problem Mathematical Model Compare Model Solution to Real World Solve Mathematical Model Refine Model

14. Homework • Read Chapters 1 and 2 in our textbook. • Read INTERFACES journal articles on three specific applications of OR discussed above. • Read the article “History in the Making:  INFORMS celebrates 50 years of problems, solutions, anecdotes and achievement”  (http://www.lionhrtpub.com/orms/orms-10-02/frhistory.html) • Problem # 1.3-2 (apply to three applications of OR discussed above).

15. References • Operations Research: A Practical Introduction by Michael W. Carter and Camille C. Price, CRC Press, 2001. • Introduction to Operations Research (8th ed) by Frederick S. Hiller and Gerald J. Lieberman, McGraw Hill, 2005. • Interfaces Journal, Jan. - Feb. Issues, Volumes 30 and 31 (http://interfaces.pubs.informs.org/)