CAREERS IN OPERATIONS RESEARCH Shafiu Jibrin
How many cars to make to maximize profit? A car manufacturer wants to produce two types of cars, model A and model B. The manufacturer has available 720 hours of assembly time and 480 hours of finishing time, and, due to differing projected demands, his managers have decided that he should make at least 20 units of model A and at least 30 units of model B. Production time and profit for each model is given in the following table. How many of each model should the manufacturer produce to maximize profit?
A mathematical model of the car manufacturing problem Let x1= Number of type A model to make x2= Number of type B model to make The model is: Maximize P = 4000x1+3000x2 (profit) Subject to: 4x1+6x2 ≤ 720 (assembly time) 6x1+3x2 ≤ 480 (finishing time) x1 ≥20 (model A demand) x2 ≥30 (model B demand) x1≥0, x2 ≥ 0
Outline • What is operations research (OR)? • History of OR • Example of OR in transportation • Solving OR problems • Job opportunities in OR • Conditions of service in OR • How to become an OR specialist?
What is operations research (OR)? • Operations research is the art of decision-making where an objective function ismaximized or minimized subject to constraints on the decision variables. • Example: How many cars to produce to maximize profitsubject toconstraints on assembly and finishing hours available?
History of operations research • Invented during World War II - planning and scheduling problems for the Air Force • George Dantzig - Chief of the Combat Analysis Branch during World War II - ‘Uncle of Operations Research’ - Invented a branch of operations research called linear programming in 1947 at the pentagon • Applications to industries after World War II
Example of operations research problem in transportation • Oilco has oil fields in San Diego and Los Angeles. The San Diego field can produce up to 500,000 barrels per day, and the Los Angeles field can produce up to 400,000 barrels per day. Oil is sent from the fields to a refinery, either in Dallas or in Houston. It costs $700 to refine 100,000 barrels of oil at Dallas and $900 at Houston. Refined fuel is shipped to customers in Chicago and New York. Chicago customers require 400,000 barrels per day of refined fuel; New York customers require 300,000. The costs of shipping 100,000 barrels of oil between cities are given in the table. Find the shipments that will meet the total demands at minimum total costs. TO FROM Dallas Houston N.Y. Chicago L.A. $300 $110 - - San Diego $420 $100 Dallas - - $450 $550 Houston - - $470 $530
Solving OR problems • Modeling – convert problem into mathematical form • Simplex method (for linear programming problems) • Statistical and mathematical solution techniques • Search for new solution techniques • Computer software e.g. LINDO, MPL, EXCEL
Job opportunities • 61, 700 jobs in 2002 • Where are the jobs? - telecommunications companies - transportation e.g. airlines - financial institutions - insurance carriers - engineering and management service firms - Federal Government e.g. in the Armed Forces - academia
Conditions of service in OR • Projects (usually teamwork) • 2002 annual earnings - average is $56,920 - less than $34,140 (lowest 10%) - more than $92,430 (top 10%) - between $43,220 and $74,140 (middle 50%) • Average earning in Federal Government is $83,740 (in 2003)
What is the job outlook in the future? • Good to at least 2012 • Continuing use of OR to improve productivity in industries and government • Jobs expected to exceed OR graduates
How to become an OR specialist? • Degrees required - Bachelor or masters in OR or management science - Dual degree in OR and computer science is very attractive! • NAU offers OR courses