Math 328 Applied Operational Research

1. Math 328Applied Operational Research Dr. Yousef Al-Saeed 2012-2011 – first semester Qassim University - College of Engineering

2. Course Contents • Introduction to operation research methodology and applications. • Building of mathematical models • Linear programming models • The simplex algorithm • Duality and sensitivity analysis • Transportation and assignment models • Network models • Integer programming • Using optimization software Qassim University - College of Engineering

3. Evaluation Method • Midterm exams • Assignments • Quizzes • Term project • Final exam Qassim University - College of Engineering

4. Text Book and References • Textbook: Hamdy A. Taha (2007); Operational Research An Introduction 8th edition. • Refe: (1) Winston, Wayne I,..(2004); Operations Research, 4th edition, Duxbury. (2) Hillier, F.S. and Lieberman, G.J. (2001), Introduction to Operations Research, 7thedition. (3) Jensen and Bard (2003), Operations Research: Models and Methods. Wiley. Qassim University - College of Engineering

5. Phases Of An OR Study Nonlinear programming Integer programming Qassim University - College of Engineering

6. Examples Ex. # 1: Imagine that you have a 5-week business commitment between City A and City B. You fly out of A on Saturdays and return on Mondays. A regular round-trip ticket costs SR400, but the price is SR 320 if the dates of the ticket span a weekend. A one-way ticket in either direction costs SR 300. How should you buy the tickets for the 5- week period? Qassim University - College of Engineering

7. مثال 2: يتوفر لدى صانع الأثاث 6 قطع خشبية كبيرة و28 ساعة من الوقت الحر يستطيع أن ينجز خلاله بعض النماذج التزيينية الزخرفية. وهو يقدر أن النموذج 1 يتطلب قطعتي خشب و7 ساعات عمل بينما النموذج 2 يتطلب قطعة خشب واحدة و8 ساعات عمل وسعر النموذجين 120 ليرة للنموذج 1 و80 ليرة للنموذج 2. كم وحدة من كلا النموذجين يستطيع صانع الأثاث أن ينتج ليحصل على أكبر عائدات ممكنة؟ Qassim University - College of Engineering

8. Ex. # 3: what would be the width and the height of the maximum-area rectangle formed out of a piece of wire of length L inches? Ex. # 4:SAPTCO wants to improve its service operations by determining the number buses that can handle the transportation demands. Qassim University - College of Engineering

9. Real-Life Application-Frontier Airlines Purchases Fuel Economiclly: Ex. #5: The fueling of an aircraft can take place at any of the stopovers along the flight route. Fuel price varies among the stopovers, and potential savings can be realized by loading extra fuel (called tankering) at a cheaper location for use on subsequent flight legs. The disadvantage of tankering is the excess burn of gasoline resulting from the extra weight. LP (and heuristics) is used to determine the optimum amount of tankering that balances the cost of excess burn against the savings in fuel cost. The study, carried out in 1981, resulted in net savings of about $350,000 per year. Qassim University - College of Engineering

10. The Transportation Problem Ex. #6: An essential component of our modern life is the shipping of goods from where they are produced to markets worldwide. Nationally, within the USA alone transportation of goods is estimated to cost over $trillion/year. The aim of this problem is to find a way of carrying out this transfer of goods at minimum cost. Qassim University - College of Engineering

11. The Assignment Problem Ex. # 7: Consider a company that has divided their marketing area into n zones based on the characteristics of the shoppers, their economic status, etc. They want to appoint a director for each zone to run the marketing effort there. They have already selected n candidates to fill the positions. The total annual sales in a zone would depend on which candidate is appointed as director there. Based on the candidates skills, demeanor, and background, it is estimated that $cij million in annual sales will be generated in zone j if candidate i is appointed as director there, and this (cij) data is given. The problem is to decide which zone each candidate should be assigned to, to maximize the total annual sales in all the zones (each zone gets one candidate and each candidate goes to one zone). Qassim University - College of Engineering

12. Blending Problems Ex. # 8: Blending is concerned with mixing different materials called the constituents of the mixture (these may be chemicals, gasolines, fuels, solids, colors, foods, etc.) so that the mixture conforms to specifications on several properties or characteristics. Qassim University - College of Engineering

13. Product Mix Problems Ex. #9: Product mix problems are an extremely important class of problems that manufacturing companies face. Normally the company can make a variety of products using the raw materials, machinery, labor force, and other resources available to them. The problem is to decide how much of each product to manufacture in a period, to maximize the total profit subject to the availability of needed resources. Qassim University - College of Engineering