...PRINCIPLES AND APPLICATIONS OF OPERATIONS RESEARCH * Jayant Rajgopal Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania ABSTRACT This chapter will provide an overview of Operations Research (O.R.) from the perspective of an industrial engineer. The focus of the chapter is on the basic philosophy behind O.R. and the so-called “O.R. approach” to solving design and operational problems that industrial engineers commonly encounter. In its most basic form, O.R. may be viewed as a scientific approach to solving problems; it abstracts the essential elements of the problem into a model, which is then analyzed to yield an optimal solution for implementation. The mathematical details and the specific techniques used to build and analyze these models can be quite sophisticated and are addressed elsewhere in this handbook; the emphasis of this chapter is on the approach. A brief review of the historical origins of O.R. is followed by a detailed description of its methodology. The chapter concludes with some examples of successful real-world applications of O.R. * Maynard's Industrial Engineering Handbook, 5th Edition, pp. 11.27-11.44. 1.1 INTRODUCTION Although it is a distinct discipline in its own right, Operations Research (O.R.) has also become an integral part of the Industrial Engineering (I.E.) profession. This is hardly a matter of surprise when one considers that they both share many of the same objectives, techniques and application areas...
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...Year | 2015-16 | Academic Term | T1☐ T2☐ T3☐ T4☐ T5☐T6☐ | Functional Areas | OPERATIONS MANAGEMENT | Core ☐ Elective x☐x | Title | Quantitative Methods II | Abbreviation | QM-II | Course Coordinator | Prof. RAVI SHANKAR | Teaching Members | | Course Revision Record Version | Version Date | Recommendation | 1 | 05 Sept 2015 | | Credits | 3 | Contact Hours | 30 | Learning Hours | 60 | Office Hours | 30 | Contact Details | 09811033937 | Course eMail | r.s.reaches@gmail.com | Course Descriptor Course Overview(200 words) | Quantitative Methods-II, focuses on ‘Operations Research’ tools which helps in solving problems in different functional domain of business. It also helps to optimize business operations/processes. The Quantitative Method-II tools act as aids to decision makers to take best decision for effective & efficient use of resources which ultimately lead to profit maximization or to achieve multiple goals or objective. | Course must be aligned with a strategic objective of the program Prerequisites/Co-requisites | Quantitative Methods I | Learning Objectives | To learn basic optimization techniques and their managerial applications with a focus on methodologies such as Linear Programming, Transportation models, Assignment Models, Transhipment Models, Games Theory, Queuing Models, Goal Programming, Integer Programming, Non-linear Programming, Simulation and Decision Theory. | Learning objectives must be aligned with learning...
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...weekly meeting will be scheduled at which time students may ask questions, discuss homework exercises, etc. Attendance at this meeting is optional. Grading System • There will be 2 examinations, one at the middle of the course, and one at the end. • Homework will be assigned each week, but this will not be given to the instructor to be graded. Students are encouraged to work together on homework assignments. • There will be a short (multiple choice) quiz each week which tests whether you have understood the homework assignment. Only the best 10 quizzes for each student will be used in computing the course grade. Midcourse Examination Final Examination Weekly Quizzes (best ten) 30% 50% 20% page 3 What is “Operations Research”? • other names: management science, decision science • application of information technology for decision-making • designing systems to operate in the most effective way or deciding how to allocate scarce human resources, money, equipment, or facilities • closely related to several other fields: o applied mathematics, o computer science, o economics, o industrial engineering, and o systems engineering page 4 Typical problems faced by an O.R. practitioner: • In what sequence should parts be produced on a machine in order to minimize the change-over time? • How can a dress manufacturer lay out its patterns on rolls of cloth to minimize wasted material? • How many elevators should be installed in a new office ...
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...Operational Research Models and Methods in CIM1 Abstract : Many models and methods of Operational Research can be adapted for industrial applications. In this chapter, we show on one hand the main problems of a manufacturing system and, on the other hand, how they can be ranged in a hierarchical order, derived from a CIM architecture (from the strategic decisions to the production constraints). Then, we present an Operational Research tool for solving each of these problems. 1 Introduction Flexible Manufacturing Systems (FMS) are nowadays installed in the mechanical industry, especially in car factories. However, the market constraints impose to always improve the production system and the whole production organization. The concepts developed by Taylor and applied at the beginning by Ford are progressively abandoned and replaced by the Just-In-Time concept and the Computer Integrated Manufacturing philosophy (CIM). One of the aims of the CIM philosophy is to provide an integrated information system which avoids the rigid separations between the different functionalities of a complete production system. With such integrated information systems, the loss of time on one hand between the customer order and the part delivery, on the other hand between the product design and its manufacture will be drastically reduced. To understand the complete production system, it is relatively easy to find in the scientific literature excellent general books explaining the different aspects...
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...ASSIGNMENT ON OPERATION RESEARCH ( FIN – 3104 ) 3RD YEAR , 1ST SEMESTER BBA – 3RD BATCH DEPARTMENT OF FINANCE JAGANNATH UNIVERSITY TOPIC Quantitative Analysis for Optimization : Using Linear Programming & Transportation Problem Group Name Name & ID No. of the Group Members: |Sl. No. |Name |ID No. | | | | | |01 |Suman Chandra Mandal (Group Leader) |091557 | | |Md. Nahid Islam |091604 | |02 | | | | | | | |03 |Mahbuba Mehreen |091619 ...
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...Operations Research OR - Development of OR - England , world war → determining the last utilization of limited resources - USA → 1947 → simplex method - Development → computer science - OR models mathematical model → variables, Function Optimal solution according to different techniques Simulated model → study for a specific system at Certain time period and simulate this system Heuristic model → empirical rules to find Approximate solution from point to another in the System Mathematical Model 1- Decision variables and parameters unknown values we need to solve equations to get these values EX: parameter → determine system We need to determine level of production for a specific good based on raw material, machine capacity Unknown parameter→ level of production, Unknown variable → number of units produced 2- Constraints or restrictions → row material 3- Objective function → EX: profit function maximization cost function Minimization EX: production planning machine 1 2 3 Profit/unit Time per unit (minutes) Machine Product1 product2 product3 capacity 1 2 1 430 3 0 2 460 1 4 0 420 3 2 5 OR mathematical model X1 → amount product1 X2 → amount product2 X3 → amount product3 Profit function: Constraints 1x1 + 2x2 + 1x3 ≤ 430 3x1 + 0x2 + 2x3 ≤ 460 1x1 + 4x2 + 0x3 ≤ 420 Additional non negativity constraints x1 ≥ 0 , x2 ≥ 0 , x3 ≥ 0 We are looking for optimum sol for x1 , x2 , x3 to maximize objective function subject to constraints Introduction to optimization & linear...
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...Operations Research and its Prospects in Pakistan Prof. Dr. Shoaib ud Din Mathematics Department Punjab University, Lahore, Pakistan Operations Research has had an increasingly great impact on the management of organizations in the recent years. In fact, with the exception of advent of electronic computer, the extent of this impact seems to be unrivalled by that of any other recent development. However, all the development in this field has gone almost unnoticed in most developing countries including Pakistan. This article is an effort to introduce Mathematics community in the country to the subject and its achievements. A brief history In order to appreciate the importance of OR in the world today it is important that we know something of its history and evolution. Although roots of Operations Research can be traced back many decades, it is generally agreed that this discipline began during World War II. During the War team of British scientists with diverse background were called upon to study the strategic and tactical problems associated with air and land defense of the country. The establishment of this scientific team marked the first formal Operations Research activity. Their efforts were allegedly instrumental in winning the Air Battle of Britain, The Island Campaign in the Pacific, the Battle of the North Atlantic, and so on. The name Operations Research-Operational Research in the United Kingdom – was apparently coined because the problems assigned to this team...
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...ADVANCED OPERATION RESEARCH ASSIGNMENT OF O.R. METHODOLOGY DEVELOPMENT DEVELOPMENT OF TRANSPORTATION METHODOLOGY IN OPERATION RESEARCH “PENGEMBANGAN METODE TRANSPORTASI DALAM OPERASI PENELITIAN” TYPE II – COMPARE & CONTRAST IQBAL TAWAKKAL - 1506694736 PROGRAM MAGISTER TEKNIK INDUSTRI - SALEMBA UNIVERSITAS INDONESIA 1. INTRODUCTION A special class of linear programming problem is Transportation Problem, where the objective is to minimize the cost of distributing a product from a number of sources (e.g. factories) to a number of destinations (e.g. warehouses) while satisfying both the supply limits and the demand requirement. Because of the special structure of the Transportation Problem the Simplex Method of solving is unsuitable for the Transportation Problem. The model assumes that the distributing cost on a given rout is directly proportional to the number of units distributed on that route. Generally, the transportation model can be extended to areas other than the direct transportation of a commodity, including among others, inventory control, employment scheduling, and personnel assignment. Transportation was one of the earliest application areas of operations research, and important transportation problems, such as the traveling salesman problem, vehicle routing problem, and traffic assignment problem, contributed to fundamental knowledge in operations research. Transportation remains one of the most important and vibrant areas of operations research...
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...MIS 208 SPRING 2015 HOMEWORK 1 (due 13:15 on Monday, 6 April 2015, in class at 101) Reading Assignment: Please read section Duality and Sensitivity Analysis of the text book Winston. You will be responsible on that section in the exam. Question 1: Two different products, P1 and P2 can be manufactured by one or both of two different machines, M1 and M2. The unit processing time of either product on either machine is the same. The daily capacity of machine M1 is 200 units (of either P1 or P2, or a mixture of both) and the daily capacity of machine M2 is 250 units. The shop supervisor wants to balance the production schedule of the two machines such that the total number of units produced on one machine is within 5 units of the number produced on the other. The profit per unit of P1 is $10 and that P2 is $15. Set up the problem as an LP in equation form. Question 2: A company manufactures purses, shaving bags and backpacks. The construction includes leather and synthetics, leather being the scarce raw material. The production process requires two types of skilled labor: sewing and finishing. The following table gives the availability of the resources, their usage by the three products, and the profits per unit. a) Formulate the problem as a linear program and find the optimal solution by using appropriate Simplex Methods that you have seen in the class b) From the optimum solution determine the status of each resource. Question 3: The following tableau...
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...On the 22nd of June 1941 Hitler launched Operation Barbarossa; an offence led by The Axis that forced its way into USSR soil. What had become a major power within Europe had taken aggressive military action towards one of the biggest existing nations of the time – one that was considered extremely backwards socio-economically. On the 23rd of August 1942 the USSR launched a major counterattack against the Nazi-German forces trapping them within the city of Stalingrad and thus initiating the controversial battle of Stalingrad. This action, Operation Uranus – approved by Stalin, would mark the retreat from the Nazi invasion of Europe that would not end until Berlins fall on May 1945. Thus this battle catalysed the conclusion to one of the most horrifying wars of our time. Few events have been up for as much analysis of historical importance as this military action. This due to how it had the ability to cause such an immense war loss and the eventual retreat of Nazi-Germany - particularly after Nazi-Germany´s consecutive military triumphs since the dawn of World War Two. Few, including...
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...World War II happened from 1939 to 1945. The Battle of Normandy lasted from June 1944 to August 1944. On June 6th a.k.a. D-Day Operation Overlord began. Operation Overlord was an operation that had about 156,000 American, British, and Canadian forces landed on multiple beaches along a stretch of 50 miles. “Prior to D-Day, the Allies conducted a large-scale deception campaign designed to mislead the Germans about the intended invasion target.” (http://www.history.com/) “In January 1944, General Dwight Eisenhower (1890-1969) was appointed commander of Operation Overlord. In the months and weeks before D-Day, the Allies carried out a massive deception operation intended to make the Germans think the main invasion target was Pas-de-Calais (the...
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...Journal of Business & Economics Research – July 2005 Volume 3, Number 7 Operations Research And Operations Management: From Selective Optimization To System Optimization Jack A. Fuller, (E-mail: jfuller@wvu.edu), West Virginia University C. Lee Martinec, West Virginia University ABSTRACT The focus of this research paper is to discuss the development of Operations Management (OM) and Operations Research (OR) with respect to their use within the organization’s decision-making structure. In addition, the difference in the tools and techniques of the two fields is addressed. The question is raised as to how distinct the two academic fields have become in light of the application of their models to the service industry. Suggestions are made regarding the possibility of incorporating OM/OR models and their output into the decision making structure of the organization towards the goal of “system optimization”. ORIGINS OF OPERATIONS MANAGEMENT AND OPERATIONS RESEARCH A comparison of the origins of operations management and operations research reveals that both are an innovation of the 20th century. The origin of operations research was in England, circa 1937, and has its roots in scientific management, with its first significant applications to military operations in both World War I and World War II. Operations management had its origins in the early factory system, and was more associated with physical production in a factory environment and it too was strongly influenced...
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...OPERATION RESEARCH Credits: 4 SYLLABUS Development Definition, Characteristics and phase of Scientific Method, Types of models. General methods for solving operations research models. Allocation: Introduction to linear programming formulation, graphical solution, Simplex ethod, artificial variable technique, Duality principle. Sensitivity analysis. Transportation Problem Formulation optimal solution. Unbalanced transportation problems, Degeneracy. Assignment problem, Formulation optimal solution, Variation i.e., Non-square (m x n) matrix restrictions. Sequencing Introduction, Terminology, notations and assumptions, problems with n-jobs and two machines, optimal sequence algorithm, problems with n-jobs and three machines, problems with n-jobs and m-machines, graphic solutions. Travelling salesman problem. Replacement Introduction, Replacement of items that deteriorate with time – value of money unchanging and changing, Replacement of items that fail completely. Queuing Models M.M.1 & M.M.S. system cost considerations. Theory of games introduction, Two-person zero-sum games, The Maximum –Minimax principle, Games without saddle points – Mixed Strategies, 2 x n and m x 2 Games – Graphical solutions, Dominance property, Use of L.P. to games, Algebraic solutions to rectangular games. Inventory Introduction, inventory costs, Independent demand systems: Deterministic models – Fixed order size systems – Economic order quantity (EOQ) – Single items, back ordering...
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...allocation of the resources by the firms. In other words, managerial economics involves analysis of allocation of the resources available to a firm or a unit of management among the activities of that unit... browse notes.Finance or Business AccountingAmerican Accounting Association defines accounting as "the process of identifying, measuring and communicating economic information to permit informed judgements and decisions by users of the information". Accounting refers to the actual process of preparing and presenting the accounts. In other words, it is the art of putting the academic knowledge of accountancy into practice... browse notes.Operation Research & Quantitative TechniquesThe advent of Operation Research (commonly known as OR) was second world war. The name was also derived from its use for research on Military Operations...
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...Applications of Operations Research planning, routing, scheduling, forecasting, process analysis and decision analysis. OR is also contributing greatly to healthcare services such as surgical and bed scheduling, portering operations, emergency transport, accident trend analysis and treatment optimization. In the service sector, OR techniques have been found especially helpful when dealing with variability in service delivery such as call centres, queues for service and medical wait times. A sampler of typical OR applications includes: • • • • • • • • • • • • Optimization of LTL trucking (Yellow Freight) Optimal package designs (Domtar Packaging, Ltd) Manpower planning models (Treasury Board Secretariat) Aircraft operations (Delta Airlines) Surgical bed optimization (Fraser Health Authority) Pre-board passenger screening (Vancouver International Airport ) Switching network studies (Bell-Northern Research, Ltd) Maintenance Strategies for the US Coast Guard Revenue Management (American Airlines) Resource allocation in a mental health hospital (Douglas Hospital) Routing of Waste Trucks (Waste Management Inc.) Rail Car Optimization (CP Rail) Successful OR applications can be found in a broad array of industries dealing with challenges such as OR has been applied in many industry sectors including the following: Transport and Travel. OR techniques are used by airlines and rail companies to offer varying fares and make higher revenues by filling more seats at different prices - an...
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