...Solutions 56:171 Operations Research Homework #3 Solutions – Fall 2002 1. Revised Simplex Method Consider the LP problem Maximize subject to z = 3 x1 − x2 + 2 x3 x1 + x2 + x3 ≤ 15 2 x1 − x2 + x3 ≤ 2 − x1 + x2 + x3 ≤ 4 x j ≥ 0, j = 1, 2,3 a. Let x4 , x5 , &, x6 denote the slack variables for the three constraints, and write the LP with equality constraints. Answer: Maximize z = 3 x1 − x2 + 2 x3 subject to x1 + x2 + x3 + x4 = 15 2 x1 − x2 + x3 + x5 = 2 − x1 + x2 + x3 + x6 = 4 x j ≥ 0, j = 1, 2,3, 4,5, 6 After several iterations of the revised simplex method, 1 0 the basis B={4,3,2} and the basis inverse matrix is ( AB ) −1 = 0 1 2 0 − 1 2 −1 1 . 2 1 2 b. Proceed with one iteration of the revised simplex method, by i. Computing the simplex multiplier vector π Answer: 1 0 −1 B −1 0 1 1 = 0, 3 , 1 π = CB ( A ) = [0 2 −1] 2 2 2 2 0 − 1 1 2 2 = [ 0, 1.5, 0.5] ii. “pricing”, i.e., computing the “relative profits”, of the non-basic columns. Answer: 56:171 O.R. -- HW #3 Solutions Fall 2002 page 1 of 8 Solutions 1 0 0 C = [3 0 0 ] , A = 2 1 0 −1 0 1 N N N −3 −1 C = C −π A = 1 2 2 2 The relative profits for non-basic variables are C1 = 0.5 , C5 = −1.5 , C6 = −0.5 . iii. Selecting the column to enter the basis. Answer: Only the relative profit of X 1 is positive and the problem is Max problem, and so X 1 should enter the basic. iv. Computing the substitution rates of the entering column. Answer: The substitution...
Words: 2524 - Pages: 11
...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...
Words: 30976 - Pages: 124
...Besharatian CIS 512 June 2, 2013 Memory contention Memory contention is a state an OS memory manager can reside in when to many memory requests are issued to it from an active application possibly leading to a DOS condition specific to that application. A test was run on a group of applications several times, on three different schedules, each with two different parings sharing a memory domain. The three pairing permutations afforded each application an opportunity to run with each of the other three applications with the same memory domain. The three applications being discussed in this paper are the Soplex, Sphinx, and the NAMD. The Soplex is a linear programming (LP) solver based on the revised simplex algorithm. It features preprocessing techniques, exploits sparsity, and offers primal and dual solving routines. It can be used as a standalone solver reading MPS or LP format files as well as embedded into other programs via a C++ class library. Sphinx is an open source full text search server, designed from the ground up with performance, relevance (aka search quality), and integration simplicity in mind. It's written in C++ and works on Linux (RedHat, Ubuntu, etc), Windows, MacOS, Solaris, FreeBSD, and a few other systems (Sphinx Technologies, 2013). NAMD is a parallel molecular dynamics code designed for high-performance simulation of large bimolecular systems. NAMD uses the popular molecular graphics program VMD for simulation...
Words: 1093 - Pages: 5
...------------------------------------------------- Top of Form My Courses --> HNC 310 --> EXAM SCHEDULE and GRADING print contact faculty contact tech | Pathology - Module 1: Introduction to the course - Unit 1: Course Requirements - Item Number: 1 Lecture | Title: | EXAM SCHEDULE and GRADING | Fall 2013 EXAM SCHEDULE Dates | | Percent of Grade | August 25, 2014 | Course begins | | September 18, 2014 | Exam 1 | 25% | October 16, 2014 | Exam 2 | 25% | November 13, 2014 | Exam 3 | 25% | December 11, 2014 | Exam 4 | 25% | A final average grade of C+ or better (a numerical grade of 74 or higher) is required to pass this course. ------------------------------------------------- Top of Form My Courses --> HNC 310 --> CELL PATHOLOGY print contact faculty contact tech | Pathology - Module 2: Module Two - Unit Number: 1 Unit Title: CELL PATHOLOGY Unit Objectives After reading this chapter, viewing the PowerPoint presentation and the accompanying lecture notes, and completing the study activities, the student will be able to: 1. Describe the normal structure and function of the cell. 2. Discuss the adaptive structural and functional changes that occur in cells as a result of changes in homeostasis. 3. Explain the adaptive structural and functional changes associated with atrophy, hypertrophy, hyperplasia...
Words: 13630 - Pages: 55
...Op"erations Research This page intentionally left blank Copyright © 2007, 2005 New Age International (P) Ltd., Publishers Published by New Age International (P) Ltd., Publishers All rights reserved. No part of this ebook may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the publisher. All inquiries should be emailed to rights@newagepublishers.com ISBN (13) : 978-81-224-2944-2 PUBLISHING FOR ONE WORLD NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS 4835/24, Ansari Road, Daryaganj, New Delhi - 110002 Visit us at www.newagepublishers.com PREFACE I started my teaching career in the year 1964. I was teaching Production Engineering subjects till 1972. In the year 1972 I have registered my name for the Industrial Engineering examination at National Institution of Industrial Engineering, Bombay. Since then, I have shifted my field for interest to Industrial Engineering subjects and started teaching related subjects. One such subject is OPERATIONS RESEARCH. After teaching these subjects till my retirement in the year 2002, it is my responsibility to help the students with a book on Operations research. The first volume of the book is LINEAR PORGRAMMING MODELS. This was published in the year 2003. Now I am giving this book OPERATIONS RESEARCH, with other chapters to students, with a hope that it will help them to understand...
Words: 242596 - Pages: 971
...Singapore • Spain • United Kingdom • United States This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it. For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest. An Introduction to Management Science: Quantitative Approaches to Decision Making, Revised Thirteenth Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, & Kipp Martin VP/Editorial Director: Jack W. Calhoun Publisher: Joe Sabatino Senior Acquisitions Editor: Charles McCormick, Jr. Developmental Editor: Maggie Kubale Editorial Assistant: Courtney Bavaro Marketing Communications Manager: Libby Shipp Marketing Manager: Adam Marsh Content Project Manager: Jacquelyn K Featherly Media Editor: Chris Valentine Manufacturing Coordinator: Miranda Klapper Production House/Compositor: MPS Limited, a Macmillan Company Senior Art Director: Stacy Jenkins Shirley Internal Designer: Michael Stratton/Chris Miller Design Cover Designer: Craig...
Words: 41961 - Pages: 168
...12 Integer Programming In Chap. 3 you saw several examples of the numerous and diverse applications of linear programming. However, one key limitation that prevents many more applications is the assumption of divisibility (see Sec. 3.3), which requires that noninteger values be permissible for decision variables. In many practical problems, the decision variables actually make sense only if they have integer values. For example, it is often necessary to assign people, machines, and vehicles to activities in integer quantities. If requiring integer values is the only way in which a problem deviates from a linear programming formulation, then it is an integer programming (IP) problem. (The more complete name is integer linear programming, but the adjective linear normally is dropped except when this problem is contrasted with the more esoteric integer nonlinear programming problem, which is beyond the scope of this book.) The mathematical model for integer programming is the linear programming model (see Sec. 3.2) with the one additional restriction that the variables must have integer values. If only some of the variables are required to have integer values (so the divisibility assumption holds for the rest), this model is referred to as mixed integer programming (MIP). When distinguishing the all-integer problem from this mixed case, we call the former pure integer programming. For example, the Wyndor Glass Co. problem presented in Sec. 3.1 actually would have been an IP problem...
Words: 36302 - Pages: 146
...CLASSIFICATION OF COSTS: Manufacturing We first classify costs according to the three elements of cost: a) Materials b) Labour c) Expenses Product and Period Costs: We also classify costs as either 1 Product costs: the costs of manufacturing our products; or 2 Period costs: these are the costs other than product costs that are charged to, debited to, or written off to the income statement each period. The classification of Product Costs: Direct costs: Direct costs are generally seen to be variable costs and they are called direct costs because they are directly associated with manufacturing. In turn, the direct costs can include: • Direct materials: plywood, wooden battens, fabric for the seat and the back, nails, screws, glue. • Direct labour: sawyers, drillers, assemblers, painters, polishers, upholsterers • Direct expense: this is a strange cost that many texts don't include; but (International Accounting Standard) IAS 2, for example, includes it. Direct expenses can include the costs of special designs for one batch, or run, of a particular set of tables and/or chairs, the cost of buying or hiring special machinery to make a limited edition of a set of chairs. Total direct costs are collectively known as Prime Costs and we can see that Product Costs are the sum of Prime costs and Overheads. Indirect Costs: Indirect costs are those costs that are incurred in the factory but that cannot...
Words: 17187 - Pages: 69
...2.Decision Theory - Decision Tables and Decision Trees, Game Theory 2.1 Introduction and Basic Terms Decision theory represents a generalized approach to decision making. It enables the decision maker to analyze a set of complex situations with many alternatives and many different possible consequences to identify a course of action consistent with the basic economic and psychological desires of the decision maker Decision theory problems are characterized by the following: a decision criterion a list of alternatives a list of possible future events (states of nature) payoffs associated with each combination of alternatives and events the degree of certainty of possible future events There is a wide range of management decision problems. Among them there are capacity and order planning, product and service design, equipment selection, location planning, and so on. Some examples of alternatives and possible events for these alternatives are shown in Table 2.1. Alternatives To order 10, 11, … units of a product To make or to buy a product To buy or not to buy accident insurance Events Demand for the product may be 0, 1, … units The cost of making may be 20, 22, … $thousands An accident may occur, or may not occur Table 2.1 “Examples of Alternatives and Events” Various properties of decision problems enable a classification of decision problems. Solution to any decision problem consists of these steps: 1. Identify the problem 2. Specify objectives and the decision criteria for...
Words: 13221 - Pages: 53
...length article A carbon footprint based reverse logistics network design model Devika Kannan a,∗ , Ali Diabat b , Mahmoud Alrefaei c , Kannan Govindan d , Geng Yong e,∗ a Indian Institute of Industrial Engineering, Navi Mumbai, India Engineering Systems and Management, Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates c Department of Mathematics and Statistics, Jordan University of Science and technology, Irbid 22110, Jordan d Department of Business and Economics, University of Southern Denmark, Odense, Denmark e Institute of Applied Ecology, Chinese Academy of Science, Shenyang, Liaoning Province 110016, PR China b a r t i c l e i n f o Article history: Received 2 March 2011 Received in revised form 12 March 2012 Accepted 12 March 2012 Keywords: Carbon footprint Reverse logistics Greenhouse emissions Case study a b s t r a c t Due to the environmental legislation and regulations, manufacturing firms have realized the importance of adopting environmental friendly supply chain management (SCM) practices. In this paper, a mixed integer linear model is developed for a carbon footprint based reverse logistics network design. The proposed model aims at minimizing climate change (specifically, the CO2 footprint), and it employs reverse logistics activities to recover used products, hence combining the location/transportation decision problem. The proposed model is validated by examining a case study from the plastic sector...
Words: 4160 - Pages: 17
...“AN INFORMATIVE STUDY ABOUT SHORTHAND” _____________________________ PRESENTED TO THE FACULTY OF THE COLLEGE OF OFFICE ADMINISTRATION _____________________________ SUBMITTED TO: Professor 2012 BACHELOR OF SCIENCE IN OFFICE ADMINISTRATION ACNOWLEDGEMENT We would like to dedicate this research study first to our almighty God for his Guidance and wisdom. To our family who gave us financial and moral support all throughout this research. To our professor, who thought us on the step by step process of this research and to all BSOA students that are interested to make this research as their guide for their future career. Bachelor of Science in Office Administration BACHELOR OF SCIENCE IN OFFICE ADMINISTRATION TABLE OF CONTENTS Abstract . . . . . . . . . . pg 1 Statement of the Problem . . . . . . . pg 2 Review of Related Literature . . . . . . . pg 2-10 Design of Investigation . . . . . . . . pg 11 Measurement Technique Used . . . . . . . pg 12-13 Findings . . . . . . . . . . pg 14-24 Conclusion . . . . . . . . . . pg 25 Summary . . . . . . . . . . pg 26-32 BACHELOR OF SCIENCE IN OFFICE ADMINISTRATION LIST OF FIGURES Figure Page Pitman Shorthand . . . . . . . . . 3 Munson Shorthand . . . . . . . . 3 Thomas Natural Shorthand . . . . . . . 4 Eclectic shorthand . . . . . . . . . 4 Bezenšek Shorthand . . . . . . . . 4 Boyd's...
Words: 6830 - Pages: 28
...Revised Syllabus with Credit based Semester and Grading System For The Master of Management Studies (MMS) 2Years full-time Degree Course (Effective from the academic year 2012 – 2013) MMS New Course Structure (Effective July 2012 onwards) MMS First Year: Semester I Subject/Paper Maximum Number of Marks Sessions of 90 Minutes Core Papers 1.1 Perspective Management 1.2 Financial Accounting 1.3 Managerial Economics 1.4 Operations Management 1.5 Organisational Behaviour 1.6 Business Mathematics 1.7 Information Technology & Management 1.8 Communication Skills 1.9 Marketing Management 1.10 to 1.13 Elective 1 Elective 2 Total Electives (Students need to opt for any two electives) 1.10 Selling & Negotiation Skills 1.11 High Performance Leadership 1.12 Indian Ethos in Management 1.13 Corporate Social Responsibility Projects 50 100 100 100 100 100 50 100 100 100 100 1000 18 30 30 30 30 30 18 30 30 30 30 306 Note 1: All subjects/papers for semester I will be internally assessed by the institute. Note 2: All new electives proposed to be introduced by the institute, apart from electives listed in the new syllabus; need to inform University in writing outlining the details of the course with learning objectives, learning outcomes, detail syllabus, teaching learning plan and course evaluation procedures within the pattern prescribed at least one semester in advance. Master of Management Studies First Year Semester I Sl No Code Subject/Paper No of Periods per week...
Words: 9960 - Pages: 40
...a unique way. Based on rigorous international primary research with all of our key stakeholders and involving the participation of over 6,000 individuals and organisations – members, students, employers (both existing and potential), CIMA tuition partners, universities and our examiner and marker team – we have designed a professional finance training and development solution that is second to none. I commend this revised CIMA Professional Qualification to you. It will be examined for the first time in 2010, so there is plenty of time to absorb the exciting changes contained in the pages that follow. A qualification focused on the future – fit for purpose, relevant and unique I am honoured to introduce the new 2010 Chartered Management Accounting Qualification to all of our stakeholders. With seismic shifts occurring in the world’s economy, coupled with accelerating concerns about the sustainability of our planet, never before has there been a greater need for organisations to train and develop their people to manage the impact of these changes. With this revised qualification CIMA remains true to its long and proud history of providing finance professionals with a difference – Chartered Management Accountants – who combine management and finance skills in a unique way and who fully understand the businesses they are working in. While we respect and learn lessons from the past, through this qualification we prepare our future members to be focused on the future: driving value;...
Words: 22006 - Pages: 89
...RUNNING HEAD: CERVICAL CANCER SCREENING IN PRIMARY CARE Protocol Paper Cervical Cancer Screening in Primary Care Fall, 2008 ABSTRACT In the 1970s cervical cancer was the leading cause of cancer death for women in the United States. However, in the past 40 years, the number of cases of cervical cancer and the number of deaths from cervical cancer have declined radically. This decrease is largely the result of many women getting regular Pap tests (Center for Disease Control and Prevention, 2004). Persistent infection with high-risk human papillomavirus (HPV) infections can lead to cervical cancer. Since HPV and precancerous lesions of the cervix are usually asymptomatic, prevention and regular screening remains imperative for early detection and treatment of cervical cancer. Here we examine strategies for prevention, assessment, and management for cervical cancer and contemplate briefly potential implications if left undiagnosed or untreated. Cervical Cancer Screening in Primary Care Introduction Human Papillomavirus (HPV) infection is a major health concern in the United States. Genital HPV is the most common sexually transmitted infection (STI) in America. There are more than 100 different types of HPV infections. Of these, 40 affect mucosal surfaces and more specifically anogenital epithelium including: Cervix, vagina, vulva, rectum, urethra, penis, and anus. The different strands of the HPV infections are divided into “high-risk” and “low-risk...
Words: 4718 - Pages: 19
...Chapter 3: Physical Layer Chapter Outline INTRODUCTION CIRCUITS Circuit Configuration Data Flow Communication Media Multiplexing How DSL Transmits Data COMMUNICATION MEDIA Guided Media Wireless Media Media Selection DIGITAL TRANSMISSION OF DIGITAL DATA Coding Transmission Modes Digital Transmission How Ethernet Transmits Data ANALOG TRANSMISSION OF DIGITAL DATA Modulation Capacity of a Voice Circuit How Modems Transmit Data DIGITAL TRANSMISSION OF ANALOG DATA Translating from Analog to Digital How Telephones Transmit Voice Data How Instant Messenger Transmits Voice Data VoIP IMPLICATIONS FOR MANAGEMENT SUMMARY Teaching Notes Generally preconceptions about what analog and digital transmission are vary greatly among undergraduate students. For this reason it is necessary to spend at least about 3-4 hours covering this chapter. Make sure at first that the students understand the dual characteristic state of what constitutes a circuit- the concepts of logical and physical. Circuits are probably the most important aspect of comprehending the physical layer. A circuit can be viewed and generally is viewed as a wire or a cable. This is the physical aspect of the circuit. There is also a logical aspect of a circuit. It is not just how long, wide or what type of cable; it is also what it is that propagates through the cable. When I discuss circuits and media, I try to remember to hand around twisted pair...
Words: 7080 - Pages: 29