Role Of Mathematical Programming

Role Of Mathematical Programming Introduction In order to survive and lead todays highly competitive and demand driven market, there is a great deal of pressure on management to make economical decisions. One of the essential managerial skills is the ability to allocate and utilize resources appropriately in the efforts of achieving the optimal performance efficiently. Mathematical models have long played an important role in management and economics but it is only in the last few decades that management per se has received the sort of rigorous study that permits the application of mathematics. It is one of the primary tools used by operations researchers in making decisions. Mathematical programming Mathematical programming is the OR technique that has been most widely applied in management and economics. It has been used to solve a considerable range of problems in financial markets forming portfolios of equities, bonds, loans and currencies, generalized hedging, capital budgeting, cash management, insurance management, equity and bond index tracking, estimating the implied risk neutral probabilities for options, designing leveraged leases, computing the maximum loss sustained by shareholders, spotting insolvent banks, sorting out the failure of a stock exchange and understanding the forces leading to financial innovations. It deals with models comprising of an objective function and a set of constraints. An objective function is a mathematical expression of the quantity to be maximized or minimized. For example, manufacturers may wish to maximize production or minimize costs, advertisers may wish to maximize a products exposure, and financial analysts may wish to maximize rate of return. Constraints are mathematical expressions of restrictions that are placed on potential values of the objective function. For example, production may be constrained by the total amount of labor at hand and machine production capacity, an advertiser may be constrained by an advertising budget, and an investment portfolio may be restricted by the allowable risk. Symbolically, mathematical models in operations research may be viewed generally as determining the values of the decision variables which will Optimize subject to The function is the objective function while represents the constraint, whereis constant. The constraintsare the non-negativity constraints. In general,optimization of the objective function signifies either amaximization or minimizationof this function. The types of the objective and constraint functions of a mathematical model depend directly on the systems which they represent. Thus, these functions may be linear or non-linear. Also the decision variables may be continuous or discrete and the parameters of the system may be deterministic or probabilistic. The result of this diversity in system representation is the development of a corresponding number of optimization techniques suitable for solving these models. These mainly include linear programming, integer programming, goal programming, non-linear programming, dynamic programming, and stochastic programming. The Mathematical Programming Approach There is an orderly sequence of steps that is followed for a systematic formulation, solution and implementation of a mathematical programming model. These steps could be applied to the development of any management science model. Although the practical applications of mathematical programming cover a broad range of problems, it is possible to distinguish five general stages that the solution of any mathematical programming should follow. These stages along with their main characteristics are as follows : A. Formulating the Model The first step to be taken in a practical application is the development of the model. The following are the elements that define the model structure : Selection of a time horizon Selection of decision variables and parameters Definition of constraints Selection of the objective function B. Gathering the Data After defining the model, the data required to define the parameters of the model must be collected. This involves the data regarding the objective function coefficients, the constraint coefficients and the right hand side of the constraints. C. Obtaining an Optimal Solution Due to the lengthy nature of calculations required to obtain the optimal solution of a mathematical programming model, a digital computer is invariably used in this stage of model implementation. Nowadays, all the computer manufacturers offer highly efficient codes to solve mathematical programming models. D. Applying Sensitivity Analysis Sensitivity analysis, also called post-optimum analysis, is performed on the optimal solutions obtained for the linear programming problems originally formulated. This analysis is important for several reasons : Data uncertainity Dynamic considerations Input errors E. Testing and Implementing the Solution Once the optimal solution is obtained, it should be tested fully to ensure that the model clearly represents the real situation. The importance of conducting sensitivity analysis as part of this testing effort has already been discussed. If the solution is unacceptable, new refinements have to be incorporated in the model and new solutions obtained until the mathematical programming model is adequate. When the testing is over, the model can be implemented. Implementation usually means solving the model with real data to reach a decision or a set of decisions. Types of Mathematical Programming A. Linear programming Linear programming is one of the most successful disciplines within the field of Operational Research. It arose as a mathematical model developed during the second world war to plan expenditures and returns in order to reduce costs to the army and increase losses to the enemy. It was kept secret until 1947. Post war, many industries found its use in their daily planning. Linear programming is a technique for making decisions under certainity i.e.; when all the courses of options available to an organization are known in advance and the objective of the firm along with its constraints are quantified. Out of all the possible alternative that course of action is chosen that which yields the optimal results. Mathematically, linear programming problem calls for finding non-negativeso as to maximize a linear functionsubject to a system of linear equations : There are two extensions of Linear programming which are as follows : a) Integer Linear programming The Integer Linear Programming (ILP) is an extension of Linear programming where all of the variables must only take on integer values. b) Mixed Integer Linear Programming The Mixed integer Linear Programming (MILP) is also an extension of the Linear programming, but some of the variables must take on integer values while others take on real values. B. Quadratic programming Quadratic Programming is a special type of mathematical optimization problem. It is the problem of optimizing (minimizing or maximizing) a quadratic function of several variables subject to linear constraints on these variables. C. Goal Prgramming Goal Programming is promulgated as an aid for decision-making problems with multiple, possibly conflicting goals. In a typical goal programming model, each goal is formulated as a constraint. There are two variables associated with each goal (each constraint), over-achievement deviation and under-achievement deviation. The value of these two deviational variables measure how well the corresponding goal is accomplished. An objective function in a goal programming formulation is usually a linear function in deviational variables. Specifically, the objective function takes the weighted summation of the deviational variables. The weights assigned to a deviational variable indicate the importance of the corresponding goal in decision-making process. The objective is thus to minimize the weighted sum of deviations from goal achievement, i.e., to accomplish the best overall achievement. D. Dynamic Programming Dynamic Programming is a mathematical programming technique which fragments a large problem into several smaller problems. The approach is to solve the all the smaller, easier problems individually in order to reach a solution to the original problem. This technique is useful for making decisions that consist of several steps, each of which also requires a decision. In addition, it is assumed that the smaller problems are not independent of one another given they contribute to the larger question. E. Stochastic Programming Many optimization problems are described by uncertain parameters. When these uncertain parameters can be considered as random variables and have known probability distributions, new optimization problems can be formulated that involve expected values of these random variables. In this manner, a new problem (called the deterministic equivalent) is obtained that removes the uncertainty and results in a deterministic optimization problem. This is the approach of Stochastic Programming. Application areas of Mathematical Modeling The applications of mathematical modeling in management and economics today are so manifold that it is difficult to list them down. A few of the major application areas of mathematical models are as follows :

Discussion Questions for Operational Management

Discussion Questions for OM 5016 Class 2 Ch 1 &2. Operations Management Introduction and Strategy 1. What is Operations Management? What are major OM decisions? 2. What are the key differences between goods and services? 3. What a role does productivity play? How to measure productivity and what challenges do we have in measuring and improving productivity? 4. What is mission and strategy? How important is it for an organization to develop a mission and strategy? 5. What is OM strategy? How can operations management help a company achieve competitive advantages? 6.What is SWOT (strength, weakness, opportunity and threat) analysis? Under what circumstances do you think should we conduct SWOT analysis? Class 3 Southwest Airlines 1. Why has Southwest Airlines been so successful? 2. What recommendations would you make about the issues raised on pages 13 – 15 of the case? 3. What are the implications for Southwest of the actual or threatened bankruptcies of other major U. S. airlin e? Class 4 Ch 05. Product and Service Design 1. Why do companies need to continuously develop new products? How to generate new ideas? 2. What factors should be considered in product development?Describe the typical phases of product development and evaluate their relative importance. 3. What is the role of quality function deployment (QFD)? How is Quality of House working in product development? 4. Describe the main techniques used in designing products. Give some real world examples. What strategic advantages do techniques provide? 5. Describe the documents used to define and produce a product? How are they important and necessary? 6. Describe four organizational approaches to product development. What pros and cons do they have? 7. What are the key differences between product design and service design? 8.What an impact does environmental friendly design have on product development? How do you address conflicts between ethical design and company profitability? Class 6 Discussion q uestions for IDEO If you have interest, watch the video on Youtube: the Deep Dive Q1. How would you characterize IDEO’s design process, organization, culture and management? Q2. Should IDEO accept the Visor project as is (on a dramatically reduced schedule)? Should they try to persuade Handspring’s management to change its aggressive launch schedule? Or should they simply decline the project? Please consider both the IDEO and Handspring perspectives.Class 7 Process and Layout Strategy 1. What process strategies does an organization usually use? What key factors does a company consider in choosing its process strategy? What are the competitive advantages a firm (producing goods or service) has by using different process strategy? 2. What is mass customization? What major factors contribute to the success of mass customization? 3. How to analyze and design a process by using different tools? 4. What process strategies should be used for service? What are the key differen ces between a service process and a product process? How to improve the service process? . What layout strategies can a company use? What are the main characteristics and concerns of these strategies? 6. What are the relationships between process and layout? Class 8 Mass Gen Hospital Q1. What are primary challenges in improving operating processes in a health care environment such as that of MGH? Why choose CABG for care path? Q2. What implementation approach would you recommend for Bohmer and Torchiana? Be specific as to where you would start, what resources you would bring to bear, what performance you would expect, and what timeline you would hope to follow.What would you recommend MGH to do for its longer-term process improvement? Q3. How should MGH balance the tension between process standardization and process customization? What are the hazards of standardizing the process too rigorously? What are the dangers of allowing too much freedom to customize? Class 9 Capacity Plannin g and Location 1. What is capacity decision about? Why is it important? 2. Distinguish between design capacity and effective capacity, between utilization and efficiency. 3. What factors should be considered in determining the capacity? 4. What approaches are used and when to use them to expand the capacity? . Describe approaches used to determine the capacity. (You do not need to know how to calculate, but have to know the idea and assumptions of the approaches) 6. What are the goals, criteria and factors does a company consider in choosing a location? What are the trends of location decision? 7. Describe techniques used for location decision and identify the situations and assumptions under which these techniques should be applied. Class 10 Questions for Alden 1. Looking back, do you agree with the logic that led API in 1962 to consolidate its European production into a single facility? 2.What is your evaluation of the Uniplant’s performance during the 1980s? 3. What recomm endations would you make to Mr. Genet, API-Europe’s Executive VP, as regards the operations strategy his organization should follow in the future? Specifically, which option should it take, where should it be located, and how should it be managed? Class 12 Questions for Supply Chain Management (SCM) 1. What is a supply chain? What are the differences between SCM and OM? Describe the various stages in the supply chain and the different flows involved. 2. What is the goal and main decisions of supply chain? 3.What is your evaluation between single supplier and multiple suppliers? 4. What is push/pull view of a supply chain? What product characteristics influence the choice of push/pull SC 5. What is bullwhip effect? Why does it happen and how to reduce this effect? 6. What is an integrated supply chain? What are the key challenges and how to make it a success? Class 13 Discussion questions for Crocs 1. What are Croc’s core competencies? 2. How do they exploit these compe tencies in the future? Consider the following alternatives: a. Further vertical integration into materials. b. Growth by acquisition. c.Growth by product extension 3. To what degree do the alternatives in question 2 fit the company’s core competencies, and to what degree do they defocus the company away from its core competencies? Class 14 Inventory Management 1. What is inventory? What types of inventory are there? What are the major causes of inventory? 2. What is the purpose of ABC classification system and how is it working? 3. What types of costs associated with an inventory system? What are the objectives and key decisions of inventory management? 4. What are the assumptions and objective of EOQ model? Are these assumptions reasonable? . What are the major differences between EOQ and production order quantity (POQ) model? Why is the production inventory quantity larger than the economic order quantity, given other things equal? 6. What is â€Å"safety stock†? Wha t does safety stock provide safety against? How to calculate safety stock based on the required service level? 7. How to determine inventory size when there is uncertainty with demand/lead time? 8. What are the main challenges in inventory management, in your opinion? Class 15 Sport Obermeyer 1. What challenges does Sport Obermeyer have in production planning with uncertain demand? . What are your recommendations for production planning prior to and after observing the Las Vegas show? 3. What operational changes would you recommend to Wally to reduce markdown and stockout costs? 4. What are your views on sourcing from Hong Kong versus China? Class 16 Aggregate planning and ERP 1. What is aggregate planning and what aggregate means? 2. What are the strategic objectives of aggregate planning? Which one of these is most often addressed by the quantitative techniques of aggregate planning? 3. What strategies are used in developing a plan?What options are available for each strategy and what are the pros and cons of each option? 4. How does aggregate planning in service differ from aggregate planning in manufacturing? What is yield management and where are they implemented? 5. What is the relationship between the aggregate planning and the master production schedule (MPS)? What is the relationship between MPS and material requirements planning (MRP)? How to develop a MRP? 6. How does MRP, as an approach to inventory management, differ from the approach taken in the chapter Inventory Management, dealing with economic order quantities? 7.What is ERP and what benefits and disadvantages of ERP have? Class 17 Cisco Systems 1. At the end of the case, Pete Solvik has a number of questions. Please think about these questions, and be prepared to give your answers: What factors had contributed to the success of the ERP implementation? What obstacles did Cisco overcome for the ERP project? How? Where had the EPR team been â€Å"smart†? Where had the ERP team been just plain lucky? Do you think that the ERP project a complete success? Do you think that the Cisco team could do such a project again if they had to? Why? Why not? 2. How important is the ERP to the overall architecture?Do you see the ERP component as something that will be undertaken by some, most or all companies as they build their Information Age IT architectures? Class 18 Just-in-Time (JIT) 1. What is JIT, the Toyota Production System (TPS) and lean operations? What are the underlying philosophies? 2. Does JIT mean zero inventory? How to use EOQ and POQ models in inventory management to determine the lot size in a JIT system? 3. What are the differences between JIT and customization? 4. What are the characteristics of JIT partnerships with respect to suppliers? 5. How can layout help a company achieve JIT? How are JIT and quality related? . What is level scheduling? Discuss how the Japanese word for card has been applied in the study of JIT. 7. JIT attempts to remove delays that do not add value. How does JIT cope with weather and its impact on crop harvest and transportation times? 8. Does lean techniques work for service industry, such as a restaurant? If so, how? Class 19 Toyota Motor Manufacturing 1. What are the possible causes of the seat problem? What is the real problem facing Doug Friesen? 2. What are the key elements of TPS? Where, if at all, does the current routine for handling defective seats differ from the principles of TPS? . As Doug Friesen, what would you do to address the seat problem? Where would you focus your attention and solution efforts? Class 20 Quality and TQM 1. What is quality? What factors are used to determine quality for goods and services? 2. What are costs of quality? How can improving quality reduce costs? 3. What is Total Quality Management (TQM)? What concepts are used to implement an effective TQM program? Explain them. How are they related to Deming’s 14 points? 4. What are seven tools of TQM? What are their purpo ses and when to use them? 5. How does fear in the workplace inhibit learning? . Philip Crosby said that quality is free. What does it mean and why? 7. What roles do operations managers play in addressing the major aspects of service quality? 8. Good quality products last a long time, which in turn may reduce the sales of the product and thus the profit. How do you explain this? Class 21 Ritz-Carlton 1. What is the essence of the Ritz-Carlton experience? What is the Ritz-Carlton selling? 2. How does Ritz-Carlton create â€Å"Ladies and Gentlemen† in only 7 days? 3. Should McBride lengthen the 7 Day Countdown? Any other alternatives?

Why Everybody Is Mistaken About Essay Topics for American Gods

Why Everybody Is Mistaken About Essay Topics for American Gods There are several intriguing topics that could be become a persuasive essay if you take the opportunity to consider about doing it. Least expensive essay is an essay service which will help to compose a topic about American Government, they have a broad group of professional writers that will help you about it. Simply locating an excellent subject to speak about in a persuasive essay is insufficient to find a top grade. Now, you've got loads of topics to select from and lay down your thoughts on paper. How to compose a fantastic analysis essay ap english download an incident report should include all the vital information regarding the crash or near-miss. Following are different kinds of essay topics for students that are categorized in many sections so you can easily chose the topic depending on your need and requirement. Just choose your interested area of study or research and begin writing. What Everybody Dislikes About Essay Topics for American Gods and Why The primary goal of writing an argumentative essay is to understand how to convince individuals to modify their perception of things they strongly believe in. You might believe that interesting essay titles do all of the work, enabling you to add obvious examples and share ordinary ideas. It's important to understand that essay topics are just basic ideas that leave you pondering a notion that might be a huge deal to somebody else. Select an intriguing essay topic, and you're going to start enjoying it. Most movie makers have a tendency to alter facts due to several factors. The movie describes the life span of an ordinary Chinese family for over thirty decades. The movie story happens during the conclusion of the Civil War. The essence of movies is in most situations, for entertainment and perhaps education. Compare and contrast how folks are filmed in two movies. This god's idea holds truth for the true world, as lots of people are drawn to the television, and a lot of people do sacrifice a huge part of their time for it. It's even scary to imagine the sort of future society made from the same men and women. Soap not only the object but the practice of making it's a sign of the brutality and violence of the actual world, a world which most people would rather ignore. Sporting activities have existed for a number of millenniums. Every American should learn how to speak English. 2017 is a superb year for essays. Influence of cricket in the invention of softball sports. You'd be hard-pressed to spot any element of our modern world that wasn't influenced by ancient Greece in some manner. In some movies the alteration is to such extent that there's no any true information that could be relied on. One needs to investigate the many sides of the argument as a way to write an amazing argumentative essay which allows them to make an educated position. Therefore, a simple means to select one of the numerous theology essay topics is to concentrate on your own opinion about religion and explore it from that point. This belief enables the previous gods to remain alive. Nevertheless, they're not the enemy. This is due to the original sin that resulted in our imperfection. Knowledge about God is really the most valuable sort of knowledge because human knowledge is ultimately corrupted due to the Fall. Odysseus is passionate about the topic of guest treatment and generosity. God is the great inventor of the universe. And above all, we want to love God in return. Anyway, poetry is crucial for all literature classes, which means you can't avoid it. Every essay writer is a person who has the greater education. Thus, settle back and relax, you ought to be able to come up with an outstanding Odyssey essay topic after reading this. In a fashion, how Gaiman wrote the novel can be associated with the topic of the fresh itself.

The Primary Care Clinic Essay - 1464 Words

Assignment 1-The Primary Care Clinic Tasha Hornsby Dr. Kevin Williams HSA 300-0001030 Health Service Organization Management January 26, 2011 Discuss the key political, economic, and social forces that may have influenced the development of the clinic. Economic and social conditions that affect people’s lives determine their health. People who are poor are less likely to seek proper medical care, as opposed to people who are of middle-class status and above. Citizens with more social status, money, and education have a plethora of choices and control over things, such as the neighborhoods, their salaries, occupational opportunities, etc. (Jin, Shah, Svoboda, September, 1995, 153(5)) Dennis Raphael of the CSJ Foundation for†¦show more content†¦In order to know what is really going on in the organization, you must speak with the employees that are on the forefront. They can offer suggestions for streamlining tasks, such as customer check-in. They are usually the first people that hear praise or complaints from the patient, so their feedback is invaluable. How would you approach decisions regarding clinic ex pansion and annual plan approval? Due to the healthcare reform laws that were passed during the Obama Administration, there is a very real possibility that many people will be dropped from their employer-sponsored healthcare to the increased costs in 2014. (Diamond, 2010) Four major U.S. firms have come to the realization that millions, possibly, billions of dollars can be kept in the company coffers if they decide to cease healthcare benefits for their employees. The companies--ATT, Caterpillar, Deere, and Verizon Communications—made announcements in March and April of 2010 that it would less costly to pay the government-imposed fines, as opposed to absorbing the increased costs of the overhaul. The bill reduces employers’ tax deductions. 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