Strategic Allocation of Resources Using Linear Programming Model .. TABLE OF CONTENTSDECLARATIONABSTRACTACKNOWLEDGEMENTSTABLE OF CONTENTSLIST OF FIGURESLIST OF TABLESLIST OF ABBREVIATIONSCHAPTER 1 INTRODUCTION1. HISTORY1. 2 PRINCIPLES OF MATHEMATICAL PROGRAMMING1. LINEAR PROGRAMMING1. Limitations of LP model. MOTIVATION1. 4. 1 Examples of successful LP applications. CHARACTERSTICS OF LINEAR PROGRAMMING1. SOLVING LP PROBLEMS1. BASIC STEPS FOR SOLVING A LP MODEL1. Recognize the problem. Define the problem. Define the decision variables. What is the Salary of an IAS Officer? Understand the latest IAS salary structure based on 7th Pay Commission recommendations. Problems from H C Verma. Here you can find the solutions to the problems. Indian Space Research Organisation Collect the necessary parametric data. Formulate a model. Neurophysiology of Chemotherapy-Induced Nausea and Vomiting. The vomiting reflex is present in many animal species, ranging from fish to higher mammals, and has been. These CVPR 2015 papers are the Open Access versions, provided by the Computer Vision Foundation. The authoritative versions of these papers are posted on IEEE Xplore. UxHREZ http:// uxHREZ http:// 16/08/10: x: Could you ask him to: Could you ask him to call me? Title Edition Author ISBN; 100 Cases Histories in Clinical Medicine for MRCP (Part-1) 1/e Farrukh Iqbal. Studyplan 4 years Ago 802 Comments. Article: People Have NDEs While Brain Dead: The Case of Pam Reynolds: Book: Light and Death: One Doctor's Fascinating. The holistic merger of science and spirituality : The scientific discovery of the nature of light is the. Solve the model. 1. Verify and validate the model. NEET Exam Books PDF Download PDF Biology Physics Chemistry Recommended Books Arihant Publication Available on Amazon Flipkart Best Books List for NEET. Academy of Social Sciences ASS The United Kingdom Association of Learned Societies in the Social Sciences formed in 1982 gave rise to the Academy of Learned. From millions of real job salary data. Average salary is Detailed starting salary, median salary, pay scale, bonus data report. Hi Insights, Am a student of your PT test series for PT 2015 and have benefitted immensely by it. Am very confident of clearing PT now ( After initial hiccups, and. Analyze model output. Interpret model results. Recommend a course of action. FORMULATING LP PROBLEMS1. OBJECTIVES OF THE PRESENT WORK1. ORGANISATION OF THE DISSERTATION1. SUMMARYCHAPTER 2 LITERATURE REVIEW2. INTRODUCTION2. 2 DECISION MAKING IN POM2. THE SIMPLEX METHOD2. THE COMMAND linprog. USING EXCEL SOLVER OPTIMIZATION PROBLEM2. Spreadsheet modeling & Excel Solver. PRODUCTION OUTSOURCING: A LP MODEL FOR THE TOC2. GENERAL RESOURCE ALLOCATION MODEL2. SUMMARYCHAPTER 3 LINEAR PROGRAMMING MODEL 2. INTRODUCTION3. 2 THE PROBLEM STATEMENT3. FORMULATION OF LP MODEL3. SOLUTION USING MATLAB3. THE COMMAND simlp. THE OPTIMAL SOLUTION USING MATLAB3. SOLUTION USING EXCEL SOLVER3. OPTIMAL SCHEDULING ON MACHINES3. Assumptions in sequencing problem. Processing two jobs through four machines. SUMMARYCHAPTER 4 INTERPRETING COMPUTER SOLUTIONS OF LP PROBLEM 3. INTRODUCTION4. 2 TERMS4. Slack variables. 4. Basic & non- basic variables. ANSWER REPORT ANALYSIS4. SENSITIVITY ANALYSIS4. Find the bottleneck. Find the range over which the unit profit may change. Find the marginal benefit of increasing the time availability. Find the range over which the time availability may change. PARAMETRIC ANALYSIS4. SUMMARYCHAPTER 5 RESULT & DISCUSSIONS 4. INTRODUCTION5. 2 SEARCH FOR THE OPTIMAL SOLUTION5. BOTTLENECKS5. 4 RANGE OVER WHICH THE UNIT PROFIT MAY CHANGE5. MARGINAL BENEFIT OF INCREASING THE TIME AVAILABILITY5. RANGE OVER WHICH THE TIME AVAILABILITY MAY CHANGE5. REDUCED COST FOR NON- BASIC VARIABLES5. SLACK VALUES FOR CONSTRAINTS5. RECOMMENDED COURSE OF ACTION5. Product Outsourcing. One- time cost. 5. Cross Training of one machine operator. Possibility of third product manufacturing. Optimal sequencing to process jobs on machines. SUMMARYCHAPTER 6 CONCLUSIONS 5. INTRODUCTION6. 2 SUMMARY OF THE PRESENT WORK6. SUMMARY OF CONTRIBUTION6. SCOPE FOR FUTURE WORK6. CONCLUDING REMARKSREFERENCESLIST OF FIGURESFigure 1. Flow chart of Formulation of LP problem. Figure 3. 1 The resource time per product in minutes. Figure 3. 2 MATLAB graph. Figure 3. 3 Excel spreadsheet for a LP model. Figure 3. 4 Solver parameters dialogue box. Figure 3. 5 Graphical solution of 2 jobs and 4 machines. Figure 3. 6 Gantt Chart. Figure 4. 1 Solver results dialogue box. Figure 4. 2 Answer report. Figure 4. 3 Sensitivity report. Figure 4. 4 Jensen LP solver spread sheet. Figure 4. 5 Parametric response of RHS constraint. Figure 4. 6 Parametric response of coefficient of variable PFigure 4. Parametric response of coefficient of variable QFigure 5. Corners of the feasible region. Figure 5. 2 Answer Report of one- time cost. LIST OF TABLESTable 3. Characterstics of LP problems in POMTable 4. Changes in Z with changes in the RHSTable 4. Parametric analysis of RHS of constraint. Table 4. 3 Parametric analysis of coefficient of variables PTable 4. Parametric analysis of coefficient of variables QTable 5. Optimum values. Table 5. Range of objective function coefficient. Table 5. 3 Shadow prices for constraints. Table 5. 4 Range of RHS coefficients. Table 5. 5 Slack variables for constraints. Table 5. 6 Product Outsourcing Data. LIST OF ABBREVIATIONSillustration not visible in this excerpt. CHAPTER 1 INTRODUCTION1. HISTORYLinear programming was developed as a discipline in the 1. Its development accelerated rapidly in the postwar period as many industries found valuable uses for linear programming. The founders of the subject are generally regarded as George B. Dantzig, who devised the simplex method in 1. John von Neumann, who established the theory of duality that same year. The Nobel prize in economics was awarded in 1. Leonid Kantorovich (USSR) and the economist Tjalling Koopmans (USA) for their contributions to the theory of optimal allocation of resources, in which linear programming played a key role. Many industries use linear programming as a standard tool, e. Examples of important application areas include airline crew scheduling, shipping or telecommunication networks, oil refining and blending, and stock and bond portfolio selection. Linear programming (LP) is one of the most important general methods of operations research. Countless optimization problems can be formulated and solved using LP techniques. Operations research (OR) is a discipline explicitly devoted to aiding decision makers. Operations research was born with the increasing need to solve optimal resource allocation during WWII- Air Battle of Britain- North Atlantic supply routing problems- Optimal allocation of military convoys in Europe. PRINCIPLES OF MATHEMATICAL PROGRAMMINGMathematical programming is a general technique to solve resource allocation problems using optimization. Mathematical models are designed to have optimal (best) solutions. Optimization problems are real world problems we encounter in many areas such as mathematics, engineering, science, business and economics. In these problems, we find the optimal, or most efficient, way of using limited resources to achieve the objective of the situation. This may be maximizing the profit, minimizing the cost, minimizing the total distance travelled or minimizing the total time to complete a project. For the given problem we formulate a mathematical description called a mathematical model to represent the situation. Types of problems: - Linear programming- Integer programming- Dynamic programming- Decision analysis- Network analysis and CPM ( Critical Path Method )1. LINEAR PROGRAMMINGCompany managers are often faced with decisions relating to the use of limited resources. These resources may include men, materials and money. In other sector, there are insufficient resources available to do as many things as management would wish. The problem is based on how to decide on which resources would be allocated to obtain the best result, which may relate to profit or cost or both. Linear Programming is heavily used in Micro- Economics and Company Management such as Planning, Production, Transportation, Technology and other issues. Although the modern management issues are ever changing, most companies would like to maximize profits or minimize cost with limited resources. Therefore, many issues can be characterized as Linear Programming Problems (Sivarethinamohan, 2. A linear programming model can be formulated and solutions derived to determine the best course of action within the constraint that exists. The model consists of the objective function and certain constraints. A typical mathematical program consists of a single objective function, representing either a profit to be maximized or a cost to be minimized, and a set of constraints that circumscribe the decision variables. In the case of a linear program (LP) the objective function and constraints are all linear functions of the decision variables. At first glance these restrictions would seem to limit the scope of the LP model, but this is hardly the case. Because of its simplicity, software has been developed that is capable of solving problems containing millions of variables and tens of thousands of constraints. Countless real- world applications have been successfully modeled and solved using linear programming techniques. It is defined as a specific class of mathematical problem, in which a linear objective function is maximized (or minimized) subject to given linear constraints. This problem class is broad enough to encompass many interesting and important applications, yet specific enough to be tractable even if the number of variables is large. Typical optimization problems maximize or minimize the value of a given variable (such asprofit, total costs, etc.) when other specified variables (production capacity, required product quantities, etc.) are constrained. The field of mathematical programming includes a number of optimization methods, each described by a mathematical model. In such a model, there is one expression– the objective function – that should be maximized or minimized (or in somecases set to a desired value). In addition, the model must include constraints that are described by mathematical expressions. The most widely used models include only linear relationships, and belong to the field of linear programming. In such models both the objective function and the constraints are linear mathematical expressions. Mathematical model is a set of equations and inequalities that describe a system. Limitations of Linear Programming Model- It is applicable to only static situations since it does not take into account the effect of time. The OR team must define the objective function and constraints which can change due to internal as well as external forces- It assumes that the values of the coefficients of decision variables in the objective function as well in all the constraints are known with certainity. Since in most of the business situations, the decision variable coefficients are known only probabilistically, it cannot be applied to such situations- In some situations it is not possible to express both the objective function and constraints in linear form. For example, in production planning we often have non- linear constraints on production capacities like setup and takedown times which are often independent of the quantities produced. The misapplication of LP under non- linear conditions usually result in an incorrect solution- Linear programming deals with problems that have a single objective.
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