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Chapter 1 Introduction Exposure to quantitative methods will teach managers to ask the right questions. Quantitative Decision Making 1 Introduction • Quantitative methods can be applied to decision making (business problems) in general and can be used by individuals (managers) or groups, in every type of organizations. • It is important to know quantitative methods and how they can be used in solving variety of actual problems such as: 2 Managing R&D Determining Number of Bank Tellers Locating Warehouses Designing Ports Developing Fire Fighting Companies Investing Distribution Managing Inventory Scheduling Flights 3 Further Successes 4 Optimizing Agriculture Waiting in Lines Satellite Communications Political Campaign Strategies Quantitative Methods Classification I. II. III. IV. 5 Resource Allocation Distribution, Routing, and Scheduling Inventory Management Simulation and Waiting Lines Management Science and Operations Research Management Science & Operation Research: are concerned with selecting the best alternative course of action whenever mathematics can be helpful in reaching a decision. Finding Optimal Solutions: an optimal solution is the one that yields maximum profit or minimizing cost. 6 Management Science and Operations Research Moreover, is some applications, an optimal solution might be the most effective alternative in terms of time, reliability, or one of many kinds of measures. Mathematical Optimization Procedures: a Mathematical Optimization Procedure can be defined as the particular quantitative method for finding the best solution. 7 Models and Decision Making Alternatives & Quantitative Methods: every decision-making situation involves possible alternatives. Therefore, quantitative methods are used to select the alternative that best satisfies the decision maker’s goals. The Mathematical Model (Parameters & Variables): the first step in applying quantitative methods is generally to express the problem mathematically. Such a formulation is called a mathematical model. 8 Models and Decision Making All mathematical models consists of “variables” and constant terms, which are sometimes referred to as “parameters”. The variables and parameters are usually linked by algebraic expressions that reflect the decision maker’ goals and any special limitations on the kinds of alternatives to be considered. Constraints & Feasible Solutions: sometimes a mathematical model incorporates constraints are often expressed algebraically. 9 Models and Decision Making Constraints and Feasible Solutions Q < 300 Feasible solution: values of Q not exceeding 300 units. whereas infeasible solution values of Q exceeding 300 units. Optimal Solutions 2 Ak Q hc Quantitative methods are employed to solve the problem by finding the value of the variables that meets the requirements of the mathematical model 10 Algorithms and Model Types Algorithms: refer to the solution procedures used to solve a problem. Models classes are deterministic and stochastic models. Deterministic models contain certain (known & fixed) constants throughout their formulation. Stochastic models are developed to solve problems that involve one or more uncertain quantities. 11 The Importance of Studying Quantitative Methods 12 Increases decision-making confidence. Provides problem-solving skills. Raises ability to cope with decisions. Learn spreadsheet skills. Computer Solutions Excel Spreadsheets A 13 B C D E F INVENTORY ANAYLSIS 1 2 3 Parameter Values: 4 Fixed Cost per Order: k = $ 4.00 5 Annual Number of Items Demanded: A = 1,000 6 Unit Cost of Procuring an Item: c = $ 1.00 7 Annual Holding Cost per Dollar Value: h = $ 0.20 8 9 Decision Variables: 10 Order Quantity: Q = 200.0 11 F 12 Results: 10 =SQRT((2*F5*F4)/(F7*F6)) 13 Total Annual Relevant Cost: TC = $ 40.00 F 14 13 =(F5/F10)*F4+F7*F6*(F10/2) 15 16 Computer Solutions QuickQuant 14