An Introduction to Management Science, 16e PDF

An Introduction to Management Science, 16e Chapter 1 – Introduction Anderson. Sweeney, Williams, Camm, Cochran, Fry & Ohlmann, An Introduction to Management Science - Quantitative Approaches to Decision Making, 16th Edition. © 2023 Cengage Group. All Rights...

An Introduction to Management Science, 16e Chapter 1 – Introduction Anderson. Sweeney, Williams, Camm, Cochran, Fry & Ohlmann, An Introduction to Management Science - Quantitative Approaches to Decision Making, 16th Edition. © 2023 Cengage Group. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter Contents 1-1 Problem Solving and Decision Making 1-2 Quantitative Analysis and Decision Making 1-3 Quantitative Analysis 1-4 Models of Cost, Revenue, and Profit 1-5 Management Science Techniques Summary © 2023 Cengage Group. All Rights Reserved.  Chapter Objectives After completing this chapter, you will be able to: LO 1.1 Define the terms management science and operations research. LO 1.2 List the steps in the decision-making process and explain the roles of qualitative and quantitative approaches to managerial decision making. LO 1.3 Explain the modelling process and its benefits to analyzing real situations. LO 1.4 Formulate basic mathematical models of cost, revenue, and profit and compute the breakeven point. © 2023 Cengage Group. All Rights Reserved.  Introduction The body of knowledge involving quantitative approaches to decision making is referred to as management science operations research decision science It had its early roots in World War II and is flourishing in business and industry due, in part, to: numerous methodological developments (e.g. simplex method for solving linear programming problems) a virtual explosion in computing power © 2023 Cengage Group. All Rights Reserved.  1-1 Problem Solving Problem solving is the process of identifying a difference between the actual and the desired state of affairs and then taking action to resolve the difference. The problem-solving process involves the following seven steps: 1. Define the problem. 2. Determine the set of alternative solutions. 3. Determine the criteria for evaluating alternatives. 4. Evaluate the alternatives. 5. Choose an alternative (make a decision). 6. Implement the selected alternative. 7. Evaluate the results. © 2023 Cengage Group. All Rights Reserved.  1-1 The Decision-Making Process Decision making is the term associated with the first five steps of the problem- solving process. Problems in which the objective is to find the best solution with respect to one criterion are referred to as single-criterion decision problems. Problems that involve more than one criterion are referred to as multicriteria decision problems. The decision is the choice of the best alternative. © 2023 Cengage Group. All Rights Reserved.  1-2 Quantitative Analysis and Decision Making An Alternate Classification of the Decision-Making Process The flowchart combines the first three steps of the decision-making process under the heading “Structuring the Problem” and the latter two steps under the heading “Analyzing the Problem”. © 2023 Cengage Group. All Rights Reserved.  1-2 Analysis Phase of the Decision-Making Process The Role of Qualitative and Qualitative analysis: Quantitative Analysis Based largely on the manager’s judgment and experience Includes the manager’s intuitive “feel” for the problem Is more of an art than a science Quantitative analysis: Based on the quantitative facts or data associated with the problem Uses mathematical expressions to describe objectives, constraints, and other relationships existing in the problem One or more quantitative methods may be used to make a recommendation © 2023 Cengage Group. All Rights Reserved.  1-3 Quantitative Analysis Reasons for a Quantitative Analysis Approach to Decision Making The problem is complex The Four Steps of the Quantitative Analysis Process The problem is very important The problem is new 1. Model Development The problem is repetitive 2. Data Preparation 3. Model Solution 4. Report Generation © 2023 Cengage Group. All Rights Reserved.  1-3 Step 1: Model Development Models are representations of real objects or situations. The three main model forms are: Iconic models - physical replicas (scalar representations) of real objects. Analog models - do not physically resemble the object being modeled. Mathematical models - represent real situations through mathematical expressions/formulas using assumptions, estimates, or statistical analyses. Compared to experimenting with the real situation, experimenting with models (1) requires less time, (2) is less expensive, and (3) involves less risk. The more closely the model represents the real situation, the accurate the conclusions and predictions will be. © 2023 Cengage Group. All Rights Reserved.  1-3 Example: a Simple Production Problem A mathematical model consists of an objective function described by a controllable input (called a decision variable) and subject to a set of restrictions (called constraints) under the influence of environmental factors (called uncontrollable inputs.) As an example, consider the following simple production problem: We want to find out the optimal number of units to be produced and sold each week to maximize the total weekly profit, with a unit profit of $10 per unit. We know it takes 5 hours to produce each unit and only 40 hours are available per week. © 2023 Cengage Group. All Rights Reserved.  1-3 A Mathematical Model Decision variable: x is the number of units being produced. Objective function: with a profit of $10 per unit, the objective function is 10x. Uncontrollable inputs: the profit per unit ($10), the production time per unit (5 hours), and the production capacity (40 hours) are environmental factors. Constraints: because it takes 5 hours to produce each units, and there are 40 hours available per week, the production capacity constraint is 5x ≤ 40. A complete mathematical model for our simple production problem is: Maximize: 10x (objective function) subject to: 5x ≤ 40 (production constraint) x ≥ 0 (the number of produced units cannot be negative) © 2023 Cengage Group. All Rights Reserved.  1-3 Types of Mathematical Models There are two main types of mathematical models: Deterministic model – when all uncontrollable inputs to the model are known and cannot vary. Stochastic (or probabilistic) model – when any uncontrollable input is uncertain and subject to variation. Stochastic models are often more difficult to analyze. In our simple production example, if the number of hours of production time per unit could vary from 3 to 6 hours depending on the quality of the raw material, the model would be stochastic. © 2023 Cengage Group. All Rights Reserved.  1-3 Step 2: Data Preparation All uncontrollable inputs or data must be specified before we can analyze the model and recommend a decision or solution for the problem. Data preparation is not a trivial step, due to the time required and the possibility of data collection errors. A model with 50 decision variables and 25 constraints could have over 1300 data elements! Often, a fairly large data base is needed. Information systems specialists might be needed. © 2023 Cengage Group. All Rights Reserved.  1-3 Step 3: Model Solution Trial-and-Error Solution for the Production Problem Decision Alternative The analyst attempts to identify the (Production Quantity) Projected Total Hours Feasible alternative (the set of decision variable x Profit of Production Solution 0 0 0 Yes values) that provides the “best” output for the 2 20 0 Yes model, a.k.a., the optimal solution. 4 40 20 Yes If the alternative does not satisfy all the model 6 60 30 Yes constraints, it is rejected as being infeasible, 8 80 40 Yes regardless of the objective function value. 10 100 50 No If the alternative satisfies all the model 12 120 60 No constraints, it is feasible and a candidate for the “best” solution. x = 8 is the optimal solution. © 2023 Cengage Group. All Rights Reserved. 1-3 A Flowchart of the Simple Production Model © 2023 Cengage Group. All Rights Reserved.  1-3 After the Solution Model Testing and Validation Report Generation Often, goodness/accuracy of a model cannot be A managerial report, based on the results of assessed until solutions are generated. the model, should be prepared. Small test problems having known, or at The report should be easily understood least expected, solutions can be used for by the decision maker. model testing and validation. The report should include: If the model generates expected solutions, the recommended decision use the model on the full-scale problem. If inaccuracies or potential shortcomings other pertinent information about the inherent in the model are identified, take results (for example, how sensitive corrective action such as: the model solution is to the Collection of more-accurate input data assumptions and data used in the model) Modification of the model © 2023 Cengage Group. All Rights Reserved.  1-4 Models of Cost, Revenue, and Profit Some of the most basic quantitative models arising in business and economic applications are those involving the relationship between a suitable decision variable and objective function. Typical decision variables in business and economics can be production or sales volume. Whereas common objective functions are cost, revenue, or profit. Through the use of these models, a manager can determine the projected cost, revenue, and/or profit associated with an established production quantity or a forecasted sales volume. © 2023 Cengage Group. All Rights Reserved.  1-4 Cost-Volume Model Example: Nowlin Plastics The Mathematical Model The Viper, a slim but very durable black and The cost–volume model for producing x units of gray plastic cover, is Nowlin Plastics’ best- the Viper can be written as selling cell phone cover. Several products are produced on the same Where is the total cost of producing a volume of manufacturing line, and a setup cost of x units. $3,000 is incurred each time a changeover is made for a new product. The marginal cost is defined as the cost increase associated with a one-unit increase in This setup cost is a fixed cost that is incurred the production volume. regardless of the number of produced units. In the cost-volume equation above, we see that In addition, suppose that there is a $2 the total cost will increase by $2 for each unit variable cost, due to the cost of labor and increase in the production volume. material for each unit produced. Thus, the marginal cost is $2 © 2023 Cengage Group. All Rights Reserved.  1-4 Revenue and Profit-Cost Models Revenue-Volume Model Profit-Volume Model Suppose that each Viper cover sells for $5. The The total profit, , is total revenue minus total model for total revenue can be written as cost that is associated with producing and selling x units. Where is the total revenue associated with the sale Thus, the profit-volume model can be derived of x units. from the revenue-volume and cost-volume models. The marginal revenue is defined as the increase in total revenue resulting from a one-unit increase in sales volume. In the cost-revenue equation above, we see that Using this equation, we can now determine the the total revenue will increase by $5 for each total profit associated with any production additional unit sold. volume x. Thus, the marginal revenue is $5. © 2023 Cengage Group. All Rights Reserved.  1-4 Breakeven Analysis The volume that results in total revenue equaling total cost, is called the breakeven point. We can find the breakeven point by setting the total profit equal to zero and solving for x. units Thus, production and sales of the product must be greater than 1,000 units to obtain a profit. © 2023 Cengage Group. All Rights Reserved.  1-5 (Most Frequent) Management Science Techniques Linear programming is a problem-solving approach developed for situations involving maximizing or minimizing a linear function subject to linear constraints that limit the degree to which the objective can be pursued. Integer linear programming is an approach used for problems that can be set up as linear programs with the additional requirement that some or all of the decision recommendations be integer values. Distribution and network models are specialized solution procedures for problems in transportation system design, information system design, and project scheduling. Simulation is a technique that employs a computer program to perform simulation computations and model the operation of a system. © 2023 Cengage Group. All Rights Reserved.  1-5 (Other) Management Science Techniques Nonlinear programming is a technique that allows PERT (Program Evaluation and Review Technique) for maximizing or minimizing a nonlinear function and CPM (Critical Path Method) help managers subject to nonlinear constraints. responsible for planning, scheduling, and controlling projects consisting of numerous tasks. Inventory models help maintain inventories to Decision analysis determines optimal strategies in meet demand for goods while minimizing inventory situations involving several decision alternatives holding costs. and an uncertain pattern of future events. Waiting line (or queuing) models help managers Analytic hierarchy process is a multi-criteria understand and make better decisions concerning decision-making technique that permits the the operation of systems involving waiting lines. inclusion of subjective factors in arriving at a Forecasting methods are techniques used to recommended decision. predict the future aspects of a business operation. Markov-process models study the evolution of Goal programming is a technique for solving systems over repeated trials (such as describing multi-criteria decision problems, usually within the the probability that a machine, functioning in a framework of linear programming. period, will break down in another one. © 2023 Cengage Group. All Rights Reserved.  Summary This text is about how management science may be used to help managers make better decisions. The focus of this text is on the decision-making process and on the role of management science in that process. Mathematical models are abstractions of real-world situations and, as such, cannot capture all the aspects of the real situation but just the major relevant aspects of the problem and provide a solution recommendation. One of the characteristics of management science is the search for the “best” or optimal solution to the problem. © 2023 Cengage Group. All Rights Reserved.