Management Science PDF

CHAPTER 1: MANAGEMENT SCIENCE Overview Management science can be defined as the application of a scientific techniques in solving various kinds of phenomena or problems which cannot be easily understood by way of simple approaches. Its application is widespread to include problem...

CHAPTER 1: MANAGEMENT SCIENCE Overview Management science can be defined as the application of a scientific techniques in solving various kinds of phenomena or problems which cannot be easily understood by way of simple approaches. Its application is widespread to include problems in the military and even for such complex problems that need to be simplified through modelling technique to make it easily understood so as to institute much reliable solution through the use of some mathematical equations. Thus solutions are credible and reliable hence it relies on data using mathematical formulas. The applications of management science techniques are widespread, and they have been frequently credited with increasing the efficiency and productivity of business firms. Management science (also referred to as operations research, quantitative methods, quantitative analysis, and decision sciences) is part of the fundamental curriculum of most programs in business. Learning Outcomes At the end of this chapter, students must be able to: 1. Define management science 2. Illustrate and discuss the process of management science 3. Appreciate the importance of break-even analysis 4. Differentiate management science modelling techniques 5. Apply the different management science techniques 6. Appreciate and discuss the business usage of management science 7. Illustrate and explain the relevance of management science in decision support system COURSE MATERIALS Management Science Definition and Process Management science encompasses a logical, systematic approach to problem solving, which closely parallels what is known as the scientific method for attacking problems. It follows a generally recognized and ordered series of steps: (1) observation (2) definition of the problem (3) model construction (4) model solution (5) implementation of solution results. 1 Observation The first step in the management science process is the identification of a problem that exists in the system (organization). The person who normally identifies a problem is the manager because managers work in places where problems might occur. Figure 1.1 The management science process However, problems can often be identified by a management scientist, a person skilled in the techniques of management science and trained to identify problems, who has been hired specifically to solve problems using management science techniques. Definition of the Problem Once it has been determined that a problem exists, the problem must be clearly and concisely defined. Because the existence of a problem implies that the objectives of the firm are not being met in some way, the goals (or objectives) of the organization must also be clearly defined. A stated objective helps to focus attention on what the problem actually is. Model Construction A management science model is an abstract representation of an existing problem situation. It can be in the form of a graph or chart, but most frequently a management science model consists of a set of mathematical relationships. These mathematical relationships are made up of numbers and symbols. As an example, consider a business firm that sells a product. The product costs $5 to produce and sells for $20. A model that computes the total profit that will accrue from the items sold is Z = $20x - 5x x represents the number of units of the product that are sold, and Z represents the total profit that results from the sale of the product. The symbols x and Z are variables. The term variable is used because no set numeric value has been specified for these items. Z is a dependent variable because its value is dependent on the number of units sold; x is an independent variable because the number of units sold is not dependent on anything else (in this equation). The numbers $20 and $5 in the equation are referred to as parameters. Parameters are constant values that are generally coefficients of the variables (symbols) in an equation. 2 Parameters usually remain constant during the process of solving a specific problem. The parameter values are derived from data (i.e., pieces of information) from the problem environment. The equation as a whole is known as a functional relationship (also called function and relationship). The term is derived from the fact that profit, Z, is a function of the number of units sold, x, and the equation relates profit to units sold. Let us assume that the product is made from steel and that the business firm has 100 pounds of steel available. If it takes 4 pounds of steel to make each unit of the product, we can develop an additional mathematical relationship to represent steel usage: 4x = 100 lb. of steel This equation indicates that for every unit produced, 4 of the available 100 pounds of steel will be used. Now our model consists of two relationships: Z = $20x - 5x 4x = 100 The profit equation in this new model is an objective function, and the resource equation is a constraint. In other words, the objective of the firm is to achieve as much profit, Z, as possible, but the firm is constrained from achieving an infinite profit by the limited amount of steel available. To signify this distinction between the two relationships in this model, we will add the following notations: maximize Z = $20x - 5x subject to 4x = 100 This model now represents the manager’s problem of determining the number of units to produce. You will recall that we defined the number of units to be produced as x. Thus, when we determine the value of x, it represents a potential (or recommended) decision for the manager. Therefore, x is also known as a decision variable. The next step in the management science process is to solve the model to determine the value of the decision variable. Model Solution A management science solution technique usually applies to a specific type of model. Thus, the model type and solution method are both part of the management science technique. We are able to say that a model is solved because the model represents a problem. When we refer to model solution, we also mean problem solution. Note, however, that the value of the decision variable does not constitute an actual decision; rather, it is information that serves as a recommendation or guideline, helping the manager make a decision. Some management science techniques do not generate an answer or a recommended decision. Instead, they provide descriptive results: results that describe the system being modeled. 3 For example, suppose the business firm in our example desires to know the average number of units sold each month during a year. The monthly data (i.e., sales) for the past year are as follows: Monthly sales average 40 units (480 ÷ 12). This result is not a decision; it is information that describes what is happening in the system. The results of the management science techniques in this text are examples of the two types shown in this section: (1) solutions/decisions and (2) descriptive results. Implementation The final step in the management science process for problem solving described in Figure 1.1 is implementation. Implementation is the actual use of the model once it has been developed or the solution to the problem the model was developed to solve. Frequently the person responsible for putting the model or solution to use is not the same person who developed the model, and thus the user may not fully understand how the model works or exactly what it is supposed to do. Individuals are also sometimes hesitant to change the normal way they do things or to try new things. If the management science model and solution are not implemented, then the effort and resources used in their development have been wasted. Model Building: Break-even Analysis Break-Even Analysis In this section we will continue to explore the process of building and solving management science models, using break-even analysis, also called profit analysis. Break-even analysis is a modeling technique to determine the number of units to sell or produce that will result in zero profit. The break-even point gives a manager a point of reference in determining how many units will be needed to ensure a profit. Components of Break-Even Analysis The three components of break-even analysis are volume, cost, and profit. Volume is the level of sales or production by a company. It can be expressed as the number of units (i.e., quantity) produced and sold, Two type of costs are typically incurred in the production of a product: fixed costs and variable costs. Fixed costs are generally independent of the volume of units produced and sold. That is, fixed costs remain constant, regardless of how many units of product are produced within a given range. Fixed costs can include such items as rent on plant 4 and equipment, taxes, staff and management salaries, insurance, advertising, depreciation, heat and light, and plant maintenance. Taken together, these items result in total fixed costs. Variable costs are determined on a per-unit basis. Thus, total variable costs depend on the number of units produced. Variable costs include such items as raw materials and resources, direct labor, packaging, material handling, and freight. Total variable costs are a function of the volume and the variable cost per unit. This relationship can be expressed mathematically as Total variable cost = vcv where cv = variable cost per unit and v = volume (number of units) sold The total cost of an operation is computed by summing total fixed cost and total variable cost, as follows: total cost = total fixed cost + total variable cost TC = cf + vcv Where cf = fixed cost The third component in our break-even model is profit. Profit is the difference between total revenue and total cost. Total revenue is the volume multiplied by the price per unit, total revenue = vp where p = price per unit Now that we have developed relationships for total revenue and total cost, profit (Z) can be computed as follows: The break-even volume can be determined using the following formula: Sensitivity Analysis This relationship enables us to see how the level of profit (and loss) is directly affected by changes in volume. However, when we developed this model, we assumed that our parameters, fixed and variable costs and price, were constant. In reality such parameters are frequently uncertain and can rarely be assumed to be constant, and changes in any of the parameters can affect the model solution. The study of changes on a management science model is called sensitivity analysis—that is, seeing how sensitive the model is to changes. Sensitivity analysis can be performed on all management science models in one form or another. In fact, sometimes companies develop models for the primary purpose of 5 experimentation to see how the model will react to different changes the company is contemplating or that management might expect to occur in the future. Management Science Modeling Techniques Two of the five steps of the management science process - model construction and solution are the two steps that use the management science techniques. The techniques presented in this text can be loosely classified into four categories The term programming used to identify this technique does not refer to computer programming but rather to a predetermined set of mathematical steps used to solve a problem. This particular class of techniques holds a predominant position in this text because it includes some of the more frequently used and popular techniques in management science. In general, linear programming models help managers determine solutions (i.e., make decisions) for problems that will achieve some objective in which there are restrictions, such as limited resources or a recipe or perhaps production guidelines. Manufacturing companies develop linear programming models to help decide how many units of different products they should produce to maximize their profit (or minimize their cost), given scarce resources such as capital, labor, and facilities. Probabilistic Techniques Probabilistic techniques are distinguished from mathematical programming techniques in that the results are probabilistic. Mathematical programming techniques assume that all parameters in the models are known with certainty. Therefore, the solution results are assumed to be known with certainty, with no probability that other solutions might exist. A technique that assumes certainty in its solution is referred to as deterministic. In contrast, the results from a probabilistic technique do contain uncertainty, with some possibility that alternative solutions might exist. An example of a probabilistic technique is decision analysis, decision analysis, it is shown how to select among several different decision alternatives, given uncertain (i.e., probabilistic) future 6 conditions. For example, a developer may want to decide whether to build a shopping mall, build an office complex, build condominiums, or not build anything at all, given future economic conditions that might be good, fair, or poor, each with a probability of occurrence. Network Techniques Networks consist of models that are represented as diagrams rather than as strictly mathematical relationships. As such, these models offer a pictorial representation of the system under analysis. These models represent either probabilistic or deterministic systems. a network is drawn that shows the relationships of all the tasks and activities for a project, such as building a house or developing a new computer system. This type of network can help a manager plan the best way to accomplish each of the tasks in the project so that it will take the shortest amount of time possible. Other Techniques The analytical hierarchy process (AHP) easily classified. It is a mathematical technique for helping the decision maker choose between several alternative decisions, given more than one objective; however, it is not a form of linear programming, as is goal programming. Simulation, probably the single most unique topic in the text. It has the capability to solve probabilistic and deterministic problems and is often the technique of last resort when no other management science technique will work. In simulation, a mathematical model is constructed (typically using a computer) that replicates a real-world system under analysis, and then that simulation model is used to solve problems in the ―simulated‖ real-world system. In general, historical sales and demand data are used to build a mathematical function or formula that can be used to estimate product demand in the future. Business Usage of Management Science Techniques Not all management science techniques are equally useful or equally used by business firms and other organizations. Some techniques are used quite frequently by business practitioners and managers; others are used less often. The most frequently used techniques are linear and integer programming, simulation, network analysis (including critical path method/project evaluation and review technique [CPM/PERT]), inventory control, decision analysis, and queuing theory, as well as probability and statistics. An attempt has been made in this text to provide a comprehensive treatment of all the topics generally considered within the field of management science, regardless of how frequently they are used. Although some topics may have limited direct applicability, their study can reveal informative and unique means of approaching a problem and can often enhance one’s understanding of the decision-making process. The variety and breadth of management science applications and of the potential for applying management science, not only in business and industry but also in government, health care, and service organizations, are extensive. Areas of application include project planning, capital budgeting, production planning, inventory analysis, scheduling, marketing planning, quality control, plant location, maintenance policy, personnel management, and product demand forecasting, among others. 7 Management Science Models in Decision Support Systems Historically, management science models have been applied to the solution of specific types of problems; for example, a waiting line model is used to analyze a specific waiting line system at a store or bank. A decision support system (DSS) is a computer-based system that helps decision makers address complex problems that cut across different parts of an organization and operations. A DSS is normally interactive, combining various databases and different management science models and solution techniques with a user interface that enables the decision maker to ask questions and receive answers. In its simplest form any computer-based software program that helps a decision maker make a decision can be referred to as a DSS. Alternatively, enterprise-wide DSSs can encompass many different types of models and large data warehouses, and they can serve many decision makers in an organization. They can provide decision makers with interrelated information and analyses about almost anything in a company. A DSS can be primarily a data-oriented system, or it can be a model-oriented system. A new type of DSS, called an online analytical processing system, or OLAP, focuses on the use of analytical techniques such as management science models and statistics for decision making. A desktop DSS for a single user can be a spreadsheet program such as Excel to develop specific solutions to individual problems. On the other end of the DSS spectrum, an enterprise resource planning (ERP) system is software that can connect the components and functions of an entire company. It can transform data, such as individual daily sales, directly into information that supports immediate decisions in other parts of the company, such as ordering, manufacturing, inventory, and distribution. A large-scale DSS such as an ERP system in a company might include a forecasting model to analyze sales data and help determine future product demand; an inventory model to determine how much inventory to keep on hand; a linear programming model to determine how much material to order and product to produce, and when to produce it; a transportation model to determine the most cost-effective method of distributing a product to customers; and a network flow model to determine the best delivery routes. All these different management science models and the data necessary to support them can be linked in a single enterprise wide DSS that can provide many decisions to many different decision makers. 8