As indicated in the previous section, management science encompasses a logical, systematic approach to problem solving, which closely parallels what is known as the ## Figure 1.1. The management science process## (This item is displayed on page 3 in the print version)
The steps of the scientific method are (1) observation, (2) problem definition, (3) model construction, (4) model solution, and (5) implementation . ## ObservationThe first step in the management science process is the identification of a problem that exists in the system (organization). The system must be continuously and closely observed so that problems can be identified as soon as they occur or are anticipated. Problems are not always the result of a crisis that must be reacted to but, instead, frequently involve an anticipatory or planning situation. The person who normally identifies a problem is the manager because the managers work in places where problems might occur. 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. A management scientist is a person skilled in the application of management science techniques . ## Definition of the ProblemOnce it has been determined that a problem exists, the problem must be clearly and concisely defined . Improperly defining a problem can easily result in no solution or an inappropriate solution. Therefore, the limits of the problem and the degree to which it pervades other units of the organization must be included in the problem definition. 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 A model is an abstract mathematical representation of a problem situation . 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 = $20 x - 5 x A variable is a symbol used to represent an item that can take on any value . In this equation 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 Parameters are known, constant values that are often coefficients of variables in equations . The numbers $20 and $5 in the equation are referred to as Data are pieces of information from the problem environment . The equation as a whole is known as a A model is a functional relationship that includes variables, parameters, and equations . Because only one functional relationship exists in this example, it is also the model . In this case the relationship is a model of the determination of profit for the firm. However, this model does not really replicate a problem. Therefore, we will expand our example to create a problem situation. 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: 4 x = 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:
We say that the profit equation in this new model is an
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 ## Model SolutionA management science technique usually applies to a specific model type. Once models have been constructed in management science, they are solved using the management science techniques presented in this text. 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.
For the example model developed in the previous section,
the solution technique is simple algebra. Solving the constraint equation for x , we have
Substituting the value of 25 for x into the profit function results in the total profit:
Thus, if the manager decides to produce 25 units of the product and all 25 units sell, the business firm will receive $375 in profit. 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 . 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:
A management science solution can be either a recommended decision or information that helps a manager make a decision . 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. |

Introduction to Management Science (10th Edition)

ISBN: 0136064361

EAN: 2147483647

EAN: 2147483647

Year: 2006

Pages: 358

Pages: 358

Authors: Bernard W. Taylor

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