Introduction to Management Science College of Business Administration, CAU 안 봉 현 2005. 3. 3

Contents The Management Science Approach Problem Solving and Decision Making Quantitative Analysis and Decision Making Quantitative Analysis Model Development Data Preparation Model Solution Report Generation & Implementation Models of Cost, Revenue, and Profit Management Science Techniques

The Management Science Approach An approach to decision making based on the scientific method The application of a scientific approach to solving management problems in order to help managers make better decisions. The terms interchangeably - Management Science, Operations Research, Quantitative Methods, Quantitative Analysis, Decision Science Fredric W. Taylor – quantitative methods in management (early 1900s) World War II period – deal with strategic and tactical problems faced by the military (mathematicians, engineers, and behavioral scientists) Post-World War II – Methodological developments (ex. simplex method) and Computing Power Management Science can be used in a variety of organizations to solve many different types of problems In this course all of the modeling techniques and solution methods are mathematically based. The purpose of this course is to provide students with a sound conceptual understanding of the role that management science plays in the decision-making process

Problem Solving and Decision Making Problem solving – the process of identifying a difference between the actual and the desired state of affairs and the taking action to resolve the difference Decision making – generally associated with the first five steps of the problem-solving process Define the Problem Identify the Alternatives Determine the Criteria Evaluate the Alternatives Choose an Alternative Implement the Decision Evaluate the Results Problem Solving Decision Making < The Relationship between Problem Solving and Decision Making >

Problem Solving and Decision Making Single-criterion and Multicriteria decision problem Alternative Starting Salary Potential for Advancement Job Location 1. Rochester $38,500 Average 2. Dallas $36,000 Excellent Good 3. Greensboro 4. Pittsburgh $37,000 < Data for the Job Evaluation Decision-Making Problem > < An Alternate Classification of the Decision-Making Process >

Quantitative Analysis and Decision Making The reasons why a quantitative approach might be used in the decision-making process The Problem is complex, and the manager cannot develop a good solution without the aid of quantitative analysis The problem is especially important, and the manager desires a thorough analysis before attempting to make a decision The problem is new, and the manager has no previous experiences from which to draw The problem is repetitive, and the manager saves time and effort by relying on quantitative procedures to make routine decision recommendations Analyzing the Problem Qualitative Analysis Structuring the Problem Define the Problem Identify the Alternatives Determine the Criteria Summary and Evaluation Make the Decision Quantitative Analysis < The Role of Qualitative and Quantitative Analysis >

Quantitative Analysis – Model Development Model – the presentation of real objects or situations and can be presented in various forms. Iconic Models – physical replicas of real objects (ex. child’s toy truck). Analog Models – physical in form but do not have the same physical appearances as the object being modeled (ex. speedometer, thermometer) Mathematical Models – representations of a problem by a system of symbols and mathematical relationships or expressions. (ex. P = 10x ; total profit earned by selling x units) The purpose, or value, of any model is that it enables us to make inferences about the real situation by studying and analyzing the model. Experimenting with models requires less time and less expensive than experimenting with the real object or situation. Models also have the advantage of reducing the risk associated with experimenting with the real situation The value of model-based conclusions and decisions is dependent on how well the model represents the real situation. Because this course deals with quantitative analysis based on mathematical models, let us look more closely at the mathematical modeling process.

Quantitative Analysis – Model Development Objective function – the problem’s objective Such as maximization of profit or minimization of cost Constraints – possibly a set of restrictions Such as production capacities The success of the mathematical model and quantitative approach will depend on heavily on how accurately the objective and constrains can be expressed in terms of mathematical equations or relationships. ex.) complete mathematical model Maximize P = 10x objective function Subject to (s.t.) 5x ≤ 40 constraints X ≥ 0 Flow Chart for the Production Model Deterministic model – If all uncontrollable inputs to a model are known and cannot vary Stochastic or probabilistic model – If any of the uncontrollable inputs are uncertain and subject to variation

Quantitative Analysis – 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 Using the general notation c = profit per unit a = production time in hours per unit b = production capacity in hours General model Max cx S.t ax ≤ b x ≥ 0

Quantitative Analysis – Model Solution The analyst will attempt to identify the values of the decision variables that provide the “best” output for the model Optimal solution – the specific decision-variable value or values providing the “best” output for the model Infeasible – If a particular decision alternative does not satisfy one or more of the model constraints regardless of the objective function value. Feasible – If all constraints are satisfied. Decision alternative (Production Quantity) x Projected Profit Total Hours of Production Feasible solution? (Hours Used ≤ 40) Yes 2 20 10 4 40 6 60 30 8 80 100 50 No 12 120 < Trial-and-Error Solution for the Production Model >

Quantitative Analysis – Report Generation & Implementation The results of model must appear in a managerial report that can be easily understood by the decision maker. The report includes the recommended decision and other pertinent information about the results that may be helpful to the decision maker. The manager must oversee the implementation and follow-up evaluation of the decision During the implementation and follow-up, the manager should continue to monitor the contribution of the model. At times, this process may lead to requests for model expansion or refinement that will cause the management scientist to return to an earlier step of the quantitative analysis process. One of the most effective ways to ensure successful implementation is to include users throughout the modeling process.

Models of Cost, Revenue, and Profit Cost and Volume Models Fixed Cost & Variable Cost C(x) = 3000 + 2x Marginal Cost – the rate of change of the total cost with respect to production volume Revenue and Volume Models R(x) = 5x Marginal Revenue – the rate of change of the total revenue with respect to sales volume. Profit and Volume Models Derived from the revenue-volume and cost-volume models P(x) = R(x) - C(x) = 5x – (3000 + 2x) = -3000 + 3x Breakeven Analysis Breakeven point – the volume that result in total revenue equaling total cost P(x) = -3000 + 3x = 0 x = 1000

Management Science Techniques Linear Programming a problem-solving approach developed for situations involving maximization or minimization a linear function subject to linear constraints that limit the degree to which the objective can be pursued Integer Linear Programming Linear programs which the additional requirement that some or all of the decision recommendations be integer values Network Models A graphical description model of a problem consisting of circles called nodes that are interconnected by lines called arcs Project Scheduling: PERT/CPM Techniques that help managers carry out their project responsibilities for planning, scheduling, and controlling Inventory Models Maintaining sufficient inventories to meet demand for goods and, at the same time, incurring the lowest possible inventory holding costs Waiting Line or Queuing Models Techniques that help managers understand and make better decisions concerning the operation of systems involving waiting lines

Management Science Techniques Simulation A computer program to model the operation and perform simulation computations Decision Analysis Determine optimal strategies in situations involving several decision alternatives and an uncertain or risk-filled pattern of events Goal Programming A technique for solving multicriteria decision problems, usually within the framework of linear programming Analytic Hierarchy Process Multicriteria decision-making technique permits the inclusion of subjective factors in arriving at a recommended decision Forecasting Predict future aspects of a business operation Markov Process Models The evolution of certain systems over repeated trials Dynamic Programming An approach that allows us to break up a large problem in such a fashion that once all the smaller problems have been solved, we are left with an optimal solution to the large problem

Quantitative Analysis – Model Development (ctn’d) < Flow Chart for the Production Model >