Introduction to Management Science Chapter 1

Introduction to Management Science

• Management science is a body of knowledge focused on quantitative approaches to decision-making.
• It includes decision science and operations research.
• It has roots in World War II and is used extensively in businesses and industries.
• Key factors driving its success include methodological developments, particularly in linear programming (e.g., simplex method), and the explosion of computing power.

Chapter 1 - Introduction

• Chapter Objectives: Define management science, operations research, and decision science. List steps in decision-making, describing both qualitative and quantitative approaches. Explain the modeling process. Formulate basic models for cost, revenue, and profit to calculate the breakeven point.
• Chapter Contents: The chapter covers Problem Solving and Decision Making, Quantitative Analysis and Decision Making, Models of Cost, Revenue, and Profit, and Management Science Techniques.

1-1 Problem Solving

• Problem solving is the process of identifying a difference between the actual and desired state and then taking action to resolve it.
• Seven steps:
  • Define the problem
  • Determine alternative solutions
  • Determine criteria for evaluating solutions
  • Evaluate alternatives
  • Choose an alternative (make a decision)
  • Implement the selected alternative
  • Evaluate the results

1-1 Decision-Making Process

• Decision-making refers to the first five steps of the problem-solving process.
• Single-criterion problems: focus on finding the best solution based on a single criterion.
• Multi-criteria problems: involve more than one criterion.
• Decision is the choice of the best alternative.

1-2 Quantitative Analysis and Decision Making

• Decision-making process: A flowchart for structuring and analyzing the problem combines the first three steps (defining the problem, identifying alternatives, determining criteria) under "Structuring the problem" and the last two steps (evaluating alternative and choosing an alternative) under "Analyzing the problem".
• Qualitative analysis: Based largely on the manager's judgment and experience. Includes intuitive "feel" for the problem. More of an art than science.
• Quantitative analysis: Based on the quantitative facts or data associated with the problem. Uses mathematical expressions to describe objectives, constraints, and other relationships in the problem. One or more quantitative methods may be used to make a recommendation.

1-3 Quantitative Analysis

• Reasons for using quantitative analysis:
  • Complex problems
  • Very important problems
  • New problems
  • Repetitive problems
• Four steps of quantitative analysis:
  • Model development
  • Data preparation
  • Model solution
  • Report generation

1-3 Step 1: Model Development

• A model is a representation of a real object or situation.
• Main model forms:
  • Iconic models: physical replicas of real objects
  • Analog models: do not physically resemble the object
  • Mathematical models: use expressions/formulas with assumptions and statistical analyses
• Models can save time, reduce cost, and reduce risk when compared with experimenting with the real situation.

1-3 Example: Simple Production Problem

• A mathematical model has an objective function with controllable inputs (decision variables), and constraints influenced by uncontrollable inputs (environmental factors).
• An example problem seeks the optimal production volume maximizing profit.

1-3 A Mathematical Model

• Decision variable: number of units produced.
• Objective function: with 10$ profit per unit is 10*x.
• Uncontrollable Inputs: Example; profit per unit ($10) & production time per unit(5 hours).
• Constraints: The production capacity is 40 hours/week - Example ; 5x ≤ 40.

1-3 Types of Mathematical Models

• Deterministic models: all inputs known and unchangeable.
• Stochastic models: one or more inputs are uncertain & variable.

1-3 Step 2: Data Preparation

• Data preparation must specify all uncontrollable inputs before analysis.
• Prepare enough data to form the mathematical model- data preparation can be complex with many errors.

1-3 Step 3: Model Solution

• Trial-and-error process to find an optimal solution for a mathematical model.
• Identify decision variable values yielding the best output, the optimal solution.
• Infeasible alternatives may not satisfy all constraints.

1-3 A Flow Chart of Simple Production Model

• Summarizes all input and how the model works.

1-3 After the Solution

• Model validation: use small known issues as a test for the larger problem
• Report generation: report should be easy to understand, the report should include recommended decision and other relevant information (Example: sensitivity of model to assumptions/data).

1-4 Models of Cost, Revenue, and Profit

• Quantitative models relating decision variables (e.g., production or sales volume) to objective functions (e.g., cost, revenue, profit).

1-4 Cost-Volume Models

• Example given to find the total cost of producing a certain number of units (e.g. total cost of producing a volume of x units of the Viper).
• The marginal cost = the increase in cost associated with producing one more unit.

1-4 Revenue and Profit-Cost Models

• Models relating revenue (and associated profit) to the volume of goods sold, considering the total revenue from selling x units.

1-4 breakeven analysis

• Total revenue equals total costs, point where there is no profit, nor loss
• Finding a breakeven point involves setting the total profit = 0 & solving for x (volume).

1-5 (Most Frequent) Management Science Techniques

• Linear programming: Maximizing/minimizing a linear function subject to linear constraints.
• Integer linear programming: Linear programming with integer requirement constraints.
• Distribution & network models: Specialized solutions for transportation, network, information systems, and project scheduling problems.
• Simulation: computer programs for simulation computations modeling a system's operation.

1-5 (Other) Management Science Techniques

• Nonlinear programming: Maximizing/minimizing a nonlinear function with nonlinear constraints.
• Inventory models: Maintaining required inventory while minimizing inventory costs.
• Waiting line models: Assessing and improving decision-making of waiting lines/queues.
• Forecasting methods: Prediction of future aspects.
• Goal programming: Solving multi-criteria decision problems within linear programming frameworks.
• Analytic hierarchy process, PERT & CPM: Aids in planning tasks.
• Decision analysis: Determines optimal strategies in the presence of multiple alternatives & uncertain future outcomes.
• Markov-process models: Analyzing how systems evolve over repeated trials.

Summary

• Management science helps managers make better decisions by providing quantitative tools for analyzing and resolving real-world business problems.
• Mathematical models represent real-world situations with key aspects but are not perfect representations.
• Management science aims to find the "best" or optimal solution for a problem.

Explore the fundamental concepts of management science in this quiz based on Chapter 1. Learn about operations research, decision-making processes, and various models used in quantitative analysis. Understand how these principles apply to real-world business scenarios, including cost, revenue, and profit calculations.