Introduction to Management Science and Quantitative Analysis

The Body of Knowledge: Management Science, Operations Research, and Decision Science

• The body of knowledge involving quantitative approaches to decision making is known by several names, including Management Science, Operations Research, and Decision Science.

• This field established its early roots during World War II.

• Management Science is currently flourishing in business and industry due to two primary factors:

  • Numerous methodological developments, such as the simplex method used for solving linear programming problems.

  • A virtual explosion in computing power available to organizations.

Problem Solving and Decision Making

• Problem solving is a comprehensive seven-step process. The first five steps of this process constitute the decision-making phase.

• Steps of Problem Solving:

  1. Define the problem.

  2. Determine the set of alternative solutions.

  3. Determine the criteria for evaluating the alternatives.

  4. Evaluate the alternatives.

  5. Choose an alternative (This step completes the decision-making process).

  6. Implement the selected alternative.

  7. Evaluate the results.

• Structuring the problem involves defining the problem, identifying alternatives, and determining criteria.

• Analyzing the problem involves evaluating the alternatives and choosing the final alternative.

Categorization of Decision Problems

• Decision problems are classified based on the number of criteria used for evaluation:

  • Single-criterion decision problems: Problems in which the objective is to find the best solution with respect to only one criterion.

  • Multicriteria decision problems: Problems that involve more than one criterion in the evaluation of alternatives.

Qualitative and Quantitative Analysis

• The analysis phase of the decision-making process can involve qualitative or quantitative approaches.

• Qualitative Analysis:

  • Largely based on the manager's personal judgment and experience.

  • Includes the manager's intuitive "feel" for the specific problem.

  • Characterized as being more of an art than a science.

• Quantitative Analysis:

  • Concentrates on quantitative facts or data associated with the problem.

  • Involves developing mathematical expressions that describe the objectives, constraints, and other existing relationships within the problem.

  • Uses one or more quantitative methods to generate a recommendation.

• Reasons to use a Quantitative Analysis approach:

  • The problem is complex.

  • The problem is very important.

  • The problem is new.

  • The problem is repetitive.

The Quantitative Analysis Process

• The quantitative analysis process follows a structured sequence of four main stages:

  • Model Development

  • Data Preparation

  • Model Solution

  • Report Generation

Models in Decision Making

• Models are representations of real objects or situations.

• Forms of Models:

  • Iconic models: Physical replicas or scalar representations of real objects.

  • Analog models: Physical in form but do not physically resemble the object being modeled.

  • Mathematical models: Represent real-world problems through a system of mathematical formulas and expressions based on key assumptions, estimates, or statistical analyses.

• Advantages of experimenting with models compared to real situations include:

  • Requires less time.

  • Is less expensive.

  • Involves less risk.

• The accuracy of conclusions and predictions depends on how closely the model represents the actual situation.

Components of Mathematical Models

• Objective Function: A mathematical expression describing the problem's objective, such as maximizing profit or minimizing cost.

  • Example: If profit is $10$ per unit and $x$ is the number of units produced, the objective function is $10x$.

• Constraints: A set of restrictions or limitations, such as production capacities.

  • Example: If each unit requires $5$ hours to produce and only $40$ hours are available per week, the constraint is $5x \le 40$.

• Uncontrollable Inputs: Environmental factors not under the control of the decision maker (e.g., the $10$ profit per unit, the $5$ hours required per unit, and the $40$ hour capacity).

• Decision Variables: Controllable inputs or decision alternatives specified by the decision maker (e.g., the production quantity $x$).

• Mathematical Model for Production:

  • Maximize $10x$

  • Subject to:

    • $5x \le 40$

    • $x \ge 0$ (Reflects that manufacturing a negative number of units is impossible).

Classification and Selection of Mathematical Models

• Models are classified based on the certainty of their inputs:

  • Deterministic Model: All uncontrollable inputs are known and cannot vary.

  • Stochastic (or Probabilistic) Model: Any uncontrollable inputs are uncertain and subject to variation. These models are often more difficult to analyze.

  • Example of Stochasticity: If the time required to produce a unit could vary between $3$ and $6$ hours based on raw material quality, the model is stochastic.

• Model Selection Considerations:

  • Cost/benefit considerations are critical when selecting a model.

  • A less complicated (and perhaps less precise) model may be more appropriate than a complex one due to considerations of cost and ease of solution.

Management Science Techniques

• Linear Programming: A problem-solving approach for maximizing or minimizing a linear function subject to linear constraints.

• Integer Linear Programming: Used for problems that function as linear programs but require some or all decision recommendations to be integer values.

• Nonlinear Programming: Used when objective or constraints involve non-linear relationships.

• Network Models (Distribution/Network Models): Specialized solution procedures for transportation system design, information system design, and project scheduling.

• Project Scheduling (PERT/CPM): Program Evaluation and Review Technique and Critical Path Method help managers plan, schedule, and control projects consisting of numerous separate tasks.

• Inventory Models: Used to maintain sufficient inventories to meet demand while incurring the lowest possible holding costs.

• Waiting Line (Queuing) Models: Help managers understand and make decisions regarding the operation of systems with waiting lines.

• Simulation: Employs computer programs to model the operation of a system and perform computations.

• Decision Analysis: Determines optimal strategies in situations with several alternatives and an uncertain pattern of future events.

• Forecasting: Techniques used to predict future aspects of business operations.

• Goal Programming: A technique for solving multicriteria decision problems, usually within a linear programming framework.

• Analytic Hierarchy Process (AHP): A multicriteria decision-making technique that allows for the inclusion of subjective factors.

• Markov-Process Models: Useful for studying the evolution of systems over repeated trials, such as the probability of machine failure or functioning over time.

Frequently Used Quantitative Methods

• Linear programming

• Integer programming

• Network models (such as transportation and transshipment models)

• Simulation