Operations Research Models

Operations Research (OR) and Management Science (MS)

• Operations Research (OR) is another term for Management Science (MS).
• In the US, OR and MS are combined to form OR/MS or ORMS.
• Other terms used in this field include Industrial Engineering (IE) and Decision Science (DS).

Operations Research Models

• Deterministic Models: assume all data are known with certainty, involve optimization, and examples include Linear Programming, Network Optimization, Integer Programming, Nonlinear Programming, and Inventory Models.
• Stochastic Models: explicitly represent uncertain data via random variables or stochastic processes, characterize/estimate system performance, and examples include Discrete-Time Markov Chains, Continuous-Time Markov Chains, Queuing Theory, Decision Analysis, Game Theory, Inventory Models, and Simulation.

History of Operations Research (OR)

• OR is a relatively new discipline, emerging in the late 1930s.
• Key contributors to the development of OR include Frederick Taylor, Henry Gannt, F.W.Harris, William Shewart, Andrey A. Markov, E.K. Erlang, H. Dodge, and H.R. Roming.

Problem Solving Process

• The goal is to solve a problem, involving a valid and tractable model, that provides a useful solution.
• The process involves formulating the problem, constructing a model, preparing data, testing the model and solution, and implementing the solution.

The Situation and Problem Formulation

• The situation may involve current operations or proposed expansions due to market shifts.
• The problem may become apparent through consumer complaints, employee suggestions, or a conscious effort to improve efficiency or respond to an unexpected crisis.
• Problem formulation involves describing the system, defining variables, stating assumptions, and selecting performance measures.

Data Preparation and Constructing a Model

• Data preparation is a critical step, requiring a significant amount of time and attention to avoid data collection errors.
• A model translates the problem from verbal, qualitative terms to logical, quantitative terms, and may take the form of iconic, analog, or mathematical models.
• Mathematical models represent real-world problems through a system of mathematical formulas and expressions based on key assumptions, estimates, or statistical analyses.

Model Development and Mathematical Models

• Models are representations of real objects or situations, and may be iconic, analog, or mathematical.
• Mathematical models relate decision variables with fixed or variable parameters, and frequently seek to maximize or minimize some objective function subject to constraints.
• Mathematical models may be stochastic or deterministic, and the values of the decision variables that provide the mathematically-best output are referred to as the optimal solution.

Example: Iron Works, Inc. Mathematical Model

• The total monthly profit is a function of the monthly production levels of product 1 and product 2.
• The mathematical model involves maximizing the total monthly profit subject to constraints on steel usage, production levels, and non-negativity.

This quiz covers various models in Operations Research, including deterministic and stochastic models, linear programming, network optimization, and more.