Key Operations Research Techniques

Why This Matters

Operations research (OR) is the backbone of industrial engineering—it's where math meets real-world problem-solving. When you're tested on OR techniques, you're being evaluated on your ability to select the right tool for the right problem. Can you recognize when a situation calls for optimization versus simulation? Do you understand why some problems need integer solutions while others work with continuous variables? These distinctions matter because industrial engineers don't just crunch numbers—they translate messy business problems into solvable mathematical models.

The techniques in this guide fall into distinct categories: optimization methods, stochastic modeling, planning tools, and predictive analytics. Each category addresses a fundamentally different type of decision problem. Don't just memorize definitions—know what makes each technique appropriate for specific scenarios and how they connect to broader concepts like resource allocation, uncertainty management, and system efficiency. That's what separates a strong exam response from a mediocre one.

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Optimization Methods

These techniques find the best possible solution given constraints. The core principle: translate real-world limitations into mathematical inequalities, then systematically search for the optimal point.

Linear Programming

• Maximizes or minimizes a linear objective function subject to linear constraints—the foundation of all optimization in OR
• Decision variables are continuous, meaning solutions can take any value (e.g., 3.7 units), which simplifies computation
• Graphical solutions work for two variables; the simplex algorithm handles larger problems by moving along constraint boundaries

Integer Programming

• Requires some or all decision variables to be whole numbers—essential when fractional solutions don't make sense (you can't hire 2.3 employees)
• Computationally harder than LP because you can't simply round; the discrete solution space eliminates efficient gradient-based methods
• Branch-and-bound algorithms systematically explore possible integer solutions by dividing the problem into smaller subproblems

Network Analysis

• Models systems as nodes and arcs to find optimal paths, flows, or assignments—think supply chains, transportation routes, and communication networks
• Shortest path, maximum flow, and minimum spanning tree are the classic problem types you'll encounter
• Transportation and assignment problems are special cases with efficient solution algorithms beyond general LP

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Stochastic and Probabilistic Models

When uncertainty drives the system, deterministic optimization won't cut it. These techniques incorporate randomness and probability to model real-world variability.

Queuing Theory

• Analyzes waiting line behavior using arrival rates ($\lambda$) and service rates ($\mu$) to predict congestion and delays
• Key metrics include average wait time, queue length, and utilization—critical for designing service systems that balance cost and customer satisfaction
• M/M/1 and M/M/c models represent single-server and multi-server systems with Poisson arrivals and exponential service times

Markov Chains

• Models state transitions where the future depends only on the present—the "memoryless" property simplifies complex dynamic systems
• Transition probability matrices capture the likelihood of moving between states, enabling steady-state analysis
• Applications span equipment replacement, brand loyalty modeling, and machine maintenance scheduling

Simulation

• Mimics system behavior over time when analytical solutions are impossible or impractical—your go-to for complex, stochastic systems
• Monte Carlo methods use random sampling to estimate outcomes; discrete-event simulation tracks state changes at specific points
• Enables "what-if" analysis without disrupting real operations—test a new factory layout virtually before spending millions

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Planning and Scheduling Tools

These techniques structure complex projects and manage resources across time. The focus shifts from finding optimal values to coordinating activities and managing timelines.

Project Management (PERT/CPM)

• CPM identifies the critical path—the longest sequence of dependent tasks that determines minimum project duration
• PERT incorporates uncertainty by using three time estimates (optimistic, most likely, pessimistic) to calculate expected durations and variance
• Float/slack analysis reveals which activities can be delayed without affecting the project deadline—essential for resource leveling

Inventory Management

• EOQ (Economic Order Quantity) balances ordering costs against holding costs: $EOQ = \sqrt{\frac{2DS}{H}}$ where $D$ is demand, $S$ is ordering cost, and $H$ is holding cost
• Reorder point models determine when to place orders based on lead time and demand variability
• JIT (Just-In-Time) systems minimize inventory by synchronizing supply with production—reduces holding costs but increases vulnerability to disruptions

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Decision Support and Prediction

These techniques help engineers make better choices under uncertainty and anticipate future conditions. The emphasis is on structuring decisions and extracting patterns from data.

Decision Analysis

• Decision trees structure sequential choices by mapping alternatives, outcomes, and probabilities into a visual framework
• Expected value calculations weight outcomes by their probabilities: $EV = \sum p_i \cdot v_i$ where $p_i$ is probability and $v_i$ is value
• Sensitivity analysis tests how robust your decision is to changes in assumptions—critical when probabilities are estimated

Forecasting Techniques

• Time series methods (moving averages, exponential smoothing) extrapolate patterns from historical data—best when past behavior predicts the future
• Regression models identify relationships between variables to predict outcomes based on causal factors
• Forecast accuracy metrics (MAD, MSE, MAPE) quantify prediction error and guide method selection

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Quick Reference Table

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Self-Check Questions

1. A company needs to determine how many warehouses to open and where to locate them. Would you use linear programming or integer programming? Why?

2. Compare queuing theory and simulation: under what conditions would you choose simulation over an analytical queuing model?

3. A project manager knows task durations precisely from past experience. Should they use PERT or CPM, and what's the key difference?

4. Which two techniques both use probability distributions but serve fundamentally different purposes—one for modeling system states and one for making choices?

5. An FRQ asks you to recommend an OR technique for a manufacturing company facing highly variable customer demand and complex production constraints. Which technique allows testing multiple scenarios without real-world disruption, and why is it preferred over optimization methods here?