Unit 1: Introduction to Operations Research [5 Hours]
This unit lays the conceptual foundation for OR as a discipline. It traces the origin and growth of OR, introduces the tools and methodology used, and defines the roles of the people involved. Understanding this unit is essential before studying any specific OR technique — every later topic builds on what is covered here.
1.1 Introduction to Operations Research
Core Definition
Operations Research (OR) is a scientific discipline that applies mathematical models, statistical analysis, and systematic reasoning to support complex decision-making in organizations. Its goal is to identify the best possible course of action from a set of alternatives under given constraints.
Think of OR as a toolbox for managers. Instead of guessing or relying on intuition, OR gives a structured method to analyze a problem, build a model, and find the solution that works best — whether that means lowest cost, shortest time, or maximum profit.
Detailed Explanation
OR originated in the military context of World War II and later expanded into business, industry, and government. The core idea is to treat complex management problems as systems that can be described mathematically and then solved analytically.
Several defining characteristics shape OR as a discipline:
- Systems approach: OR looks at the problem as a whole, not in isolated parts. Changing one variable may affect the entire system.
- Scientific method: Problems are defined, hypotheses (models) are formed, tested, and validated before implementation.
- Interdisciplinary nature: OR draws from mathematics, statistics, economics, engineering, computer science, and management.
- Model-based reasoning: OR represents real problems as mathematical or simulation models, which are then solved to identify optimal solutions.
- Goal — optimization: The purpose is always to find the best outcome: maximize profit, minimize cost, or optimize performance within constraints.
OR is also known as Operational Research, Management Science, or Decision Science in different academic and geographic contexts. All three terms refer to the same core discipline.
Let's Break It Down
Imagine a hospital needs to schedule doctors and nurses across three shifts to cover patients while keeping overtime costs low. A manager guessing the schedule might overstaff one shift and understaff another. OR builds a mathematical model of the problem — staff hours, patient demand, cost per shift — and solves it to find the most efficient assignment. That is OR: replacing guesswork with a calculated, defensible optimal decision.
Summary
- OR applies scientific methods and mathematical models to complex organizational decision problems.
- It is interdisciplinary, drawing on math, statistics, economics, and management science.
- Its core goal is optimization: the best outcome under given constraints.
- Also known as Management Science, Operational Research, or Decision Science.
- OR treats organizations as systems, not collections of isolated parts.
One-Liner Revision
Operations Research is a scientific, model-based approach to finding the best possible decision in complex organizational problems.
1.2 History of Operations Research
Core Definition
The history of Operations Research traces the discipline's evolution from its military origins in World War II to its widespread application in business, industry, and government through the latter half of the twentieth century.
OR started during WWII when governments needed a smarter way to solve military logistics problems — radar deployment, convoy routing, bombing efficiency. After the war, the same scientific methods moved into factories, airlines, hospitals, and corporations.
Detailed Explanation
The major milestones in OR's development:
Pre-WWII Foundations: Scientific management (Frederick Taylor, early 1900s) and the work of A.K. Erlang on queuing theory (1909) laid conceptual groundwork. These were isolated contributions rather than a unified discipline.
WWII Birth of OR (1939–1945): British military scientists formed the first formal OR groups. P.M.S. Blackett led a multidisciplinary team that applied scientific methods to optimize radar positioning, bombing missions, and convoy strategy. Their work produced measurable military improvements and demonstrated that operational problems could be solved scientifically. The United States followed with its own OR groups across military branches.
Post-WWII Expansion (late 1940s–1950s): After the war, OR techniques transferred rapidly into industry. In 1947, George Dantzig developed the Simplex Method for solving Linear Programming problems — one of the most important algorithmic contributions in OR history. Industry adopted OR for production planning, distribution, and resource management.
Institutionalization (1950s): Professional societies were established. The Operations Research Society of America (ORSA) was founded in 1952. Academic journals and university programs followed, embedding OR as a recognized formal discipline.
Computer Era (1960s–present): Computers transformed OR's practical scope. Problems too large for hand calculation became solvable. Simulation, nonlinear programming, and large-scale network models all became feasible with increasing computing power. Today, OR techniques run inside airline booking systems, supply chain software, and financial trading algorithms.
Memory Hook
Remember the OR timeline with: W-D-O-C — War (WWII birth) → Dantzig Simplex 1947 → ORSA 1952 → Computers scale it up (1960s+).
Summary
- OR was born during WWII when British scientists (led by Blackett) solved military logistics problems scientifically.
- George Dantzig's Simplex Method (1947) was the critical post-war breakthrough, making LP practically solvable.
- Post-war OR moved from defense into industry, healthcare, and transportation.
- ORSA (1952) marked OR's recognition as a formal academic and professional discipline.
- Computers from the 1960s onward enabled large-scale OR application that was previously impossible.
One-Liner Revision
OR emerged from WWII military science, was formalized with Dantzig's Simplex Method (1947) and ORSA (1952), and scaled with computers from the 1960s into modern industry.
1.3 Stages of Development of Operations Research
Core Definition
The stages of development of an OR study are the systematic phases through which a real-world problem is converted into a solvable mathematical model, solved, validated, and implemented as an organizational decision. These stages form the standard OR methodology.
The stages are the workflow of OR: observe the problem carefully, build a model that represents it, solve the model, check that the solution makes sense, put it into practice, and keep watching to make sure it still works as conditions change.
Detailed Explanation
An OR study follows six defined phases. They are iterative, not strictly linear — findings at a later stage often send the analyst back to revise an earlier one.
Stage 1: Problem Formulation
The OR process begins by clearly defining the problem. This involves identifying the decision-maker's objective (e.g., minimize transportation cost), the decision variables (what can be controlled), and the constraints (what limits the choices). A poorly defined problem leads to a model that solves the wrong thing. The manager and OR specialist must agree on what the problem is before any modeling begins.
Stage 2: Model Construction
A mathematical or simulation model is built to represent the problem. The model translates real-world relationships into equations, inequalities, or algorithms. Every model is a simplification — it includes the critical variables and ignores minor details. The quality of the final solution depends directly on how well the model captures the essential structure of the problem.
Stage 3: Model Solution
Appropriate OR techniques are applied to solve the model. For linear programming problems, the Simplex Method is used. For queuing problems, analytical formulas apply. For complex or stochastic systems, simulation is run. The output is an optimal or near-optimal solution within the model's structure — not necessarily in the real world yet.
Stage 4: Model Validation
The solution is tested against reality. The model is run against historical data to check whether it would have produced results consistent with known outcomes. Sensitivity analysis is also performed — parameters are varied to see how stable the solution is. If the model behaves unrealistically, it must be revised before implementation. This stage is the quality gate of the entire process.
Stage 5: Implementation
The validated solution is presented to management and put into operational practice. This means translating a mathematical result into a real decision: a new production schedule, a revised route plan, or an updated inventory policy. Successful implementation requires clear communication and genuine buy-in from the people who will use the solution.
Stage 6: Monitoring and Control
After implementation, the solution is tracked over time. Conditions change — demand shifts, costs fluctuate, regulations change. The model must be updated when the real-world situation diverges significantly from its assumptions. OR is an ongoing process, not a one-time event.
The flow: Problem Formulation → Model Construction → Model Solution → Model Validation → Implementation → Monitoring and Control
Let's Break It Down
A courier company wants to reduce fuel costs. Stage 1: define the objective as "minimize total daily fuel use across all routes." Stage 2: build a network model with distances, delivery points, and vehicle capacities. Stage 3: a routing algorithm finds the shortest paths. Stage 4: test the model using last month's delivery data — did it predict actual fuel use accurately? Stage 5: assign drivers the optimized routes. Stage 6: track monthly fuel bills. If costs creep up again after three months, revisit the model with updated road and delivery data.
Common Mistake
Students list these as strictly sequential steps and assume validation always follows solution without looping back. In reality, validation frequently reveals flaws in the model construction, requiring a return to Stage 2. The stages are iterative. Describing them as linear misrepresents how OR actually works.
Test Yourself
- Why is problem formulation considered the most critical stage in OR?
- What is the purpose of model validation, and what happens when validation fails?
- Why is the monitoring stage necessary even after a successful implementation?
Answers:
1) A poorly defined problem leads to a model that solves the wrong objective. All later stages depend entirely on getting Stage 1 correct.
2) Validation verifies that the model reflects real-world behavior by testing against historical data. If it fails, the model is revised before any decision is implemented, preventing costly mistakes.
3) Real-world conditions change over time. A solution that was optimal when built can become suboptimal or counterproductive as demand, costs, or constraints shift.
Summary
- Six iterative stages: Problem Formulation → Model Construction → Solution → Validation → Implementation → Monitoring.
- Problem formulation is the most critical stage; an incorrect objective invalidates all subsequent work.
- Model validation uses historical data and sensitivity analysis as a quality gate before real-world action.
- The stages are iterative: validation or implementation findings often require returning to earlier stages.
- Monitoring ensures the solution remains effective as real-world conditions evolve.
One-Liner Revision
OR follows six iterative stages from problem definition to monitoring, with model validation as the critical checkpoint before any real-world decision is implemented.
1.4 Relationship between Manager and OR Specialist
Core Definition
The relationship between the manager and the OR specialist is a collaborative partnership in which the manager contributes organizational context and decision authority, while the OR specialist provides analytical modeling and technical expertise to solve the defined problem.
The manager knows what the problem is and has the power to act on the solution. The OR specialist knows how to model and solve it mathematically. Neither can succeed alone — the manager without modeling tools, the specialist without domain knowledge.
Detailed Explanation
The two roles are complementary but distinct:
The Manager's Role:
- Defines the problem and sets the organizational objectives.
- Provides domain knowledge, historical data, and real-world constraints.
- Evaluates the practical feasibility of proposed solutions.
- Makes the final decision and authorizes implementation.
- Ensures organizational support and resource allocation for the OR project.
The OR Specialist's Role:
- Translates the manager's problem description into a mathematical or simulation model.
- Selects appropriate OR techniques and applies them correctly.
- Validates the model and interprets results in business terms.
- Communicates findings in language the manager can act on — not buried in equations.
- Proposes alternative approaches when the initial model is insufficient.
Why collaboration is essential: If the manager does not communicate the problem clearly, the OR specialist builds a model solving the wrong objective. If the specialist presents results in pure mathematical notation, the manager cannot interpret or implement them. The project fails at either breakdown point.
Common challenges in the relationship:
- Communication gap: OR specialists use technical language; managers may not follow the methodology. Specialists must translate results into plain business terms.
- Trust gap: Managers may distrust solutions that conflict with their intuition or years of experience.
- Data access problems: OR specialists need accurate, complete data. Managers control data availability and its quality.
- Implementation resistance: Even a correct solution may be set aside if management is not convinced of its validity or relevance.
Test Yourself
- What specific contribution does each party make to an OR project?
- What is the most common source of failure in the manager-specialist relationship, and how can it be addressed?
Answers:
1) The manager contributes organizational knowledge, data, business constraints, and decision authority. The OR specialist contributes model construction, technique selection, and analytical interpretation.
2) The communication gap. It is addressed by requiring OR specialists to present results in business language — decisions, costs, trade-offs — rather than mathematical formulations alone.
Summary
- The manager defines the problem and implements solutions; the OR specialist models and solves it.
- Collaboration is essential: the manager provides business context; the specialist provides analytical rigor.
- A communication gap between the two is the most common failure point in OR projects.
- OR specialists must translate mathematical results into actionable business decisions.
- Trust, data access, and organizational support are recurring practical challenges.
One-Liner Revision
The manager defines and decides; the OR specialist models and solves — but both must communicate effectively for the project to succeed.
1.5 OR Tools and Techniques
Core Definition
OR tools and techniques are the mathematical, statistical, and computational methods used to model and solve decision problems. Each technique is suited to a specific class of problem structure, and selecting the right tool is as important as applying it correctly.
OR tools are the problem-solving instruments of the discipline. Choosing the right one depends on the nature of the problem — just as a surgeon picks a different instrument for each procedure, the OR specialist selects the technique that fits the problem's structure.
Detailed Explanation
The major OR tools and techniques, each with its domain of application:
1. Linear Programming (LP)
Optimizes (maximizes or minimizes) a linear objective function subject to linear inequality constraints. Applied in production planning, resource allocation, diet formulation, and blending problems. The Simplex Method is the primary solution algorithm for LP.
2. Integer Programming
A variant of LP where some or all decision variables must be whole numbers (integers). Used when partial solutions are meaningless — for example, you cannot assign 2.5 machines to a task or build 3.7 factories.
3. Transportation and Assignment Models
Specialized LP models. The Transportation Model finds the minimum-cost way to ship goods from multiple sources to multiple destinations. The Assignment Model optimally assigns n jobs to n workers or machines to minimize total cost or time.
4. Network Analysis — PERT and CPM
PERT (Program Evaluation and Review Technique) and CPM (Critical Path Method) are project management techniques that schedule tasks, identify the critical path (the sequence of tasks that determines minimum project duration), and highlight bottlenecks. PERT handles uncertain task durations; CPM assumes known durations.
5. Queuing Theory (Waiting Line Models)
Analyzes systems where customers (people, machines, jobs) arrive at service points and must wait. Used to find the optimal balance between waiting time and service capacity cost in banks, hospitals, call centers, and manufacturing lines.
6. Simulation
When the real system is too complex or stochastic for exact analytical modeling, a computer simulation mimics system behavior over time using random inputs. It is the most flexible OR tool but yields approximate rather than provably optimal solutions.
7. Game Theory
Studies strategic decision-making in situations where two or more decision-makers (players) have conflicting or partially aligned interests. Applied in competitive pricing, bidding strategy, and negotiation analysis.
8. Decision Analysis
Provides frameworks for making decisions under uncertainty or risk. Includes decision trees, expected value analysis, and Bayesian updating. Applied when outcomes depend on uncertain future events (nature, competitor actions, market conditions).
9. Inventory Models
Determine optimal inventory policies — how much to order and when — to minimize total cost (holding cost + ordering cost + shortage cost). The Economic Order Quantity (EOQ) model is the foundational result.
10. Dynamic Programming
Solves multi-stage decision problems by breaking them into smaller, overlapping subproblems and combining optimal sub-solutions. Applied in resource allocation over time, equipment replacement scheduling, and shortest-path routing.
11. Goal Programming
An extension of LP for problems with multiple, possibly conflicting objectives. Instead of optimizing a single goal, it minimizes total deviation from several priority targets simultaneously. Used when trade-offs between objectives must be formalized.
Summary
- LP optimizes linear problems; Integer Programming extends it to whole-number decisions.
- Transportation and Assignment models are specialized LP variants for logistics and job scheduling.
- PERT/CPM manage project schedules and identify critical paths.
- Queuing theory optimizes waiting line systems; simulation handles complex stochastic systems.
- Decision analysis, game theory, inventory models, dynamic programming, and goal programming each address specific problem types — uncertainty, competition, stock control, multi-stage decisions, and multiple objectives.
Test Yourself
- What is the difference between Linear Programming and Integer Programming?
- When would a practitioner prefer simulation over an analytical OR technique?
- Name the OR technique used to schedule project tasks and identify bottlenecks.
Answers:
1) In LP, decision variables can take fractional values; in Integer Programming they must be whole numbers, making the problem computationally harder.
2) When the system involves randomness, complex interdependencies, or is too large to represent exactly with equations — simulation gives approximate but practical results.
3) PERT (for uncertain durations) and CPM (for known durations) — both are network analysis techniques.
One-Liner Revision
OR tools range from LP and queuing models for exact optimization to simulation and game theory for complex or competitive problems — each matched to a specific problem structure.
1.6 Applications of Operations Research
Core Definition
The applications of Operations Research span every sector where complex decisions must be made under constraints — including defense, manufacturing, transportation, finance, healthcare, agriculture, and public administration.
OR is relevant wherever there are limited resources and multiple competing objectives. That describes nearly every real organization, which is why OR techniques appear in industries as different as airlines, hospitals, and banks.
Detailed Explanation
Key application domains:
Defense and Military: OR's birthplace. Applications include optimal troop and equipment deployment, logistics and supply chain management, weapon system performance analysis, and search-and-rescue operation planning.
Manufacturing and Production: Production scheduling, machine loading, quality control, plant layout design, and workforce planning. LP models determine the optimal product mix when multiple products share limited machine time and raw materials.
Transportation and Logistics: Airline crew scheduling, vehicle routing, railway timetabling, and port container management. Airlines are among the heaviest OR users — flights, crews, and ticket prices are all OR-optimized.
Finance and Banking: Portfolio optimization (Markowitz model), credit risk analysis, cash flow management, ATM cash replenishment scheduling, and fraud detection modeling.
Healthcare: Hospital bed and operating room allocation, ambulance routing, drug supply chain optimization, nurse scheduling, and epidemic spread modeling.
Agriculture: Optimal crop mix selection under land and water constraints, fertilizer allocation, irrigation scheduling, and food distribution logistics.
Retail and Supply Chain: Inventory management using EOQ-based models, warehouse location decisions, demand forecasting integration, and supplier selection and contract optimization.
Telecommunications: Network capacity planning, call routing optimization, and radio spectrum allocation for wireless systems.
Government and Public Services: Resource allocation for public welfare programs, urban planning and zoning decisions, waste collection routing, police patrol deployment, and emergency service positioning.
Summary
- OR applies across defense, manufacturing, transportation, finance, healthcare, agriculture, retail, telecom, and government.
- The common thread: limited resources, multiple objectives, and decisions too complex for intuition alone.
- Airlines are a prominent OR example — scheduling, crew assignment, and pricing are all OR-optimized.
- Healthcare OR ranges from nurse scheduling to epidemic modeling and resource allocation.
One-Liner Revision
OR applies wherever decisions must be optimized under constraints — from military logistics and airline scheduling to hospital resource planning and investment portfolio design.
1.7 Limitations of Operations Research
Core Definition
The limitations of Operations Research are the practical, mathematical, and organizational barriers that reduce the accuracy, accessibility, or applicability of OR models in real-world decision-making environments.
OR is powerful but not perfect. Real problems are messier than any model can fully represent, and not every organization has the resources or willingness to apply OR methods effectively.
Detailed Explanation
The key limitations of OR, each with its cause and consequence:
1. Mathematical Complexity: Many OR models involve advanced mathematics — linear algebra, calculus, probability theory, and combinatorics. Most managers lack the technical background to understand, evaluate, or challenge the models being used on their behalf. This creates a dependency on specialists and reduces accountability.
2. Difficulty in Quantifying All Variables: Not all relevant factors can be expressed as numbers. Human behavior, organizational culture, political pressures, employee morale, and ethical considerations are difficult or impossible to incorporate into a mathematical model. OR handles what can be quantified; everything else is excluded, even when it matters.
3. Unrealistic Assumptions: OR models simplify reality through assumptions — linear relationships between variables, constant demand, independent decision variables, stable cost structures. If these assumptions do not hold in the actual environment, the model's output can be misleading or actively wrong. A model optimized under false assumptions may produce a worse outcome than the original decision.
4. High Cost of Development: Building, validating, and maintaining an OR model requires significant investment in time, expert personnel, software, and data infrastructure. This makes OR inaccessible to small organizations with limited budgets, and the investment may not be justified for low-frequency or low-stakes decisions.
5. Resistance to Implementation: Even a mathematically correct solution may be rejected by managers who distrust model-based decisions or by employees who fear the operational changes it implies. Organizational culture and human resistance to change can prevent sound OR solutions from ever being acted on.
6. Dependence on Accurate Data: OR models are only as reliable as the data fed into them. Inaccurate, outdated, or incomplete data leads to flawed outputs regardless of the model's sophistication. This is the "garbage in, garbage out" problem: the model cannot compensate for bad inputs.
7. Static Models in Dynamic Environments: Most OR models represent the system at a point in time. Real-world conditions change continuously — prices shift, regulations change, technology evolves, demand fluctuates. A model that was optimal when built may become suboptimal quickly without constant revision and updating.
8. Requirement for Specialized Expertise: OR teams need professionals skilled in mathematics, computer science, statistics, and domain knowledge simultaneously. Such personnel are scarce and expensive. In developing economies and small organizations, the shortage of trained OR specialists is a practical ceiling on adoption.
Common Mistake
Students confuse model assumptions with model limitations. An assumption is a deliberate simplification chosen to make the model tractable. A limitation is what happens when that simplification breaks contact with reality. Every model has assumptions; limitations describe when and why those assumptions cause the model to fail — these are not the same thing.
Test Yourself
- Why can OR models not fully represent all factors relevant to a real-world decision?
- What is the "garbage in, garbage out" problem in OR?
- Why might a mathematically correct OR solution still fail to be implemented in practice?
Answers:
1) Many relevant factors — human behavior, organizational culture, political pressures — cannot be quantified and therefore cannot be included in a mathematical model.
2) If input data is inaccurate, outdated, or incomplete, even a well-structured model will generate incorrect results. The quality of the output is bounded by the quality of the input data.
3) Organizational resistance, manager distrust, or employee reluctance to change can prevent a valid solution from being adopted. Implementation failure is often a human and organizational challenge, not a technical one.
Summary
- OR requires mathematical expertise, accurate data, and significant development resources — limiting accessibility.
- Models rely on simplifying assumptions that may not hold in real environments.
- Non-quantifiable factors — behavior, culture, ethics — are excluded from mathematical models.
- Static models become outdated as real-world conditions change over time.
- Implementation may fail due to organizational resistance, even when the model is correct.
One-Liner Revision
OR is limited by mathematical complexity, unrealistic assumptions, data dependence, inability to quantify all factors, high development cost, and organizational resistance to model-based decisions.
Whole Chapter Summary
- Introduction to OR: A scientific, interdisciplinary, model-based discipline that applies mathematical optimization and statistical analysis to complex organizational decision problems. Also called Management Science or Decision Science.
- History: Born in WWII British military science (P.M.S. Blackett); expanded post-war with Dantzig's Simplex Method (1947) and the founding of ORSA (1952); scaled by computers from the 1960s onward into every major industry.
- Stages of Development: Six iterative phases — Problem Formulation, Model Construction, Model Solution, Model Validation, Implementation, and Monitoring — each building on the previous one, with feedback loops back to earlier stages when needed.
- Manager-Specialist Relationship: A collaborative partnership where the manager provides business context, data, and decision authority; the specialist provides analytical modeling and technique expertise. Communication breakdown between the two is the primary project failure risk.
- Tools and Techniques: A broad toolkit — LP, integer programming, transportation models, PERT/CPM, queuing theory, simulation, game theory, decision analysis, inventory models, dynamic programming, and goal programming — each matched to a specific problem structure.
- Applications: OR is applied across defense, manufacturing, transportation, finance, healthcare, agriculture, retail, telecommunications, and government — wherever constrained optimization decisions arise.
- Limitations: Mathematical complexity, unrealistic model assumptions, inability to quantify all factors, data dependence, high development cost, static models in dynamic environments, and organizational resistance all constrain OR's real-world effectiveness.
Key Points Sheet
| Concept / Tool | Key Meaning / Application |
|---|
| Operations Research (OR) | Scientific, model-based approach to optimal decision-making in complex systems |
| P.M.S. Blackett | Pioneer of OR; led WWII British military OR groups (radar, convoy optimization) |
| Simplex Method | Algorithm for solving Linear Programming problems; developed by George Dantzig in 1947 |
| ORSA (1952) | Operations Research Society of America — first formal OR professional body |
| 6 Stages of OR | Problem Formulation → Model Construction → Solution → Validation → Implementation → Monitoring |
| Linear Programming (LP) | Optimize a linear objective under linear constraints; solved by Simplex Method |
| Integer Programming | LP extended to whole-number decision variables |
| Transportation Model | Minimum-cost shipping from multiple sources to multiple destinations |
| Assignment Model | Optimal 1-to-1 assignment of n jobs to n workers/machines |
| PERT / CPM | Project scheduling and critical path identification; PERT for uncertain, CPM for known durations |
| Queuing Theory | Models waiting lines; balances waiting time against service capacity cost |
| Simulation | Computer-based approximation for complex or stochastic systems |
| Game Theory | Strategic decision-making in competitive or conflicting-interest scenarios |
| Decision Analysis | Decision-making under uncertainty using decision trees and expected value |
| EOQ (Inventory) | Economic Order Quantity — optimal order size minimizing total inventory cost |
| Dynamic Programming | Multi-stage optimization by decomposing into subproblems |
| Goal Programming | LP extension for multiple conflicting objectives |
Last-Minute Revision Sheet
- OR → scientific + mathematical + interdisciplinary → optimal decisions under constraints
- Also called → Management Science / Operational Research / Decision Science
- Born → WWII Britain → Blackett → radar, convoy, bombing optimization
- Simplex Method → Dantzig → 1947 → core LP algorithm
- ORSA → 1952 → OR recognized as formal discipline
- Computers → 1960s onward → enabled large-scale OR application
- 6 Stages → Define → Model → Solve → Validate → Implement → Monitor (iterative, not linear)
- Validation → tests model vs historical data → may loop back to model construction
- Manager → defines problem, authorizes action; OR Specialist → models and solves
- Communication gap → most common manager-specialist failure point
- LP → linear objective + linear constraints → Simplex solves it
- Integer LP → whole-number decisions only (e.g., number of machines)
- Transport model → min cost shipping, multiple sources to destinations
- PERT → uncertain durations; CPM → known durations; both → critical path
- Queuing → waiting lines → minimize wait time + service cost
- Simulation → complex/stochastic → approximate, not exact
- Game Theory → conflicting players → competitive strategy
- EOQ → optimal inventory order quantity (holding + ordering cost)
- Dynamic Programming → multi-stage problems → subproblem decomposition
- Goal Programming → multiple conflicting objectives → minimize deviations
- Limitations → can't quantify all factors, needs accurate data, costly, static models, resistance to change
