Operations Research (OR) is often described as the “science of better.” It is the discipline of applying advanced analytical methods to help make better decisions. Whether a logistics company is trying to find the shortest delivery route or a factory is looking to maximize profit while dealing with limited raw materials, Operations Research provides the mathematical framework to find the “optimal” solution. For students, this unit is a fascinating blend of linear algebra, probability, and pure logic.
Below is the exam paper download link
PDF Past Paper On Operations Research For Revision
Above is the exam paper download link
To help you move from basic calculations to strategic optimization, we have broken down the core pillars of Operations Research into a high-impact revision guide.
What is ‘Linear Programming’ (LP) and why is it central to OR?
Linear Programming is the most recognizable tool in the OR toolkit. it involves creating a mathematical model to represent a real-world problem. You define an Objective Function (what you want to maximize, like profit, or minimize, like cost) and a set of Constraints (limitations like labor hours, machine capacity, or budget). In exams, you will often use the Graphical Method for two variables or the Simplex Method for more complex scenarios to find the “Feasible Region” where all constraints are met.
How do we solve ‘Transportation Problems’?
A transportation problem is a specific type of linear program where the goal is to minimize the cost of distributing goods from several supply points (factories) to several demand points (warehouses). During revision, you must master three main starting methods:
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North-West Corner Rule: Quick but rarely optimal.
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Least Cost Method: Focuses on the cheapest routes first.
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Vogel’s Approximation Method (VAM): Usually provides the best starting solution by considering the “penalty” of not taking the cheapest route.
What is the ‘Assignment Problem’?
While similar to transportation, the Assignment Problem is about matching items on a one-to-one basis—for example, assigning four specific jobs to four specific machines to minimize total time. The Hungarian Method is the standard algorithm used here. The key is to reduce the “opportunity cost” in the matrix until an optimal assignment can be made.
What does ‘Network Analysis’ involve?
In a project management context, Operations Research uses tools like CPM (Critical Path Method) and PERT (Program Evaluation and Review Technique). These help managers identify which tasks are critical to the project’s timeline and which have “slack” (extra time).
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Critical Path: The longest sequence of tasks that determines the shortest possible project duration.
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PERT: Uses three time estimates (Optimistic, Most Likely, and Pessimistic) to handle uncertainty in project timelines.
How does ‘Queuing Theory’ help businesses?
Queuing theory is the mathematical study of waiting lines. It helps businesses find the balance between the cost of hiring more staff (servers) and the “cost” of making customers wait. By calculating the Arrival Rate ($\lambda$) and the Service Rate ($\mu$), an analyst can predict the average length of the queue and the average time a customer spends in the system.
Why is ‘Duality’ important in Linear Programming?
Every Linear Programming problem (the Primal) has a twin (the Dual). If the Primal is about maximizing profit, the Dual is about minimizing the costs of the resources used. The “Shadow Price” found in the Dual solution tells a manager exactly how much more profit they would make if they had one extra unit of a limited resource—information that is gold for business expansion.
Conclusion
Operations Research is a practical subject. You cannot learn it by reading alone; you have to draw the networks, set up the Simplex tables, and calculate the ratios. By practicing with past papers, you learn to spot the “logic” of the question before you even pick up your calculator.
To help you master these optimization techniques and ace your upcoming exam, we have provided a full revision PDF below.
Last updated on: March 24, 2026