Operations Research
What is Operations Research?
A scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control.
Key formula / rule: Linear Programming (Objective Function)
Key points
- Understand the scope and applications of Operations Research.
- Formulate real-world problems into mathematical models.
- Apply various OR techniques to solve optimization problems.
- Interpret the results of OR models for decision-making.
Common exam trap
Incorrect formulation of the objective function or constraints.
Definitions
- Term
Operations Research (OR)
- Meaning
A scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control.
- Term
Linear Programming (LP)
- Meaning
A mathematical technique for optimizing a linear objective function, subject to linear equality and inequality constraints.
- Term
Objective Function
- Meaning
The function that a decision-maker aims to maximize or minimize in an optimization problem.
- Term
Constraints
- Meaning
Limitations or restrictions that must be satisfied by the decision variables in an optimization problem.
- Term
Feasible Region
- Meaning
The set of all possible solutions that satisfy all the constraints of an optimization problem.
- Term
Optimal Solution
- Meaning
A feasible solution that yields the best possible value for the objective function.
- Term
Queuing Theory
- Meaning
The mathematical study of waiting lines (or queues), analyzing arrival rates, service rates, and waiting ×.
- Term
Critical Path
- Meaning
The sequence of activities in a project network that determines the shortest possible project duration; any delay in a critical path activity delays the entire project.
Learning objectives
Understand the scope and applications of Operations Research.
Formulate real-world problems into mathematical models.
Apply various OR techniques to solve optimization problems.
Interpret the results of OR models for decision-making.
Analyze and improve operational efficiency.
Formulae
- Name
Linear Programming (Objective Function)
- Note
Where Z is the objective function, ci are coefficients, and xi are decision variables.
- Expression
Maximize/Minimize Z = c1*x1 + c2*x2 + ... + cn*xn
- Name
Linear Programming (Constraints)
- Note
Subject to various inequality or equality constraints representing resource limitations or requirements.
- Expression
a11*x1 + a12*x2 + ... + a1n*xn ≤ b1
- Name
Queuing Theory (Little's Law)
- Note
L is the average number of customers in the system, λ is the average arrival rate, and W is the average time a customer spends in the system.
- Expression
L = λW
- Name
Queuing Theory (Average Waiting Time in Queue)
- Note
Wq is the average waiting time in the queue, Lq is the average number of customers in the queue.
- Expression
Wq = Lq / λ
- Name
Critical Path Method (CPM) - Activity Duration
- Note
Used to determine the minimum time required to complete a project.
- Expression
Duration(Activity) = Latest Finish Time - Earliest Start Time
- Name
Critical Path Method (CPM) - Slack
- Note
The amount of time an activity can be delayed without delaying the project completion.
- Expression
Slack = Latest Finish Time - Earliest Finish Time = Latest Start Time - Earliest Start Time
Prerequisites
Basic algebra and calculus.
Understanding of matrices and vectors.
Basic probability and statistics.
Logical reasoning and problem-solving skills.
Common mistakes
Incorrect formulation of the objective function or constraints.
Assuming linearity where it doesn't exist.
Misinterpreting the results of the model.
Over-simplification of the real-world problem.
Ignoring the dynamic nature of some systems.
Keywords
Operations Research
Optimization
Linear Programming
Simplex Method
Queuing Theory
Network Analysis
PERT
CPM
Simulation
Decision Making
Resource Allocation
Practice preview
Which of the following is a fundamental assumption of Linear Programming?…
easy
In a project network, the critical path represents:…
medium
Consider a primal Linear Programming problem with 'm' constraints and 'n' decision variables. Its dual problem will have:…
hard