Overview

motivation

1. organizational goals
2. organizational resources

→ Resource allocation uses operational research

• names of simmilar subjects:
  • management science
  • decision science
  • optimization method/algorithms
  • mathematical programming

business analytics

• Data Analysis
  1. Descriptive analytics: what happened?
  2. Predictive analytics: what will happen?
• Operational Research
  1. Prescriptive analytics: what should we do? (Allocate resources and solve problems)

process of conducting an OR study

flowchart TD
  A(Collect data) --> B(Define the problem)
  B --> C{Data are sufficient?}
  C -->|No| A
  C -->|Yes| D(Formulate a model)
  D --> E(Solve the model)
  E --> F{Model is good?}
  F -->|Yes| G(Interpret results make suggestions)
  F -->|No| D

OR cant solve everything

Aim of course: know what may be solved by OR and what cannot be solve by OR

mathematical programming

we need Model 1. describe the problem 2. better solution

model

1. descision variables
2. objective function
3. constraints

KnapSack(backpack) Problem

1. Linear Programming

\[\begin{aligned} max & \sum_{i=1}^{n} v_i x_i \\ s.t. & \sum_{i=1}^{n} w_i x_i \leq B \\ & 0 \leq x_i \leq 1 \end{aligned}\]

2. Integer Programming

\[\begin{aligned} max & \sum_{i=1}^{n} v_i x_i \\ s.t. & \sum_{i=1}^{n} w_i x_i \leq B \\ & x_i \in \{0, 1\} \end{aligned}\]