Lokesh Rajendran

# Decoding Industrial Optimization with Production planning use case

Optimization is not just confined to machine learning, it plays a vital role in making the best decisions and resource allocations in various industrial sectors. Today, we're going to delve into industrial optimization

## What is Industrial Optimization?

Industrial optimization, often referred to as operations research or management science, focuses on decision-making to make the best use of available resources. This field includes a wide range of industries including manufacturing, transportation, logistics, healthcare, finance, and energy, among others.

At its core, industrial optimization aims to design and operate systems optimally by considering complex interactions among various components of the system. This includes finding the best allocation of limited resources, routing and scheduling, portfolio optimization, process optimization, and many other related problems.

In simple words, the optimizer takes into account all the constraints you have (like how much raw materials you have or how much time you can spend), and it also considers your objective (like maximizing profit or minimizing costs). Then it uses mathematical techniques to find the best combination of actions to achieve that objective

## Techniques in Industrial Optimization

At the core of industrial optimization are mathematical optimization methods. Here are few techniques used:

**Linear Programming (LP)**: This technique is used when all the mathematical functions in the problem are linear. LP is extensively used in scheduling, planning, and routing problems.**Integer Programming (IP)**: This method is used when decision variables are integers, typically used in problems like facility location and network design.**Non-linear Programming (NLP)**: When the objective function or any constraint is non-linear, NLP is employed. Examples include economic load dispatch in power systems and portfolio optimization in finance.**Dynamic Programming (DP)**: DP is used for sequential or multi-stage decision-making problems. It's commonly used in resource allocation and control problems.**Stochastic Programming (SP)**: This technique is used when the parameters of the optimization problem are uncertain and can be represented by probability distributions.**Metaheuristic Algorithms**: These are higher-level procedures designed to find the best possible solutions in complex spaces. Examples include Genetic Algorithms, Simulated Annealing, and Particle Swarm Optimization.

## Use Case: Production Planning

Let's imagine a company called "FurniCo" that manufactures two types of furniture: chairs and tables. The production of these items is constrained by available labor hours and raw material supply (wood, in this case). The company wants to maximize its profit while working within these constraints.

The following conditions are given:

Each chair produced contributes $50 to the profit, and each table contributes $120.

Each chair requires 5 hours of labor and 10 units of wood.

Each table requires 10 hours of labor and 30 units of wood.

The company has 300 labor hours available per week and 1000 units of wood.

## Problem Formulation:

We can formulate this as a linear programming problem.

Let:

X1 be the number of chairs to produce

X2 be the number of tables to produce

**Objective Function:**

Maximize Profit = 50*X1 + 120*X2

**Subject to constraints:**

Labor: 5*X1 + 10*X2 <= 300

Wood: 10*X1 + 30*X2 <= 1000

Non-negativity: X1, X2 >= 0

We can program the above linear programming problem using python.

In this script, we define a model, decision variables, an objective function, and constraints. We used __Pyomo__ to formulate the problem and __glpk__ to solve the problem.

## Other Use cases

The impact of industrial optimization on industries and businesses is vast. Here are a few examples:

**Supply Chain Management**: Optimization is used for inventory management, production planning, routing, and scheduling, leading to cost reduction and improved customer service.**Energy Systems**: Optimization helps in planning and operation of power systems, including economic load dispatch, unit commitment, and optimal power flow.**Transportation**: Optimization aids in managing and planning transportation, including airline scheduling, fleet management, and routing.**Healthcare**: Optimization contributes to healthcare resource management, scheduling of patient appointments, and medical treatment planning.**Finance**: Optimization is used in asset allocation, portfolio optimization, and risk management.

Understanding and implementing industrial optimization techniques can greatly aid in decision-making processes and resource management, leading to more efficient and cost-effective operations. Remember, in the world of industry, optimization is not just a tool, but a necessity!