**The Definition:**

**Linear programming** (**LP**, also called **linear optimization**) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. **Linear programming is a special case of mathematical programming (also known as mathematical optimization).**

**The Problem Statement**

Linear programming is a widely used optimization technique. Many problems in today’s world are of linear nature. But what does it have to do with the Melt Shops? The answer lies within the following question. If someone comes to you and asks you this- “Are you sure that you are producing castings at the lowest cost charge recipe possible all every single time? What would your answer be? That’s right. You are not sure and most likely you are not producing castings at the **lowest material cost possible**. Especially you’re **Hi-Alloy Steel** Manufacturer or into **Aluminum Alloying** or other high value metal such as** Copper Alloys** or **Bright Bar Manufacturing.**

Why? The reason is simple. You have a variety of raw materials you can use and there can be multiple recipes to achieve the final chemistry. Let’s put it this way if you need to find the value of X & Y from the following equations:

3X + 5Y = 34

X + 2Y = 13

It’s easy. As there are only 2 variables and only 2 equations. In the case of Charge Mix Recipe Calculation, there are no variables with a variety of equations. And there can be multiple solutions available. The following diagram will explain it better.

**Fig: Comparison of Linear Programming technic with Trial & Error Method**

Currently, most foundrymen have their own recipe developed using trial & error methods over the years. It’s a common scenario in melt shops that we are afraid of using low cast scrap available because of their consistency in the element recovery percentage. Even though we know that there is a possibility to prepare the metal at a low cost, we would hesitate to try it as it may create other issues such as we may end up using high value alloying material, or some other material availability constraints, etc… What if I tell all that can be managed on a figure tip?

**The Solution: OPTIMIX-ALLOY**

Luckily for **Foundries** and **Melt Shops, **the problem of calculating the **Least Cost Charge Recipe **is of the linear nature. And fortunately, there are many mathematical algorithms available to solve these sorts of linear problems. Team **Ellipsis Infotech, **who are known for their **foundry Centric ERP Solution**–** ICAST ERP,** have identified this problem and developed **Ingenious Software Solution for Modern Melt Shops** – **OPTIMIX-Alloy **using mathematical programming.

Our results have shown that OPTIMIX literally **saves up to 20% material cost** in High Alloy Steel by using linear programming techniques. It saves up to 4% in Cat and Ductile Iron as well. OPTIMIX is **Software **which not only** calculates the Minimum Cost Charge Mix Recipe, **it can also be integrated with almost all the spectrometers and **Calculates Alloy Additions** as well. It has many more functionalities which can literally help to upgrade the melt shops.

**So, would you still prefer to do it the old way or would you like to take the help of technology and upgrade your melt shop?**