Operations research (OR) is a discipline that applies mathematical and analytical techniques to solve complex decision-making problems. OR can help optimize various aspects of business, engineering, management, and science, such as scheduling, inventory, transportation, logistics, network design, and more.

One of the tools that can help solve OR problems is TORA software. TORA is a software package that provides a user-friendly interface for modeling and solving linear programming (LP), mixed integer programming (MIP), quadratic programming (QP), assignment, maximum flow, minimum cost capacitated flow, minimum spanning tree, shortest route, transportation, and transshipment problems. TORA can also perform matrix operations, queuing analysis, and simulation.

In this article, we will show you how to download and install TORA software for free, and how to use it to solve some common OR problems.

TORA software is available for free download from various sources on the internet. One of them is the following link: [^1^]. This link will take you to a YouTube video that explains how to download and install TORA software on your computer. The video also provides a link to the software file in the description.

Alternatively, you can use this link: [^3^] to download the software file directly. This link will take you to a post on a forum that contains the download link and some instructions on how to install TORA software.

Once you have downloaded the software file, you need to unzip it and run the setup.exe file. Follow the instructions on the screen to complete the installation process. You may need to change the resolution of your display to make TORA software work properly.

After installing TORA software, you can launch it from your desktop or start menu. You will see a window like this:


This is the main window of TORA software. Here you can choose the type of problem you want to solve from the menu bar. You can also access the help menu for more information and tutorials on how to use TORA software.

In this section, we will show you how to use TORA software to solve some common OR problems. We will use some examples from NCSS software documentation [^2^], which is another software package that provides tools for operations research.

Linear programming (LP) is a technique that maximizes (or minimizes) a linear objective function subject to one or more linear constraints. The objective function and the constraints can have lower and upper bounds on the variables.

For example, suppose we want to maximize the profit of producing two products A and B using two machines M1 and M2. The profit per unit of product A is $3 and the profit per unit of product B is $4. The production time per unit of product A on machine M1 is 2 hours and on machine M2 is 1 hour. The production time per unit of product B on machine M1 is 1 hour and on machine M2 is 2 hours. The total available time on machine M1 is 40 hours and on machine M2 is 36 hours. The lower bound on the production of product A is 5 units and the upper bound is 15 units. The lower bound on the production of product B is 10 units and the upper bound is 20 units.

The LP problem can be formulated as follows:

“`
Maximize z = 3×1 + 4×2
Subject to:
2×1 + x2 ≤ 40
x1 + 2×2 ≤ 36
5 ≤ x1 ≤ 15
10 ≤ x2 ≤ 20
x1 ≥ 0
x2 ≥ 0
“`

To solve this problem using TORA software, we need to follow these steps:

1. Select LP with Bounds from the menu bar.
2. Enter the number of variables (2) and constraints (2) in the corresponding boxes

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