Temporary-Ordered Routing Algorithm (TORA) – An Operations Research Software TORA is an algorithm i.e. a mathematical set of instructions or programs (mathematical-software). It is an optimization system in the area of operations research which is very easy to use. Further, TORA is menu-driven and Windows-based which makes it very user friendly.

The software can be executed in automated or tutorial mode. The automated mode reports the final solution of the problem, usually in the standard format followed in commercial packages, while the tutorial mode keeps on giving step-wise information about the methodology and solution.

TORA tutorial software deals with the following algorithms:

•Solution of simultaneous linear equations

•Linear programming

•Transportation model

•Integer programming

•Network models

•Project analysis by CPM/PERT

•Poisson queuing models

•Zero-sum games

The software provides a number of tutorial features:

1. TORA allows both user-guided (tutorial) and automated use of the software.

2. In the user-guided option, steps of the algorithms are reproduced exactly as presented in the book.

The user decides the course of the algorithmic computations with instant feedback regarding the

decisions made. The objective is to reinforce the user’s understanding of the basic ideas of the

algorithm without being “bogged” down in the computational details.

3. All the details needed to use an algorithm are given directly on the screen, thus precluding the need for a user’s manual.

SOLVING LINEAR PROGRAMMING GRAPHICALLY USING COMPUTER

The above problem is solved using computer with the help of TORA. Open the TORA package and select LINEAR PROGRAMMING option. Then press Go to Input and enter the input data as given in the input screen shown below, in Figure. Linear Programming, TORA Package (Input Screen)

Now, go to Solve Menu and click Graphical in the 'solve problem' options. Then click Graphical, and then press Go to Output. The output screen is displayed with the graph grid on the right hand side and equations in the left hand side. To plot the graphs one by one, click the first constraint equation. Now the line for the first constraint is drawn connecting the points (40, 60). Now, click the second equation to draw the second line on the graph. You can notice that a portion of the graph is cut while the second constraint is also taken into consideration. This means the feasible area is reduced further. Click on the objective function equation. The objective function line locates the furthermost point (maximization) in the feasible area which is (15,30) shown in Figure below. Graph Showing Feasible Area

Example:

A soft drink manufacturing company has 300 ml and 150 ml canned cola as its products with profit margin of Rs. 4 and Rs. 2 per unit respectively. Both the products have to undergo process in three types of machine. The following table indicates the time required on each machine and the available machine-hours per week. Available Data

Formulate the linear programming problem specifying the product mix which will maximize the profits within the limited resources. Also solve the problem using computer. Solution:

Let x1 be the number of units of 300 ml cola and x2 be the number of units of 150 ml cola to be produced respectively. Formulating the given problem, we get Objective function:

Zmax = 4x1 + 2x2

Subject to constraints,

3x1 + 2x2 ≤300 ............................(i) 2x1 +4x2 ≤ 480 ............................(ii) 5x1 +7x2 ≤ 560 ............................(iii) where x1 , x2 ≥...