TORAMarch 12, 2010 EXECUTIVE SUMMARY At every step of the process of management the managers have to take many decision. At same stages the decision are some on the basis of intuition. So there, the manager can use Tora software to solve the problem of Linear Programming, Transportation Model, Integer Programming, etc. Where as decision about technical matters like man – machine combination, which technique to use, how to reduce the total cost of production are taken by solving LPP in Tora software. In this project we have discuss how to solve LPP in Tora software which are useful in decision making process of management. Tora software especially helpful when – the problem is complex. Such complexity may arise when the problem involve a large number of decision variable. However use of Tora software necessary requires data base or data availability about the environment surrounding the problem also. Hence, operation research with the use of Tora software has evolved special techniques which can measure, compare, control and predict the probable behavior of the variables of the system in a scientific method. 1: TORA March 12.Ordered Routing Algorithm (TORA) – An Operations Research Software TORA is an algorithm i. 2010 INTRODUCTION Temporary . TORA is menu-driven and Windowsbased which makes it very user friendly. a mathematical set of instructions or programs (mathematical-software). 2: .e. Further. It is an optimization system in the area of operations research which is very easy to use. The other 3: .TORA March 12. 2010 FEATURES OF TORA The software has in-built tutorial for the novice and it also produces animated graphical linear programming solution. It can handle maximization as well as minimization problem. It uses scientific approach to arrive at the solution. It emphasizes on an overall approach to the system under consideration.TORA March 12. The tutorial mode keeps on giving step-wise information about the methodology and solution. It has an interdisciplinary team approach to find the optimum solution to a problem. It enables the instructors to demonstrate ideas that otherwise are literally impossible to present. The software can be executed in automated or tutorial mode. The automated mode reports the final solution of the problem. 2010 features of the software include dynamic construction of ‘Critical Path Method’ charts and creation of search-trees to name some. usually in the standard format followed in commercial packages. TORA also offers self-paced learning of all the computational algorithms in a manner that allows students to check their understanding of the material with immediate detailed feedback from the software. 4: . TORA March 12. CONTENTS OF TORA The various Models in Operations Research which can be solved using the Temporary-Ordered Routing Algorithm include: 5: . It is used in financial management production management. 2010 This software gives an insight into the problem areas to the manager. human resource management. accounting management. marketing management. storage manager. and SQL output viewer.TORA March 12. rollback segment monitor. instance manager. 6: . Queuing Models CPM/PERT Game Theory Matrix Inversion Simultaneous Linear Equations etc. SQL worksheet. PL/SQL editor & debugger. The functionality tools in the ‘Temporary-Ordered Routing Algorithm’ feature a schema browser. 2010 Linear Programming Graphical LPP: Transportation Models Integer Programming. linear programming. transportation model. 7: . 2010 STEPS IN SOLVING LPP STEP 1: START TORA PROGRAM It involves selection of different chapters from a number of options like linear equations. integer programming. as displayed below.TORA March 12. etc. X2 > 0 The image below shows that we have taken variables 2 and constraints 3. Also we are required to feed the number of variables and the number of constraints that are involved in the problem. For example: we have taken the problem. X1 .TORA March 12. 8: . Min z = 10 X1 + 20 X2 Subject to: 2X1 + X2 < 40 1X1+ 3X2 > 30 3X1 + 4X2 > 60 Where. After entering all the data we have to press ENTER. 2010 STEP 2: SELECT LINEAR PROGRAMMING It displays a page within which we are required to feed the problem title that is the name given to the problem. This table in TORA is known as INPUT GRID. Even lower bound and upper bound are mentioned in this table i.e. 9: .TORA March 12. X1. constraints as well as non negativity. X2 > 0. we can also take it in to consideration in this table. Therefore lower bound for all 2 variables will be 0 and the upper bound will be infinite as displayed in the image below. Also in case of any unrestricted variable. 2010 STEP 3: INPUT OF DATA This displays a table in which we have to feed the objective function. And hence we can save the data for future evidence to take quick decision. After saving. 2010 STEP 4: Next step is to click on the solve menu which displays an option whether we want to save the data or not. 10: . it displays a menu which asks that whether we want to solve it using graphical method or algebraic method.TORA March 12. TORA March 12. 11: . 2010 If we click on graphical it will display graphical chart and itself find out the variables as well as the objective function as displayed below. Various iterations: it means solving LPP different like a) All slack starting solution b) M-method c) Two Phase method d) Bounded simplex e) Dual simplex through criteria 12: . Directly get the final solution or 2. 1.TORA March 12. it offers us two option . 2010 STEP 5: If we click on the option algebraic.i.e. 2010 STEP 6: FINAL SOLUTION Once we click on final solution it displays a window in front of us which give us the solution to the LPP.H.S and maximum R.TORA March 12. 13: .S for the constraint. Any slack or surplus variables in the constraint is also display minimum objective coefficient a maximum objective coefficient and also display the minimum R.H. It displays the objective values that is minimize or maximize objective value. TORA March 12. 2010 CONCLUSION After solving LPP in TORA Software we came to a conclusion that this software is very useful in decision making process of management as this software is less time consuming. As all the organizations have to make decision about how to use their resources effectively and these resources are limited in relation to their need. This is basically a problem of internal planning in large organization as the management aims at achieving their objectives in best possible manner by using this Tora software. 14: . Hence management has to allocate these scarce resources to achieve organizational goals.