» Linear Programming
» Game Theory

Linear Programming

The learning objectives in this unit are:

1. To formulate a Linear programming problem (LPP) from set of statements.
2. To solve theLinear programming problem (LPP) using graphical method ( For 2 variables)
3. To solve theLinear programming problem (LPP) using primal simplex method ( For > 2 variables and all <= constraints)
4. To solve the Linear programming problem (LPP) using Big-M and Two-Phase methods( For > 2 variables and all mixed constraints)
5. To solve the Linear programming problem (LPP) using dual simplex method ( For > 2 variables and the solution is infeasible)
6. We also have a look at the effect of changing the values of parameters on the decision variables (Sensitivity Analysis)

Linera Programming Extension

Both transportation and assignment models are extended LPP’s. Transportation models are concerned with matching the aggregate supply and aggregate demand while still minimizing the costs or maximizing revenues. Assignment models are concerned with allocations on a one to one basis with an objective of minimizing costs or maximizing revenues. There are very many applications in real time based on the two models are how you apply them in real time situations is only limited to your comprehension.

The learning objectives in this unit are
1. To arrive at Initial Basic Feasible solutions in Transportation Models.
2. To check for optimality and to arrive at optimality in Transportation Models.
3. To solve for and learn the different assignment models.

Game Theory

A competitive situation in business can be treated similar to a game. There are two or more players and each player uses a strategy to out play the opponent.

A strategy is an action plan adopted by a player in-order to counter the other player. In our of game theory we have two players namely Player A and Player B. The basic assumption would be that

Player A – plays to Maximize profit (offensive) - Maxi (min) criteria

Player B – plays to Minimize losses (defensive) - Mini (max) criteria

The Maxi (Min) criteria is that – Maximum profit out of minimum possibilities

The Mini (max) criteria is that – Minimze losses out of maximum possibilities.

Game theory helps in finding out the best course of action for a firm in view of the anticipated counter-moves from the competing organizations. A competitive situation is a competitive game if the following properties hold good:

1. The number of competitors is finite, say N.

2. A finite set of possible courses of action is available to each of the N competitors.

3. A play of the game results when each competitor selects a course of action from the set of courses available to him. In game theory we make an important assumption that all the players select their courses of action simultaneously. As a result, no competitor will be in a position to know the choices of his competitors.

4. The outcome of a play consists of the particular courses of action chosen by the individual players. Each outcome leads to a set of payments, one to each player, which may be either positive, or negative, or zero.

Managerial Applications of the Theory of Games

The techniques of game theory can be effectively applied to various managerial problems as detailed below:

1. Analysis of the market strategies of a business organization in the long run.
2. Evaluation of the responses of the consumers to a new product.
3. Resolving the conflict between two groups in a business organization.
4. Decision making on the techniques to increase market share.
5. Material procurement process.
6. Decision making for transportation problem.
7. Evaluation of the distribution system.
8. Evaluation of the location of the facilities.
9. Examination of new business ventures and
10. Competitive economic environment.