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6 a. Explain the dominance principle in game theory. b. Describe the Constituents of a Queuing System. c. Differentiate between PERT and CPM. ( a. Dominance principle in game theory, b. Constituents of a Queuing System, c. Differences between PERT and CPM)

February 27, 2015 By: Meliza Category: 1st SEM

  1. Dominance principle in game theory,

At times, a convex combination of two or more courses of action may dominate  another  course  of  action.  Whenever  a  course  of  action  (say A s or B q ) is dominated by others, then that course of action ( A s or B q ) can be deleted from the pay-off matrix. Such a deletion will not affect the choice of the solution, but it reduces the order of the pay-off matrix. Successive reduction of the order using dominance property helps in solving games

In a game, sometimes a strategy available to a player might be found to be preferable to some other strategy / strategies. Such a strategy is said to dominate the  other one(s). The rules of dominance are used to reduce the size of the payoff matrix. These rules help in deleting certain rows and/or columns of the payoff  matrix, which are of lower priority to at least one of the remaining rows, and/or  columns in terms of payoffs to both the players. Rows / columns once deleted will  never be used for determining the optimal strategy for both the players.

This concept of domination is very usefully employed in simplifying the two – person zero sum games without saddle point. In general the following rules are used  to reduce the size of payoff matrix.

PRINCIPLES OF DOMINANCE

Rule 1: If all the elements in a row ( say ith row ) of a payoff matrix are less than or equal to the corresponding elements of the other row ( say jth row ) then the player A will never choose the ith strategy then we say ith strategy is dominated by jth strategy  and will delete the ith row.

Rule 2: If all the elements in a column ( say rth column ) of a payoff matrix are greater than or equal to the corresponding elements of the other column ( say sth column ) then the player B will never choose the rth strategy or in the other words  the rth strategy is dominated by the sth strategy and we delete rth column .

Rule 3: A pure strategy may be dominated if it is inferior to average of two or more other pure strategies.

  1. Constituents of a Queuing System,

The constituents of a queuing system include arrival pattern, service facility and queue discipline.

  1. Arrival pattern: It is the average rate at which the customers arrive.
  2. Service facility: Examining the number of customers served at a timeand the statistical pattern of time taken for service at the service facility.
  3. Queue discipline: The common method of choosing a customer for service amongst those waiting for service is ‘First Come First Serve’.
  1. Differences between PERT and CPM

There are no essential differences between PERT and CPM as both of them share in common the determination of a critical path. Both are based on the network representation of activities and their scheduling, which determines the most critical activities to be controlled in order to meet the completion date of the project.

  PERT

Some key points of PERT are as follows:

PERT was developed in connection with an Research and Development (R&D) work. Therefore, it had to cope with the uncertainties that are associated with R&D activities. In PERT, the total project duration is regarded as a random variable. Therefore, associated probabilities are calculated in order to characterise it.

It is an event-oriented network as in the analysis of a network, emphasis is given on the important stages of completion of a task rather than the activities required to be performed to reach a particular event or task.

PERT is normally used for projects involving activities of non-repetitive nature in which time estimates are uncertain.

It  helps  in  pinpointing  critical  areas  in  a  project,  so  that  necessary adjustment can be made to meet the scheduled completion date of the project.

 

  CPM

  • CPM was developed in connection with a construction project, which consisted of routine tasks whose resource requirements and duration were known with certainty. Therefore, it is basically deterministic.
  • CPM  is  suitable  for  establishing  a  trade-off  for  optimum  balancing between schedule time and cost of the project.
  • CPM is used for projects involving activities of repetitive nature.

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