(1), amount of profit in hundred Rupees. To find optimum number of tool crib clerks. And the optimum cost paths is A – B1 – C2 – D2 – E. In this problem, total numbers of possible paths are 3 × 3 × 3 × 3 = 81. This shows that out of 3 possibilities from B1 to E, the path pass through C2 is optimum and similarly optimum cost path for B3E and B2E are through C2 and C3 respectively. Thus maximum = minimax = 2-, the solution here is clear one. If non- basic variables are zero, then the solution obtained is known as “Basic solution”. Using this north-west corner method, in the west corner square put the smaller of the two values between the capacity and requirement for the required column. Methodology of operation Research/General approach to solve a problem in operations research. Thus to avoid this cumbersome method, another method is utilised to get final solution with less labour. But the graphical method is quite easy and simple. Thus there is further reduction in the transportation cost. This can be better understood by following example: A pipe line is to be laid between stations A and E passing successively through one node of each B, C and D as shown in the figure below. 21.80 per day. 21.80 + 5.80 = Rs. There are several methods to solve linear programming problems such as graphi­cal, index distribution, simplex and modified distribution (MODI) methods. Privacy Policy 9. Project Management, Decision-Making, Operation Research, Methods used in Operation Research. Thus if each player individually maximizes his own return, they end up losing Rs. If you play any other strategy, one might not win as much. Product A requires 2 hours on both machines 1 end 2, while product B needs 3 hours on machine 1 and only 1 hour on machine 2. Plagiarism Prevention 5. Step 3 – Deriving a solution – Research Definition – Research is a careful investigation or inquiry specifically through a search for new facts in any branch of knowledge. 4. It involves testing of the model used. In game theory, the decision makers are known as ‘players’, the choices are called strategies and the preferences of the decision makers called “payoffs”. Now to plot the equation 2A + 3B ≤ 12>, first find the two terminal points, and then joining these points by a straight line. The basis of this is to select the best amongst the final possible alternative decisions, ignoring all other alternatives, which do not lead to the best (i.e. If you play strategy β, you gain 2 points, if the opponent plays A or C, but lose 4 if he plays B. Thus yours own minimum again is the same as the opponent’s maximum loss. Test which corner point is most profitable. iv. 5. The next step is to know whether this solution is the best one i.e. for 3 teams) first truck was being unloaded for 80 minutes means it was detained for 50 min. extra, similarly III truck and IV truck was required to wait for 190 min, and 280 min. This is a technique to allocate scarce available resources under conditions of certainty in an optimum manner. This can be done with the help of steps I, II and III described as under: Divide each entry in the first row by 2, coefficient of C in the first equation. If both cooperate, a profit (say 100) can be made, then X + Y = 100. Dynamic programming is a mathematical technique for solving problems where a sequence of decisions are involved. 600 and Rs. In this case, the time of arrival of first truck is assumed to be at zeroth minute. Content Guidelines 2. Though this method looks a lengthy one, yet by doing this a saving of Rs. In such problems, there are number of stages and at each stage there are several alternatives available. Linear Programming is a mathematical technique for finding the best use of limited re­sources of a concern. ii. “Operation research is a scientific method of providing executive departments with a quantities basis for decisions regarding the operations under their control”. v. Machine interference problem to find out the work load of a single repair man. Four trucks are being used continuously for transporting the materials. We are required to find out the path which will require minimum costs of laying the pipe line from A to E. In such problems, solution begins from the destination E and proceeds backwards, and in first stage determine minimum cost path between D1E, D2E and D3E. 10 per hour is charged if the truck is detailed beyond 30 minutes. From the above table, it is clear that only 3 A path is suitable because only in this path there is reduction in the transportation cost (because minus sign is obtained in the result). Research The process of observation and testing characterized by the scientific method. The theory can be applied wherever queues are visible may it be bank or post office counter, rail or airline booking window, raw material or semi-finished product waiting for next operation on shop floor or material waiting for inspection or for moving to another place or turner waiting for getting tools for tool room or vehicle waiting for its turn on a petrol pump or service station. Methodology of Operation Research: Operation Research, is a scientific approach for decision-making, and therefore must follow following steps: 1. Now in the last stage, we start from point A and compute the cost for the three possibilities below: This shows that minimum cost from A to if is 50.

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