2. (a) Many values of variables of a problem are not known. Thus there is further reduction in the transportation cost. When the guaranteed minimum and maximum payoffs for two opponents are exactly equal (as in the above example), the game is said to have a Saddle Point. Let us assume that it will be 4.5 minutes. desired to maximize profit. Average time which an arrival spends in the system or say mean time in system including service. Waiting line theory can be used for efficient decision making in the following fields: i. With average arrival rate (A) as 12 per hour and average service rate (S) as 20 per hour, thus calculating as per given formulae. In the same way, multiply the new first row with (+2) and add the resultant with third row. iv. If he plays any other strategy, he could lose more. 3, 3A = 2B – 3A + 1A – 1B = 5 – 2 + 5 – 3 = Rs. For solving queuing problems mathematically, an expression known as traffic Intensity is used. 5. He cuts the price; the opponent keeps his price constant. Problems connected with the Frequency and Frequency distribution. 1000. According to the theory of probability, if Sohan chooses strategy 2 with probability p and strategy 1 with probability 1-pen when Mohan choose strategy 1, Sohan’s advantage is, when Mohan chooses strategy 2, Sohan’s advantage is, Now we want to choose p so that and y2 are both as big as possible. Break down of machine tools and other equipment’s in a machine shop of an industry. Selection of material handling equipment. Draft a mathematical model. But to get optimal solution we have to test new unused paths. 30.5) when, p = 3/4 and (1 – p) = 1/4 and y1 = y2 = 4½. Final Execution or Implementation 1. Mean number in waiting line, i.e. → x1 and x2 = controllable variable whose values are to be determined, profits per unit, cost/unit amount of resources are all uncontrollable. In simulation, experiments are conducted on the models instead of attempting the experiments on the real system. Operation research and its application 1. By using the mixed strategy, the first player (Sohan) guarantees himself an advantage of atleast 4½. With the help of following examples one illustrates the difficulties still remaining in such type of games: Doghouse problem. Simulation is a qualitative technique used for evaluating alternative courses of action based on facts and assumptions, with a mathematical model representing actual decision making under conditions of uncertainty. Now we shift C to D, and observe that many more possibilities open. In such problems, there are number of stages and at each stage there are several alternatives available. v. Machine interference problem to find out the work load of a single repair man. The calculation of traffic intensity for any system is shown below: 5, 4, 10, 6, 3, 2, 6, 4, 8, 15, 2, 5, 4, 6, 8, 7, 3, 5, 2, 5, 8, 7, 4, 3, 2, 6, 7, 4, 3, 4, 7, 5, 8, 4. In the next stage, we further proceed backwards to point B, and starts examining the optimum costs from various nodes of point B, as shown in the table. Thus to solve such problem, we employ a mixed strategy. 6 which is similar to the result obtained by north-west corner method, i.e., Rs. Thus we can rewrite the three equations as follows: Further C, D and E are known as basic variables and A and B as non-basic variables. iii. Dynamic Programming. Equation (i) = objective function (ii) and (iii) are constraints iii. 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. policy, increasing prices. To find optimum number of tool crib clerks. These are used for solving the process or situations which are probabilistic or stochastic in nature. 1. Let us rewrite the given equations in the matrix form. Evaluation of the training programme. Then cost of idle time/day, Suppose the mechanic’s average wages are Rs. iv. To get the final solution of problem, repetition of the above process of moving one unit from one centre to another at a time until optimal solution is found. Introduction of the partograph by means of a training programme. Simulation and Monte Carlo Technique. This utilizes the plant A capacity, so now move to plant B. Now for site 3, we first ship the remaining capacity (25 – 10 = 15) of plant B and remaining needed by site 3 from point C. This solution of problem now known is called “initial solution” because it is not possible to say that this distribution is most economical. By applying this plus and minus values in this dosed loop path to the transportation cost in each square we get the amount of improvement by shifting one unit of production from SB to 3A and so on. The other method commonly used is simplex method. Image Guidelines 4. E-mail : acad@biyanicolleges.org, Copyright : Biyani Institute of Science & Management. The game theory is a technique which introduces a table known as ‘payoffs matrix’, showing the expected values for various outcomes to determine the best way to ‘play’ against the opponent. – 1, 2A = 2A – 2C + 3C – 3C – 3A = 10 – 8 + 4 – 2 = Rs. (b) There is no other way to find out the values of variables. If the sum of payoff is zero, the same is said to be zero sum, but where the sum of payoff is not zero, these are called ‘non-zero sum game’. The next step is implementing the solution derived. Shifting 25 parts (least value in negative squares), the new solution is shown in Table 13. 302039 , India average length of waiting line (La), 2. But profit depends on one of the experimental automatic packing systems which will be successful. -1. ii. It is an original contribution to the existing stock of knowledge making for its advancement. 21.80 + 5.80 = Rs. Let us take a waiting line problem. 2. Table 19 shows a record in this situation. A penalty of Rs. Unit 1 {Book} 1Nature, Definition & Characteristics of Operations ResearchVIEW2Methodology of Operation ResearchVIEW3Models in Operation ResearchVIEW4Operation Research & Managerial Decision MakingVIEW5Operation Research TechniquesVIEW Unit 2 Linear Programming: {Book} {Book}1Introduction, Advantages of Linear ProgrammingVIEW2Applications … Suppose, a manufacturer who is faced with the problem of choosing a price for his product has the necessity to examine the reaction of his competitors, due to this decision about the price. by 9/5) and add the result with second. There are only 12 and 8 hours available on machine 1 and 2 respectively. This can easily be judged from Fig. Terminal co-ordination centre, its theoretical principles. In the same way, eliminate coefficient of D except second equation. Now set up the equations for the process times. Operations research is the organised application of modern science, mathematics and computer techniques to complex military, government, business or industrial problems arising in the direction and management of large systems of men, materials, money and machines.