Operations Research Exam Questions And Answers Pdf


  • The differences between manufacturing and services are described. The history and current trends of operations management are discussed, including the impact of information systems. Finally, the interaction between operations and other business...
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  • Caution: This is only a sample exam. It is intended only as a guide to the style of the The principle stage is 3 Strategic organization is that arranged of managerial decisions What are the three values of free expression cited by the Canadian...
    Link: https://csus.edu/academic-affairs/program-assessment/_internal/_documents/1617%20Report%20PDFs%20by%20clge/edu/1617-ma-school-psy.pdf
  • Total of 50 points. This is an open book, open notes, and open computers exam. This is an individual exam. No collaboration of any kind is permitted. No network connections until you post your answer files to Blackboard
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  • Daniel Kathii Q4. Explain the meaning of linear programming problem stating its uses and give its limitations. Write at least five application areas of linear programming. A small manufacturer employs 5 skilled men and 10 semi skilled men and makes an article in two qualities, a deluxe model and an ordinary model the making of deluxe model requires 2 hours work by a skilled man and 2 hours work by a semi-skilled man. The ordinary model requires 1 hour work by a skilled man and 3 hour work by a semiskilled man. By union rules no man can work more than 8 hours per day. The manufacturer's clear profit of the deluxe model is Rs. Formulate the model of the problem. Old hens can be bought for Rs. The old hens lay 3 eggs per week, and young one 5 eggs per week, each egg being worth 30 paise.
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  • A hen cost Re. If a person has only Rs. A firm manufactures three products A, B, and C. The profits are Rs. The firm has two machines and required processing time in minutes for each machine on each product is given below:Product A B C X 4 3 5 Machine Y 2 2 4Machine X and Y have and machine minutes respectively. The firm must manufacture A's, B;s and 50C's but no more than A's.
    Link: https://unl.edu/physics/docs/Syllabi/PHYS926_F15.pdf
  • The manager of an oil refinery has to decide upon the optimal mix of two possible blending processes, of which the input and output per production run are as follows:Input output ProcessCrude A Crude B Gasoline X Gasoline Y 1 5 3 5 8 2 4 5 4 4The maximum amount available of crude A and B is units and units respectively.
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  • Market requirement show that at least units of gasoline X and 80 units of gasoline y must be produced. The profit per production run from process 1 and process 2 are Rs. Formulate the problem as a linear programming problem. A firm can produce three types of clothes say, A,B and C. Three kinds of wool are required for it say, red, green and blue. One unit length of type A cloth needs 2 yard of red wool and 3 yards of blue; one unit length of type B cloth needs 3 yards of red wool, 2 yards of green and 2 yards of blue; and one unit length of type C needs 5 yards of green and 4 yards of blue wool.
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  • The firm has a stock of only 8 yards of red wool, 10 of green 15 of blue. It is assumed that the income obtained from one unit length of type A is Rs. Formulate LPP. Why do some problems have multiple optimal feasible solutions? How such information is useful for decision making? Use graphical method to solve the following problem:Q Solve by Big M-methodQ A manufacturer produces three products A, B, and C. The time required to produce one unit of each product on a machine is: Time to produce one unit Q A factory has decided to diversify its activities. The data collected by sales and production department is summarized below. Potential demand exist for three products A,B and C. For every 3 units of C produced, there will be one unit of by-product which sells at a contribution of Rs.
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  • These products require three different processes and the time required per unit product is given in the Q A manufacturing company has three factories F 1, F 2, F 3 with monthly manufacturing capacities of ,, units of a product. The product is to be supplied to seven stores. The manufacturing costs of these factories are slightly different but the important factor is the shipping cost from each factory to a particular store. Following table represent the factory capacities, store requirement and unit cost in rupees of shipping from each factory to each store and slack. Here slack is difference between total factory capacity and total store requirement. Work out a transportation plan so as to minimize the transportation cost. General electrode is a big electrode manufacturing company.
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  • It has two factories and three main distribution centers in three cities. The supply and demand conditions for units of electrode are given below along with unit cost of production. How should the trips be scheduled so that cost of production is minimized? Determine an optimum distribution for the company in order to minimize the total transportation cost. How much is the cost? Priyanshu enterprise has three auditors.
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  • Each auditor can work up to hours during the next month, during which time 3 projects must be completed. The amount in rupee per hour that can be billed for assigning each auditor to each project is given below:Project 1 Project 2 Project 3 Auditor 1 2 3 Find the optimal solution. Also find the maximum total billing during the next month. Four suppliers have submitted sealed bids that quote the price per case of hairnets delivered to four regional stores of the army. The bids are summarized in the following table. The regional stores requirements as well as supplying capacities of suppliers are also shown. Supplier 4 has quoted for only region 1. Because of previous contractual obligations, region 3 will have to get a minimum of cases from supplier 2. Determine the optimum distribution for this company to minimize cost. A company produces a small component for an industrial product and distributes it to five wholesalers at a fixed delivered price of Rs.
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  • Sales forecasts indicate that monthly deliveries will be ,,,, units to wholesalers 1, 2,3,4,5 resp. The direct costs of production of each unit are Rs. The transportation cost of shipping a unit from plants to wholesaler are given below:Wholesaler 1 2 3 4 5 Plant 1 5 7 10 15 15 2 8 6 9 12 14 3 10 9 8 10 15Find how many components each plant must supply to each wholesaler to maximize the profit? What is the maximum total profit? Take the monthly production capacities of plant 1, 2 and 3 as ,, units resp. Explain the following in the context of assignment problem: a Balanced assignment problem b The Hungarian method c An infeasible assignment Q Show that the assignment model is a special case of the transportation model.
    Link: https://quizlet.com/368137312/transportation-test-1-flash-cards/
  • P Q Solve the following assignment problem for minimum optimal cost:. A department has four subordinates and four tasks to be performed. The subordinates differ in efficiency and task differs in their intrinsic difficulty. The estimates of the profit in rupees each man would earn is given in the effectiveness matrix. How should the task be allocated, one to each man, so as to maximize the total earning? Xyz airlines operating 7 days a week has given the following time table. Crew must have a minimum layover of 5 hours between flights. Obtain the pairing of flights that minimize layover time away from home. For any given pairing the crew will be based at the city that results in the smaller layover. Solve by using the method of matrices, the following game:B 1 0 2 3 0 0 A 0 2 1Q Solve by using the method of matrices, the following game:B 1 -1 -1 -1 -1 3 A -1 2 -1Q Solve by using the method of matrices, the following rectangular game:B 3 -1 1 2 -2 3 2 3 A 2 -2 -1 1Q Solve the following game by linear programming:B 0 2 2 3 -1 3 A 4 4 -2Q Define the queue and explain the various queue disciplines.
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  • Explain characteristics and classification of queuing model. A duplicating machine maintained for office use is used and operated by people in the office who need to make copies, mostly secretaries. Since the work to be copied varies in length no. Generally the requirements for use are random over the entire 8 hour working day but arrive at a rate of 5 per hour. Several people have noted that a waiting line develops occasionally and have questioned the policy of maintaining only one unit.
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  • If the time of a secretary is valued at Rs. Data have been accumulated at a banking facility regarding the waiting time for delivery trucks to be loaded. The average time to load a truck, using 2 loaders is 10 minutes so that the service rate is 3 trucks per hour. The management is considering hiring another loader at Rs. Drivers are paid Rs.
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  • Exercise What is transportation problem? Write mathematical form of transportation problem. What do you mean by balanced transportation problem? Find an initial basic feasible solution of the following problem using north west corner rule. Determine an initial basic feasible solution of the following transportation problem by north west corner method 7. Obtain an initial basic feasible solution to the following transportation problem by using least- cost method. Consider the following transportation problem Determine initial basic feasible solution by VAM Determine basic feasible solution to the following transportation problem using North west Corner rule.
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  • Scientific basis 2. Scientists, different disciplines 3. Mention two applications of OR. Industry Planning 4. How can a hospital benefit from the application of OR methods? To solve waiting for problems 5. Decision making 7. OR gives a qualitative solution Ans. True 8. One of the OR phases is the Action phase Ans. True 9. Diagram belongs to the physical model Ans. True Allocation problems are represented by the iconic model Ans.
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  • False OR methodology consists of definition, solution and validation only. The interaction between the OR team and Management reaches peak level in the implementation phase. Inter-disciplinary OR Define the problem Model Parameters Linear An alternate course of action Fractious One of the characteristics of canonical form in the objective function must be of maximisation. Feasible Half-plan The feasible region is a convex set Ans. The optimum value occurs the anywhere infeasible region Ans. The right-hand side element of each constraint is non-negative.
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  • Matrix-minima method gives the optimum solution. In matrix-minima method, you start allocating from the left-top cell of the table. North-west corner rule gives the optimum solution. Not equal to In an AP, the constraints are of equality type. The number of facilities should be equal to the number of resources. The decision variables can take on any value. In the Hungarian method, you prepare the row-reduced matrix. The number of assignments should be equal to the number of rows for an optimum solution.
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  • There can be more than one allocation in a row. Maximisation problem Infeasible Only once Salesman Integer programming is applied to problems that involve discrete variables. If some variables take on non-negative values, then it is known as pure IPP. This book analyzes the underlying theoretical principles of multi-objective linear programming problems with multi-choice parameters. It studies transportation problems in the same domain with extension to fuzzy stochastic criteria.
    Link: https://dhhs.michigan.gov/OLMWEB/EXF/SR/Public/SRM/701.pdf
  • The main objective of O. R is to provide a Scientific basis to the decision makers. R employs a team Scientists from different disciplines 3. Mention two uses of O. How is it used in hospital. R Imbibes interdisciplinary approach. OR increases the effectiveness of Decision making ability. R gives qualitative solution. One of O. Allocation problems are represented by iconic model.
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  • R methodology consists of definition, solution and validation only. The interaction between O. R team and Management reaches peak level in implementation phase. OR imbibes Interdisciplinary team approach Linear programming is tool of OR To solve any problem through OR approach the first step is Define the problem Model represents a real life system Parameters represents the controlled variables of the system. UNIT 2 Both objective function and constraints are expressed in Linear forms. P requires existence of Alternate course of actions. Solution of decision variables can also be Fractious One of the characteristics of canonical form in the objective function must be of maximisation. The collection of all feasible solutions is known as the Feasible region. A linear inequality in two variables is known as a Half plan The feasible region is a convex set. The optimum value occurs anywhere in feasible region. The right hand side element of each constraint is non-negative. A basic solution is said to be a feasible solution if it satisfies all constraints.
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  • If one or more values of basic variable are zero then solution is said to be degenerate. The key column is determined by Zj - Cj row. The ve and infinite ratios are considered for determining key row. Artificial variables enters as Basic Variable. Dual L. P always reduces the amount of computation. It is possible to reverse the dual L. P to primal L. Fill in the blanks The coefficients of decision variable sin the objective function becomes For every L. P there exists a unique Dual problem. Optimality is reached when the resources are not fully utilized. At optimum, the relationship holds as a strict equation. Sensitivity analysis is carried out on Final simplex table. It helps us to study the effect of changes in Resource, levels on objective function. The results of sensitive analysis establishes Upper, lower and bounce for input parameters value.
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  • UNIT 5 Transportation problems are a special type of L. The number of rows and columns need not always be equal Transportation problem develops a schedule at minimum cost P can also be solved by simplex method. Matrix-minima method gives optimum solution. In Matrix-minima method we start allocating from left-top cell of the table.
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  • In vogels approximation method we first construct penalty and then start allocating. North-west corner Rule gives optimum solution. All the values of Cij - ui - vj should be or zero for the solution to be optimum. In unbalanced T. P ai is Not equal to to bj. P UNIT 6 P the constraints are of equality type. The no. The decision variables can take any value. The number of assignments should be equal to number of rows for optimum solution. There can be more than one allocation in a row. P number of rows to number of column.
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  • Hungarian method cannot be applied directly to Maximisation problem problem. In traveling salesmen problem the objective is to visit each cities Only once Salesman has n 1! UNIT 7 Integer programming is applied to problems that involve discrete variables. If some variables can take non negative values then it is known as pure I. An optimum solution to I. P is first obtained by using Simplex method. With the addition of Gomorys constraint the problem is solved by Dual simplex method.
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  • We select that variable for Gomorys constraint whose fractional value is more. Optimum values in an pure I. Branch and Bound Technique is applied when some variables have upper or lower bounds. We start the technique with lower bound. Customers arrive at a Bank at regular interval. Queuing identifies the optimal service facilities to be provided. Queuing theory is based on deterministic model. One of the indicators of efficiency of a system is Utilization factor. Analysis of Queuing system explores Various alternatives. Simulation technique can also be used for analysis. Queuing process has arrival pattern, service facility and Queue discipline as its constituents. Yes If the arrivals are completely random, then it follows poisson distribution. Multiple service channels may be arranged in Series or in parallel The service time can be Constant or varying. When customers keep in switching over from one queue to another then it is called Jockeying Balking, Collusion, Reneging, Jockeying are the types of customer behaviour.
    Link: https://jiskha.com/questions/1694928/if-you-perform-10-joules-of-work-lifting-a-10-n-box-from-the-floor-to-a-shelf-how-high-is

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