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2003 Course Operations Research & Management

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Total No. of Questions : 6] P1153 [Total No. of Pages : 6 [3664]-168 B.E. (Production S/W) OPERATIONS RESEARCH & MANAGEMENT (2003 Course) (411126) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) Answers to the two sections should be written in separate books. 2) Neat diagrams must be drawn wherever necessary. 3) Figures to the right indicate full marks. 4) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 5) Assume suitable data, if necessary. 6) All questions are compulsory. SECTION - I Q1) a) Operations Research is the out of giving bad answers to the problems, to which, otherwise have worse answers - Discuss. [4] b) A paper mill produces rolls of paper used in cash registers. Each roll of paper is 100 m in length and can be used in the widths of 3, 4, 6 and 10 cm. The company s production process results in rolls that are 24 cm in width. Thus the company must cut its 24 cm roll to the desired widths. It has six basic cutting alternatives as follows. Cutting alternatives Width of rolls (cm.) 3 4 6 10 Waste (cm.) I 4 3 II 3 2 III 1 1 1 1 1 IV 2 1 2 V 4 1 2 VI 3 2 1 1 The minimum demand for four rolls is as follows Roll width (cm.) 2 4 6 2000 3600 1600 Demand - 10 500 P.T.O. The paper mill wishes to minimise the waste resulting from trimming to size. i) Construct the L.P. model. Do not solve the problem. [6] ii) Write the dual of the above L.P. model. c) Define the following terms in L.P.P. i) Redundant constraint ii) Unbounded solution [4] [4] iii) Basic variable iv) Basic solution OR a) Solve the following L.P.P. [13] Maximise z = 4x1 + 3x2 + 6x3 S.t. 2 x1+ 3x2 + 2x3 440 + 3x3 470 4 x1 430 , x1, x2, x3 0 2 x 1+ 5 x 2 b) If above represent mathematical model for 3 resource, 3 product mix problem then i) ii) Which resource is not fully utilised? By what amount? [2] If a new product (Say 4th) consumes 3 units of all three resources for what profit, this product should be manufactured? [3] Q2) a) Solve the following transportation problem for minimisation of cost. To From ai 7 4 5 3 3 1 8 5 4 7 7 1 bj 2 6 2 14 7 9 [10] 18 b) Write the L.P. form of an assignment problem. [3] c) Travelling Salesman Problem , if solved by assignment method may have a sub-optimal solution. Comment. [3] [3664]-168 -2- OR a) A city corporation has decided to carry out road repairs on main four roads of city. The government has agreed to make a special grants of Rs. 50 lakhs towards the cost with a condition that the repairs should be done at lowest cost & if work is completed within time, additional grants, if required, can be considered. Five contractors are quoted for all roads, whose costs are given below. In order to expedite the work, one road will be awarded to only one contractor. Roads R1 R2 R3 R4 C1 9 14 19 15 C2 7 17 20 19 Contractors C 3 9 18 21 18 C4 10 12 18 19 C5 10 15 21 16 Costs in Rs. lakhs i) Find out the best way of assigning the repair work to contractors and the corresponding costs. [8] ii) If required, what is the amount of additional grants? iii) Which contractor will not get the work? b) Write short note on: [1] [1] [6] i) Unbalanced Transportation Problem. ii) Degeneracy in Transportation Problem. Q3) a) Derive basic EOQ formula. [5] b) A firm uses every year 12,000 units of raw material costing Rs.1.25 per unit. Ordering cost is Rs.15 per order and the carrying cost is 5% per year of unit cost. i) Determine EOQ and the corresponding cost. ii) If firm operates for 300 days per year and if lead time is 14 days with safety stock of 400 units, determine reorder point, maximum inventory level and the average inventory level. [3] c) Mention any four optimality criteria in sequencing problem. [3664]-168 -3- [4] [4] OR a) A workshop has six machines A, B, C, D, E, F. Two jobs have to be processed through each of these machines. The processing time on each machine and technological sequence of jobs is given below. Job 1 - A C D B E F Job 2 - A C B D F E Time in minutes on Machine Machines A B C D E F Job 1 20 30 10 10 25 15 Job 2 10 15 30 10 20 15 In which order should the jobs be done on each machine to minimise the total time required to process the job? Also find the minimum elapsed time. [6] b) A machine operator has to perform two operations, turning & threading on different jobs. The time required to perform these operations in minutes is as follows. Job - 1 2 3 4 5 6 Time for turning - 3 12 5 2 9 11 Time for threading - 8 10 9 6 3 1 Determine the order in which the jobs should be processed in order to [3] minimise the total time required to complete all jobs. Also find out total processing time and idle time for turning and threading operations. [3] c) Write a short note on ABC analysis in inventory control. [4] SECTION - II Q4) a) What are the advantages and limitations of simulation? [4] b) Preventive maintenance work in a factory can be carried by a singleman crew or by two-men crew. One-man crew is expected to take 2, 3, 3.5 or 4 hours with probabilities of 0.2, 0.3, 0.4, 0.1 resp. Two-men crew may take 1.25, 1.5, 2, 3 hours with probabilities of 0.2, 0.4, 0.25, 0.15 resp. The labour cost is Rs. 15/hour while the machine idle cost is Rs. 40/hr. Using Monte Carlo Simulation, decide one-man or two-men crew should be selected. Use following random Nos. (for both crew) - 39, 82, 06, 43, 29, 62, 31 & 36, 23, 54. [12] [3664]-168 -4- OR a) Two functionally identical machines P & Q are available in the market with no scrap value. Machine P costs Rs. 12,000 & its annual cost is Rs. 400 in the first year, progressively increases by Rs. 100/- in next two years, then by Rs. 200/- in next two years & finally by Rs. 300, 400, 600, 800 in subsequent years. Machine Q costs Rs. 13,000 & annual cost is Rs. 200, 350, 550, 750, 1000, 1300, 1800, 2400, and 3000 from year to year. If the worth of money increases by 10% every year, which is the better choice, P or Q ? And in that case what would be the replacement policy? [12] b) What is the replacement policy for the items that fail suddenly? [4] Q5) a) A repairman is to be hired to repair machines which breakdown at an average rate of 3 per hr. The breakdown follows Poisson distribution, Non-productive time of machine is considered to cost Rs. 16 per hour. Two repair men have to be interviewed: One is slow but cheap, while the other is fast but expensive. The slow repairman charges Rs. 8 per hr. and he services broken down machines at a rate of 4 per hr. The corresponding values for fast repairman are Rs.10 per hr. and 6 machines per hr. Which repairman should be hired? Assume an 8-hour working day. [9] b) Explain linear programming method to solve higher size game. [7] OR a) Two players A & B play a game of matching coins in which each has 3 coins: Rs.1, Rs.2 & Rs.5. Each player selects a coin without knowledge of other player s choice. If sum of the coins is odd, A wins B s coin & if its even, B wins A s. i) Prepare pay off Matrix. [3] ii) Find the value of Game and best strategies. [6] b) Explain Dominance in game theory. [3] c) Explain the terms: [4] i) Service discipline ii) Customer behaviour [3664]-168 -5- Q6) A small project has following data. Activity 1-2 1-3 1-4 2-4 2-5 3-6 4-6 5-6 Time Normal 6 8 5 3 5 12 8 6 (Weeks) Crash 4 4 3 3 3 8 5 6 Cost penalty/Week (Rs.) 2400 2700 1500 1200 6000 1500 The cost of completing all activities as per normal time is Rs.1,54,000/without overheads. The overheads (indirect cost) are Rs. 4800/- per week. Identify C.P., find normal duration and corresponding cost. Find out optimum duration and corresponding cost and minimum duration and corresponding cost. [18] OR a) Discuss PERT calculations wrt. probability considerations in [8] detail. b) Define. i) Activity and Event ii) [10] Dummy activity iii) Earliest start and latest start for activity iv) Slack and float v) [3664]-168 Resource levelling. -6-

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