www.Vidyarthiplus.com BA7206 APPLIED OPERATIONS RESEARCH VALLIAMMAI ENGINEERING COLLEGE DEPARTMENT OF MANAGEMENT STUDIES BA7206-APPLIED OPERATIONS RESEARCH UNIT I PART – A 1. What do you mean by Operations Research (OR)? 2. What do you mean by the Optimum Solution? 3. Write Short note on Unbounded solution 4. Write the Canonical form of LPP and the Standard form of LPP. 5. Why is two phase method better than big m method 6. What are the Assumptions & Requirements of LPP 7. What do you mean by Sensitivity analysis 8. When is Dual Simplex used? 9. What are Advantages of duality? 10. What do you mean by Infeasible solution? 11. What are the steps in Graphical method 12. What is Simplex Method? 13. Define Big M method? 14. What do you mean by Slack variable? 15. What is Surplus variable? 16. What do you mean by Artificial variable? 17. What is Difference between simplex and big M method? 18. What is Two phase method? 19. What do you mean by Duality? And What do you mean by Rules for primal and dual? 20. What is Shadow price? Dr. Radha Ganeshkumar, Asst. Prof(Sel. Gr) Mr. V.T. Balaji Amudhan, Asst. Prof(OG) Department of Management Studies 1 www.Vidyarthiplus.com www. Asst. V. x1.T.y3>=0. Prof(OG) Department of Management Studies 2 www. 3x1+x2>=30. Solve Graphically. x+y<=50.5y<=20. 2) a) Min z= 20x1+10x2 subject to x1+2x2<=40. x2>=0. X2>=300.com .Vidyarthiplus. Gr) Mr.com PART – B 1) a) Maximise z=3x+4y subject to 2x+5y<=60. 7x1+12x2>=120. 4x+2y<=40. Balaji Amudhan. 4x1+3x2>=60. Prof(Sel. 4) a) Solve by Big M Method Min z=12x1+20x2 Subject to 6x1+8x2>=100. 3) a) Solve by Simplex method. Asst. x1.x2>=0. b) Max z = 10y1+15y2+20y3 Subject to 2y1+4y2+6Y3<=24 3y1+9y2+6y3<=30.y2. Y1. b) Solve by Big M Method Dr. x1+2x2>=3. Solve by Graphical Method b)Max z=300x1+400x2 subject to 2x1+3x2<=1600. x2>=0.Vidyarthiplus. Max z=25x+10y subject to x+0. x1. Solve by Graphical Method b) Max z= 5x1+4x2 subject to x1-2x2<=1. 3x1+2x2<=1500. Solve by Graphical Method. Radha Ganeshkumar. x1+x2<=700. T.x2>=0 6) Using dual simplex method solve the LPP. Gr) Mr. Balaji Amudhan. Dr. Minimise Z=2x1+x2 3x1+2x2>=3 4x1+3x2>=6 x1+x2<=5 x1. The Profits on hats A & B are Rs.400 for Product B. Formulate the LPP and solution through Graphical Method 8) A company produces 2 types of hats A & B. Asst. Prof(Sel.com Max Z=6x1-3x2+2x3 Subject to 2x1+x2+x3<=16.Vidyarthiplus. The time required for each product and total time available in each department are as follows. The company can produce a total of 500 hats a day.5 Respectively. Every hat B requires twice as much as labour time as hat A. Each Product passes through 3 departments of the plant.x2>=0 7) A Plant Manufacturer 2 Product A & B. Department Hours Required Product A Product B Available Hours during month I 2 3 1600 II 3 2 1500 III 1 1 700 The company has a contract to supply atleast 300 units of product B per month. X2-2x3>=8 5) Write the dual of the following LPP and solve it .com . Asst. Prof(OG) Department of Management Studies 3 www. 3x1=2x2=x3<=18.www. The Profit Contribution of each product has been estimated as Rs. V. Solve the Optimal solution. Radha Ganeshkumar.300 for product A and Rs. MaxZ=4x1+2x2 Sub to the constraints -x1-x2<=-3 -x2+x2>=-2 x1.Vidyarthiplus.8 & Rs. The market limits daily sales of the A & B to 150 and 250 hats repectively. V. The choice is to be made from four different types of foods.Vidyarthiplus. Formulate and solve the LPP Machine Time/Unit (minutes) Machine Product capacity 1 2 3 Min/day M1 2 8 2 940 M2 4 - 8 970 M3 2 5 - 430 Dr. Gr) Mr. Formulate and solve the LPP Food type Yield per unit Proteins Cost per Carbohydrates unit Fats (Rs. The yields per unit of these foods are given in following table. The time required to manufacture one unit of cost of the products and the daily capacity of the three machines is given in the table below.com . Asst. Prof(Sel.www. fats and carbohydrates at the minimum cost.com 9) A person wants to decide the constituents of a diet which will fulfill his daily requirements of proteins.T.) 1 3 2 6 45 2 4 2 4 40 3 8 7 7 85 4 6 5 4 65 Minimum 800 200 700 requirements 10) A firm produces three products. Radha Ganeshkumar. Balaji Amudhan.Vidyarthiplus. Prof(OG) Department of Management Studies 4 www. Asst. These products are processors on 3 different machines. Gr) Mr.com .www.Vidyarthiplus.T. Balaji Amudhan.Vidyarthiplus. 7) What do you mean by Least cost method (LCM)? 8) What do you mean by Vogel approximation method (VAM)? 9) What is Modified distribution (MODI) method? 10) Define Degeneracy. Radha Ganeshkumar. V. Asst. Prof(Sel. Asst.com Unit-II PART – A 1) Define transportation 2) What do you mean by Balanced transportation problem? 3) What do you mean by Unbalanced transportation problem? 4) What are the Phases of transportation model? 5) Define Feasible solution? 6) Write Short Note on Optimum solution in transportation. Prof(OG) Department of Management Studies 5 www. 12) What are the Differences between transportation and transhipment? 13) What do you mean by Assignment? 14) What is Balanced assignment problem? 15) What is Unbalanced assignment problem? 16) How will you resolve degeneracy in Transporation Problem? 17) What do you mean by Maximization assignment problem? 18) Write down the Steps in Hungarian algorithm? 19) Write Short Note on Branch and bound algorithm? 20) What is the Difference between assignment and transportation Problem? Dr. 11) Define Transhipment. www. Asst. 1 2 3 4 5 6 A 9 22 58 11 19 27 B 43 78 72 50 63 48 C 41 28 91 37 45 33 D 74 42 27 49 39 32 E 36 11 57 22 25 18 F 3 56 53 31 17 28 3) A company has a team of 4 Salesman and the company wants to do business in 4 districts.Vidyarthiplus. Find the IBF of the following TP. Balaji Amudhan.T. Using NW Rule.Vidyarthiplus. Destination 3 1 7 4 2 6 5 9 8 3 3 9 2) Solve the assignment problem represented by the following matrix. Districts Salesmen 1 2 3 4 A 16 10 14 11 B 14 11 15 15 C 15 15 13 12 D 13 12 14 15 Dr.) Find the IBF of the following TP. Gr) Mr. Destination 10 0 20 11 12 7 9 20 0 14 16 18 b. Using NW Rule. Radha Ganeshkumar. Prof(OG) Department of Management Studies 6 www. the company has estimated the profit per day in Rs. V.com . Asst. Considering the capabilities of salesmen and nature of the district. Prof(Sel.com PART – B 1) a). For each salesmen in each district as follows. Machines Jobs A B C D 1 3 6 2 6 2 7 1 4 4 3 3 8 5 8 4 6 4 3 7 5 5 2 4 3 6 5 -7 6 4 6) Using Least Cost method solve the TP Destination Availability D1 D2 D3 D4 O1 5 2 4 3 22 O2 4 8 1 6 15 O3 4 6 7 5 8 Demand 7 12 17 9 7) Using VAM method solve the TP Destination Availability D1 D2 D3 D4 O1 5 2 4 3 22 O2 4 8 1 6 15 O3 4 6 7 5 8 Demand 7 12 17 9 Dr. Balaji Amudhan. Gr) Mr.T. Radha Ganeshkumar. Solve the problem to maximize total profits.com . 1 2 3 4 5 6 A 12 10 15 22 18 8 B 10 18 25 15 16 12 C 11 10 3 8 5 9 D 6 4 10 13 13 12 E 8 12 11 7 13 10 5) A company is faced with the problem of assigning 4 machines to 6 different jobs.6.Vidyarthiplus. D.Vidyarthiplus.www. C.com 4) A company has one surplus truck in each of the cities A.5. V. Find the assignment of trucks from cities in surplus to cities in deficit so that total distance covered by the vehicles is minimum.3. Prof(Sel.4. Asst. The Profit are estimated as follows. Asst. & E. and one deficit trucks in each of the citites 1.2. Prof(OG) Department of Management Studies 7 www. B. The distance between the cities in kms is shown in the matrix below. C. Asst. 150. The TP cost in Rs. Asst. Prof(OG) Department of Management Studies 8 www. Find the optimal shipping schedule. Rather than shipping directly from source to destination it is decided to investigate the possibility of transshipment. While demanded at retail stores are 100./per unit are given below.www. Supply 2 3 11 7 1 0 6 1 5 8 15 9 Demand 10) A firm has 2 factories x & y are 3 stores A. C X Y A B X 0 6 7 8 9 Y 6 0 5 4 3 A 7 2 0 5 1 B 1 5 1 0 4 C 8 9 7 6 0 Dr.Vidyarthiplus.com . The number of units of a product available at factories X & Y are 200 and 300 respectively. Prof(Sel. Balaji Amudhan. Gr) Mr.Vidyarthiplus. Radha Ganeshkumar. V. 250 respectively. B.T.com 8) Using MODI Method – Solve the following TP 21 16 25 13 17 18 14 23 32 27 18 41 9) Using Stepping stone method find the optimum solution for the TP Cost. www. 9) What is Saddle point? 10) Define Payoff matrix? 11) Define Dominance principle? 12) What is the concept of Two person zero sum game? 13) How is the concept of Game theory useful in Managerial Decision Making? 14) Define Pay off Matrix.Vidyarthiplus. 7) Define Pure strategy. 8) Write Short Note on Mixed strategy.com Unit-III PART – A 1) What do you mean by integer programming problem? 2) In what respect a mixed IPP is differ from pure IPP. Radha Ganeshkumar. Gr) Mr. V.T.Vidyarthiplus. 15) What are the basic assumptions of the Game? 16) Write down the advantages of Game theory. 17) What are the Methods of Matrices? 18) Define Graphical and LP Solutions in Game theory? 19) What is a Decision Tree? 20) How decision Tree analysis is used to improve the decision-making process? Dr. Prof(Sel. Prof(OG) Department of Management Studies 9 www. Asst.com . Asst. Balaji Amudhan. 3) What is Gomory’s fractional cut algorithm or Gomory’s slack? 4) What do you mean by Game? 5) What are the Characteristics of game? 6) Define Strategy. V. Balaji Amudhan.Vidyarthiplus. A1 A2 A3 A4 Player B B1 B2 0 -4 3 -5 -2 -1 1 0 Dr.com . Asst.x2 >=0 and are integers 2. Max Z=2x1+2x2 Sub to 5x1+3x2<=8 2x1+4x2<=8 x1.x2 >=0 and are integers 3. Find the optimum integer solution Max Z = x1+x2 Sub to 3x1+2x2<=5 x2<=2 x1.a) Find the Value of the Game Given the following Pay Off Matrix. Gr) Mr. Solve the game using dominance A/B No advertising No advertising No advertising No advertising 60 50 40 Medium advertising 70 70 50 large advertising 80 60 75 Player A 4. Prof(OG) B3 -2 1 6 4 Department of Management Studies 10 www. Using Gomory’s cutttting plane method .www. Radha Ganeshkumar.Vidyarthiplus. Asst.T. Prof(Sel.com PART – B 1. Player B B1 B2 B3 A1 -2 5 -3 A2 1 3 5 A3 -3 -7 11 Player A b) Find the Value of the Game Given the following Pay Off Matrix. com 5. Gr) Mr.) A) Solve by Dominance Rule: B1 B2 B3 B4 B5 A1 1 3 2 7 4 A2 3 4 1 5 6 A3 6 5 7 6 5 A4 2 1 6 3 1 b) Solve by Dominance Rule: B1 B2 B3 B4 B5 B6 A1 4 2 0 2 1 1 A2 4 3 1 3 2 2 A3 4 3 7 -5 1 2 A4 4 3 4 -1 2 2 A5 4 3 3 -2 2 2 7) Solve the Game Graphically: Player A Player A B1 B2 A1 -3 1 A2 5 3 A3 6 -1 A4 1 4 A5 2 2 A6 0 -5 Dr. Asst.com . Balaji Amudhan.Vidyarthiplus. Radha Ganeshkumar.www. Solve the game using a graph: (8 marks) A/B A1 A2 B1 3 5 B2 3 4 B3 4 3 B4 0 7 6. Asst.T. V.Vidyarthiplus. Prof(Sel. Prof(OG) Department of Management Studies 11 www. A wins 1 unit value when there are 2 heads. Find the Best Strategy & value of the Game. Asst. Radha Ganeshkumar.Vidyarthiplus. Asst. Determine pay-off matrix.T. Gr) Mr. Balaji Amudhan. Prof(Sel. 9) A and B play a Match(Game) in which each has 3 coins 5 paise. Each player selects a coin without the knowledge of others choice. if the coins do not match then B wins one unit of value. 10) Solve the 2 * n Game by the Method of Sub Game: B1 B2 B3 A1 1 3 11 A2 8 5 2 Dr. IF the sum is even. b) Two players A&B match coins.com 8) a) In a game of matching coins with 2 players.com . 10 paise and 20 paise.www. If the coins match then A wins one unit value. Determine Pay Off matrix and value. V. wins nothing when there are 2 tails and closes ½ unit value when there are one head and one tail. B wins A’s Coin. Prof(OG) Department of Management Studies 12 www.Vidyarthiplus. Radha Ganeshkumar. 16) What are the Procedures for price break model? 17) List out the problems which could be solved by simulation? 18) What is Safety Stock? 19) Define Decision theory. 20) What is the Classification of decision theory? Dr.Vidyarthiplus. 2) What are the Forms of inventory? 3) Write down the Objectives/significance of inventory model 4) What is Inventory Control? 5) Define Lead time. V.www. Gr) Mr. 8) What is Ordering Cost? 9) What are the models of Decision making under risk. 13) What is Production cost & Total cost. 6) What are the Types of stock replenishment? 7) Define the Basic inventory models. Prof(Sel.T. 14) Define Shortage cost/stock out cost. Prof(OG) Department of Management Studies 13 www. 15) Explain the Criteria of Decision Making under Uncertainty. Asst.com Unit-IV PART – A 1) Define inventory.Vidyarthiplus. Balaji Amudhan. 10) List out four advantages of Simulation Technique? 11) What is Total inventory cost? 12) Define Purchase cost.com . Asst. 4.400 and the holding cost/unit/month is 15 paise. 2) a) A stockiest has to supply 12000 units of a product per year to his customer. Find EBQ 4) Demand for an item in a company is 18. The Cost of one setup is Rs. 5) Find the Optimal order quantity for a product for which the price breaks are as follows: Quantity Unit Cost(Rs. 250 and purchase price is Rs.Vidyarthiplus. Prof(Sel. The ordering cost is Rs. The cost of one setup is Rs.com PART – B 1) a) Alpha industry needs 5400 units per year of a bought out component which will be used in its main product. The ordering cost per order is Rs. Gr) Mr. Asst. Balaji Amudhan. V. Find EOQ and no.Vidyarthiplus.50 per unit from the manufacturer.5% per year of the cost of product. Shortage cost of one unit is Rs. Asst. b) A company has a demand of 12000 units/year for an item and it can produce 2000 units per month. of order per year. b) A stockiest has to supply 400 units of a product every Monday to his customer. Determine the optimum manufacturing quantity and no. The cost of ordering and transportation from the manufacturer is Rs. Find EOQ. b)A contractor has to supply 10000 bearings per day to an automobile manufacturer. How frequently should production run be made and find EBQ.250 per order and the carrying cost per unit per year is Rs. Each part costs Rs. Find out EOQ 3) a) ABC manufacturing company purchases 9000 parts of a machine for its annual requirement.10 per unit.www. He finds that when he starts a production run he can produce 25000 bearings per day. Find the EOQ & Frequency of orders.20. The company can produce the items at a rate of 3000 units per month. Ordering Cost is Rs.20 per year. He gets the product at Rs.com .18.30. The cost of holding a bearing in stock for one year is 2 paise and the set up cost of the production run is Rs. of shortage. Find the optimum lot sizeand total cost per year assuming the cost of 1 unit as Rs. Radha Ganeshkumar.) O<q<500 1000 500<=Q<=750 925 750<=Q 875 Dr. The cost of carrying inventory is 7. Shortage cost is assumed to be infinite.000 units per year. Prof(OG) Department of Management Studies 14 www.T. Inventory holding cost is 20 paise per unit per month.75 per order.500 and the holding cost of one unit per month is 15 paise.15 and the carrying charges are 15% of the average inventory per year. Demand is fixed and known. Dr.www. The Cost of storage per unit per year is 10% of the unit cost. Daily demand of past experience: Daily demand 0 15 Probability 0. He cannot return unsold copies. Cost of a copy is 30 paise and sale price is 50 paise.80 1500<=q3<3000 24. Also estimate daily average demand. Asst. Ordering cost per order is Rs.12 0.30 0.Vidyarthiplus. EPPI 8) A newspaper boy has the following probability of selling a magazine.20 0.25 0.20 0.15 0.30 Find EOL and EVC 9)A Bakery keeps a stock of particular brand of cake.Vidyarthiplus. Find the stock situation if the owner makes 35 cakes everyday. 48 78 9 51 56 77 15 14 68 9 Using this sequence simulate the demand for next 10 days.20 0. The unit cost are given below: Quantity Unit Cost(Rs. Asst. 180.02 Consider the following sequence of random numbers. Of Copies 10 Probability 0. EOL. Prof(Sel.) O<q<500 25 500<=Q2<=1500 24.15 0.40 7) A newspaper boy has the following probability of selling a magazine.01 0. How many copies should he order? No.com . Balaji Amudhan.50 0. Prof(OG) Department of Management Studies 15 www. Of Copies 10 11 12 13 14 Probability 0. How many copies should he order? No. Radha Ganeshkumar.10 11 12 13 14 0.60 3000<=Q4 24.com 6) Find the optimal order quantity for a product when the annual demand for the product is 500 units. Gr) Mr.10 Find EVPI.T. Cost of a copy is 30 paise and sale price is 50 paise. 10) Describe all Decision criteria under the conditions of uncertainty.25 0.15 25 35 45 50 0. He cannot return unsold copies. V. Asst. Prof(OG) Department of Management Studies 16 www. Describe Kendall’s Notation for identifying a Queue Model with two channels. Poisson arrivals. 9. What is Waiting time cost? 5. What are the Types of queue? 6.Vidyarthiplus.Vidyarthiplus.A 1. 12.com Unit-V PART . When a Machine should be replaced? 20. Define service discipline. Radha Ganeshkumar. Balaji Amudhan. Define Replacement.? 7. exponential service and infinite calling population. 16. Define Queuing theory/waiting line. Gr) Mr. Define Group Replacement (GRP) 13. Dr.T. Define Individual relacement (IRP) 14. Define Queue. Define Idle time cost 4. Write Short note on: Calling Source Or Population 15. What are the Characteristics Of Queuing Models. 17. Prof(Sel. What are the types of Replacement models? 11. Write Kendall’s Notation 8. 3.com . What is Group Replacement Policy? 19.www. Define Jockeying. What is “Collusion” in Queue Discipline? 18. Asst. What are the Difference Between IRP & GRP. 2. What is Replacement model? 10. V. 1100.www.Vidyarthiplus. Radha Ganeshkumar.Vidyarthiplus. Asst. Balaji Amudhan.com PART – B 1) The cost of machine is Rs.60.8.com . Where “k” is 6. Maintenance Cost form for machine are as follows: Year 1 2 3 4 5 6 7 8 Maintenance Cost 300 450 600 800 100 1200 1500 2000 What should be the replacement year? 2) The following table gives to cost of spares per year.T.10(age). Prof(Sel. Age 1 2 3 4 5 Operating 10000 12000 15000 18000 20000 Cost After 5 years the operating cost is Rs. Prof(OG) Department of Management Studies 17 www. The maintenance Cost from the experience are as follows: Year 1 Maintenance 100 2 3 4 5 6 7 8 250 400 600 900 1200 1600 2000 Cost What should be the replacement year? Dr. Asst. IF the resale value decreases by 10% of purchase price each year. what is the best replacement policy? 4) A cost of a machine is 6100 and its scrap value is Rs.6000 x K. overhead cost of maintenance per year and resale value of certain equipment whose purchase price is Rs 50000: Year 1 2 Cost of Spares 10000 12000 14000 15000 17000 Overhead Maintenance Cost 5000 Resale Value 3 5000 6000 4 6000 5 8000 40000 32000 28000 25000 22000 3) A Taxi owner estimates from his past records that the cost per year for operating a taxi whose purchase price when new is Rs. V. Gr) Mr. 100.9.16100 and scrap value is Rs.000 are as follows.7. Vidyarthiplus.Vidyarthiplus. Prof(OG) Department of Management Studies 18 www. V. Should you replace it with B. 8) A super market has 2 girls running up sales at the counters.10. Find the year of replacement Year 1 2 3 4 5 6 7 8 Running cost 1100 1300 1500 1900 2400 2900 3500 4100 Resale price 3100 1600 850 475 300 300 300 300 6) Machine A Costs Rs. You have now a machine of type A which is one year old. annual operating cost is Rs. When? 7) A self-service store employs one cashier at its counter.com . Annual Operating Cost is Rs. No resale value. Gr) Mr. Assuming poisson Distribution for arrival rate and exponential distribution for service rate Find.200 for the 1st year and then increases by 2000 every year. Potential customers who arrive when all five chairs are full leave without entering the barbership.www.000 . Determine the best age at which to replace the machine. Assume the machine has no resale value.com 5) A desktop publisher finds from his previous records that the cost per year of using an inkjet printer whose purchase price is Rs 7000 is as given below.7674 per hour and spend an average of 15 minutes is the barber chair. (iii) Average time a customer spend in the system (iv) Average time a customer wait before being Served. Radha Ganeshkumar.400 for the 1st year and then increases by 800 every year. (i) Average number of customer in the system (ii) Average Number of customer in Queue. Is so. Asst. Machine B Costs Rs. 9 Customers arrive on an average every 5 minutes. Customers arrive at the average rate of 3. If the service time for each customer is exponential with mean of 4 minutes and if people arrive in a poisson fashion at the rate of 10 an hour. a) What is the probability a customer can get directly into the barber chair upon arrival? b) What is the effective arrival rate? c) How much time can a customer expect to spend in the barber shop? d) How much time can a customer expect to spend in the barber shop? e) What fraction of potential customer is timed away? Dr. (a) What is the average waiting time a customer spends in the system? (b) What is the expected percentage of Idle time for each girl? 9) A two – person barber shop has five chairs to accommodate waiting customers.9000. Balaji Amudhan.T. While the cashier can serve 10 customer in 5 minutes. Prof(Sel. Asst. IRP cost Rs 4/item.09 0.03 0. Asst.15 0.25 0.com 10) a)Find the Best Policy whether GRP or IRP.07 0. Balaji Amudhan. V.49 0. b) Compare IRP or GRP and conclude which is best.www. Find out whether IRP or GRP is best given the probability of failure.9 1 IRP Cost is Rs. Asst.15 Dr.07 0.com . Gr) Mr.60 Paise Per item.25 0.75 0. Week 1 2 3 4 5 6 Probability 0.85 097 1 c) There are 10000 bulbs.Vidyarthiplus.T. GRP cost is 80 paise/item. Radha Ganeshkumar. Week 1 2 3 4 5 6 Probability 0.45 0. IRP cost is Rs 1/bulb and GRP cost 35 paise/bulb.20 0.1. Prof(Sel.25 per item GRP Cost is Rs.40 0.15 0.? Week 1 2 3 4 5 6 7 Conditional Probability 0.Vidyarthiplus. Prof(OG) Department of Management Studies 19 www.