St. Joseph’s College of Commerce M.Com. 2014 II Sem Operations Research For Business Decisions Question Paper PDF Download

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  1.      JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

End Semester Examinations – MARCH / APRIL 2014

M.com – ii semester

OPERATIONS RESEARCH FOR BUSINESS DECISIONS

 

Duration: 3 Hrs                                                                                            Max. Marks: 100

SECTION – A

 

  1. I) Answer any SEVEN Each carries FIVE  marks.                        (7 x 5 = 35)

 

  • A) Explain the rules for constructing a dual.

 

  1. B) M/s Vikram Engineering Works have obtained a large contract for the supply of an alloy steel. The alloy needs three metals X, Y and Z. If the minimum requirement of the metals per week would be: 12 units of X, 10 units of Y and 14 units of Z. The metals are available from dealers who supply them in standardized boxes containing the metals in three different proportions. The boxes are called by code numbers: 221, 321 and 421 respectively. Box 221 contains 1 unit of X, 2 units of Y and 1 unit of Z. Box 321 contains 3 units of X, 2 units of Y and 1 unit of Z whereas Box 421 contains 1 unit each of X and Y and 5 units of Z. The cost of one Box of type 221,321 and 421 is respectively, Rs 1200, Rs 900 and Rs 1500.

Draft the problem as a linear programming problem and also fine its dual.

 

  1. Define Operation Research. Explain the main phases of an OR study.

 

  1. Maxi Taxi Service operates every day four routes with four taxies and the relevant data is given below:
Trucks                                       Routes
  A B C D
1 5.2 5.5 5.0 5.6
2 4.9 5.1 5.2 5.4
3 4.8 5.2 4.9 5.3
4 5.0 5.0 5.2 5.4
Distance to be covered 220 320 360 250

The table contains the kms per litre of diesel consumption by each of the taxies when run is given in the four routes. Find out the assignment of taxies to routes in order to reduce the consumption of diesel per day.

 

  1. What are the various methods to develop the initial feasible solution to a transportation problem? Give the steps involved in VAM. Explain with the help of an example.

 

  1. A branch of Punjab National Bank has only one typist. Since the typing work varies in length (no. of pages to be typed), the typing rate is randomly distributed approximating a Poisson distribution with mean service rate of 8 letters per hour. The letters arrive at a rate of 5 per hour during the entire 8 hour work day. If the type writer is valued at Rs 1.50 per hour, determine
  2.  a) Equipment utilization
  3. b) Average system time
  4. c) Average idle time cost of typewriter per day

 

  1. Use graphical method to solve the following problem

Max Z = 7x1+ 3x2

Subject to:

x1 + 2x2> 3

x1 +  x2< 4

0 < x1< 5/2

0< x2< 3/2

And x1, x2> 0

 

  1. Define dynamic programming with suitable examples. List and explain the terminologies of dynamic programming problem.

 

  1. Explain the following terms:
  2. i) linear programming ii) surplus variable iii) prohibited assignment
  3. iv) queue discipline  v) collusion

 

  1. A Production Manager is planning to produce a new product and he wishes to estimate the raw material requirement for that product. On the basis of usage for similar product introduced previously, he has developed a frequency distribution of demand in tonnes per day for a two month period. Use this data to simulate the raw material usage requirements for 7 days.

Random numbers are: 27,13,80,10,54,60,49,78,66,44

Demand tonnes/day      10      11        12        13        14        15        total

Frequency no. of days   6       18        15        12        6          3          60.

 

  1. A company has three production facilities S1, S2 and S3 with production capacity of 7,9 and 18 units( in 100s) per week of a product, respectively. These units are to be shipped to four warehouses D1, D2, D3 and D4 with requirement of 5, 6, 7 and 14 units (in 100s)per week respectively. The transportation costs ( in Rs)per unit between factories and warehouses per unit between factories and warehouses per unit between factories and warehouses per unit between factories and warehouses are given in the table below
  D1 D2 D3 D4 CAPACITY
S1 19 30 50 10 7
S2 70 30 40 60 9
S3 40 8 70 20 18
DEMAND 5 8 7 14 34

Formulate this transportation problem as an LP model to minimize cost.

 

SECTION –  B

 

III)   Answer any THREE questions.  Each carries FIFTEEN  marks.            (3×15 = 45)

  1. A firm has a single channel service station with the following arrival and service time probability distribution:
Inter arrival Time (min) Probability Service time (min) Probability
10 0.10 5 0.08
15 0.25 10 0.14
20 0.30 15 0.18
25 0.25 20 0.24
30 0.10 25 0.22
    30 0.14

The customer’s arrival at the service station is a random phenomenon and the time between the arrivals varies from 10 min to 30 minutes. The service time varies from 5 min to 30 min. the queuing process begins at 10 am and proceeds for nearly 8 hours. An arrival goes to the service facility immediately if it is free. Otherwise it will wait in a queue. The queue discipline is first come- first serve.

If the attendants wages are Rs 10 per hour and the customers waiting time costs Rs 15 per hour then would it be an economical proposition to engage a second attendant? Use the following random numbers, the first for arrival and second for service and so on: 20, 26, 73,43, 30, 98, 99, 87, 66, 58, 83, 90, 32, 84, 75, 60, 04,08, 15, 50, 29, 37, 62, 42, 37, 28, 68, 84, 94, 65.

 

  1. A Cheese Company has factories F1, F2 and F3 which supply to warehouses at W1, W2 and W3. Weekly factory capacities are 200, 160 and 90 units respectively. Weekly warehouse requirements are 180, 120 and 150 units respectively. Unit shipping costs in RS are as follows:
                                  Warehouse
 

 

Factory

   W1 W2 W3 SUPPLY
F1 16 20 12 200
F2 14 8 18 160
F3 26 24 16 90
DEMAND 180 120 150 450

 

Determine the optimal distribution for this company to minimize total shipping costs. Use North West Corner rule to find initial solution.

 

  1. Mc Donald’s chain wants to build four stores.in the past, the chain has used six different construction companies and having been satisfied with each, has invited each to bid on each job. The final bids ( in 000 rupees) were as shown in the following:
STORE                                 CONSTRUCTION COMPANIES
  1 2 3 4 5 6
1 853 900 875 824 891 913
2 789 845 994 804 893 884
3 820 313 285 665 804 1097
4 843 346 862 833 850 855

 

Since MC Donald’s wants to have each of the new stores, ready as quickly as possible, it will award, at most one job to a construction company. What assignment results in minimum total cost to the fast food chain?

 

  1. The extension counter of the Citizen’s bank in the premises of a state university has one drive-in counter.it is estimated that cars arrive according to Poisson distribution at the rate of 2 every 5 minutes and that there is enough space to accommodate a line of 10 cars. Other arriving car can wait outside this space, if necessary. It takes 1.5 minutes on an average to serve a customer, but the service time actually varies according to an exponential distribution. You are required to find:

 

  1. Proportion of time the facility remains idle
  2. The expected number of customers waiting but currently not being served at a particular point of time
  3. The expected time a customer spends in the system and
  4. The probability that the waiting line will exceed the capacity of the space leading to the drive-in counter.

 

  1. Discuss the important techniques used under operation research for business decisions.

 

Section – C

 

III)  Compulsory Question.                                                                              (1×20=20)

 

  1. A company produces three products P1, P2 and P3 from two raw materials A and B, and labor L. one unit of product P1 requires one unit of A,3 units of B and 2 units of labor.one unit of product P2 requires 2 units of A and B each and 3 units of L, while one unit of P3 requires 2units of A, 6 units of B and 4 units of L. The company has a daily availability of 8 units of A, 12 units of B, and 12 units of L. It is further known that the unit contribution margin for the products is Rs 3, 3 and 5 respectively for P1, P2 and P3.

Formulate this problem as a linear programming problem and then solve it to determine the optimum product mix. Is the solution obtained by you unique? Identify an alternate optimum solution if any.

 

 

 

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