INDIAN INSTITUTE OF MATERIALS MANAGEMENT
Post Graduate Diploma in Materials Management
Graduate Diploma in Materials Management
Paper No. 2
QUANTITATIVE TECHNIQUES AND OPERATIONS RESEARCH
Date: 10.06.2018 Max .Marks: 100.
Time: 2.00 to 5.00 p.m. Duration: 3 hours
Instructions:
1. The Question Paper is in two parts- Part A (compulsory) and Part B.
2. From Part A answer all the questions. Each question carries 1 mark, total 25 marks. (Total Marks 25)
3. From Part B answer any five questions out of 7 questions .Each question carries 15 marks, total 75 marks.
4. Use of non-scientific calculator and/or mathematical tables is permitted.
5. Graph paper can be used wherever necessary.
PART A 25 x1 25 marks)
Compulsory)
Q.1 State True Or False 15 marks
a. Analysis of behaviour of a gas container developed by Markov
b. Processing n jobs in two machines can be done by Johnson rule
c. VAM is used in dual programming
d. Dynamic model is representation of the bevavior of real problem
e. Moving average is used in inventory analysis
f. To calculate floats CPM is to be applied
g. Cost slope is starting point of crashing of activities in a net work
h. Exponential smoothing is a forecast model
i. At break even point fixed cost is not equal to contribution
j. Simplex method is also known as simplex algorithm
k. Stochastic variable is known as chance variable
l. Two tails of normal distribution will never touch axis
m. Net present value method does not recognise time value of money
n. Queuing model does not specify by service channels
o. A POISSON distribution is a discrete probability distribution.
Q.2 Fill up the blanks 5 marks
a. VMI stands for
b. LP model solves the problem of product
c. MARKOV CHAIN PROCESS is used for brand
d. Two machines and N no of jobs can be scheduled by
e. EOQ model is applicable when there is demand
June 2018
Q.3 Abbreviate the following 5 marks
a. IRR
b. OR
c. NPV
d. TPM
e. DCF
PART B
(Answer any five) 5 x15 75 marks
Q.4 There are 4 jobs can be manufactured at 4 machines 4. One job is allocated to one machine unit production cost of the jobs on each machine centre is given in the table 15 marks
1 2 3 4
A 5 4 2 6
B 3 2 5 4
C 1 4 2 3
D 2 3 4 5
Find the allocation of jobs to machine centre so that total cost of process will be minimum.
Q.5 find the project duration time and identify critical path 15 marks
ACTIVITY A B C D E F G H I
DURATION 3 2 3 4 2 3 4 2 2
Interdependence B A G C E H,F
Q.6 Machine operator has to perform two operations turning, and threading on no of jobs . Time required to perform the operation in minutes are given
Determine the order in which the job is to be processed in order to minimise total time required to finish the jobs also find the idle time on the two machines 15 marks
JOB TIME (TURNING MIN TIME (THREADING MIN
1 3 8
2 12 10
3 5 9
4 2 6
5 9 3
6 11 1
Q.7 A firm uses lathes ,milling, and griding machines to produce two parts. machine times reqd for each part is shown and max time available and profit are also shown, find the no of part each to manufacture per week to maximise the profit
a. Formulate the linear programming model 8 marks
b. Use graphical method or simplex method to solve the problem. 7marks
TYPE OF MACHINE TIME MAX AV TIME PER WEEK
M/C 1 M/C2
LATHE 12 6 3000
MILLING 4 10 2000
GRINDING 2 3 900
PROFIT PER UNIT RS 40 RS 100 time all in minutes
Q8 Discuss in brief NPV method 5 marks
The xyz co ltd is planning for three investments A B C each requires an investment of Rs 4900 and each has economic life of 3 years and total cash inflow over that period Rs 6000. The pattern for each proposal is 10 marks
YEAR ANNUAL CASH IN FLOW
A B C
1 RS 1000 RS 2000 RS 3000
2 2000 2000 2000
3 3000 2000 1000
Calculate the NPV of each proposal if required rate of return 10 percent.
Q.9 A self service store employ one cashier at the counter. 9 customers at every 5 minutes while cashier can serve10 customer in 5 minutes 15 marks
Assuming poissons distribution on arrivalrate and exponential on service rate find
1 . Average no of customer in the system
2 Average queue lenth
3 AV time a customer spends in the system
4 AV time a customer waits before served
Q.10 a. What is EOQ 5 marks
b. A firm uses 12000 units a year of a material costing Rs 1.25per unit. Ordering cost Rs 15 per
order holding cost is 5 percent per year of average inventory Find the EOQ 5 marks
c.Firm follows EOQ and it operates for 300 days per year, procurement time 14 days and safety
stock is 400 units. Find re order level max inventory and av inventory. 5 marks
Q.11 An auto rickshaw driver finds from his previous record that the cost of running an auto, whose purchase price is rs 7000 is as below 15 marks
YEAR 1 2 3 4 5 6 7 8
RUNNING COST 1100 1300 1500 1900 2400 2900 35OO 4100
RESALEPRICE 3100 1600 850 475 300 300 300 300
AT WHAT AGE IS THE REPLACEMENT DUE?
Q. 12 What is Breakeven Analysis Discuss in detail. 15 marks