Question Paper: Production Planning and Control : Question Paper May 2014 - Mechanical Engineering (Semester 7) | Mumbai University (MU)
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## Production Planning and Control - May 2014

### Mechanical Engineering (Semester 7)

TOTAL MARKS: 100
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks.

### Attempt any four.

1 (a) Competitive Advantage(5 marks) 1 (b) M R P ? II(5 marks) 1 (c) Explain the need of simulation(5 marks) 1 (d) Economic order quantity(5 marks) 1 (e) Input-Output Analysis(5 marks) 1 (f) Purchasing in MPC(5 marks) 2 (a) Solve the following L P problem using simplex method :
Maximum : z=3x1+2x2+5x3
Subjected to the Constraints, -x1-2x2-x3≥ 430
3x1 + 2x3 ≤ 460
x1 +4 x2 ≤ 420
x1, x2, x3
(12 marks)
2 (b) Find the trend by least square method for data as follows :

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 Year 2007 2008 2009 2010 2011 2012 2013 Demand in 1000 Units 85 75 80 72 65 60 55

Also find the demand for 2016(10 marks) 3 (a) An automobile dealer wishes to put four repairmen to four different jobs. The repairmen have some what different kinds of skills and they exhibit different levels of efficiency from one job to another. The dealer has estimated the number of man-hours that would be required for each job - man combination. This is given in the matrix from in adjacent table.
<colgroup width="148"> </colgroup> <colgroup width="138"> </colgroup> <colgroup width="143"> </colgroup> <colgroup width="131"> </colgroup> <colgroup width="101"> </colgroup>
 Job/Man A B C D 1 5 3 2 8 2 7 9 2 6 3 6 4 5 7 4 5 7 7 8

Find the optimum assignment that will result in minimum man-hours needed
(10 marks)
3 (b) A man goes to market to purchase buttons. He needs at least 20 large buttons and at least 30 small buttons. The shopkeeper sells buttons in two forms (i) boxes and (ii) cards. A box contains 2 large and 5 small buttons and a card 10 large and 5 small buttons. Find graphically the most economic way in which the man should purchase the buttons, if a box costs to paise and a card 25 paise only.(10 marks) 4 (a) Explain the following :-
(i) Monte Carlo Technique
(ii) Capacity planning in MPC system
(10 marks)
4 (b) The Bombay Transport company has trucks available at four different sites in the following numbers.
<colgroup width="" 148""=""> </colgroup> <colgroup width="" 138""=""> </colgroup> <colgroup width="" 143""=""> </colgroup> <colgroup width="" 131""=""> </colgroup> <colgroup width="" 101""=""> </colgroup>
 Site A B C D No. of Trucks 5 10 7 3

Customers W,Y and Y require trucks as shown:
<colgroup width="" 148""=""> </colgroup> <colgroup width="" 138""=""> </colgroup> <colgroup width="" 143""=""> </colgroup> <colgroup width="" 131""=""> </colgroup>
 Customers W X Y No. of Trucks 5 8 10

variable costs of getting trucks to the customers are- From A to W- Rs 7, to X - Rs 3, to Y - Rs 6
From C to W - Rs 5 , to X - Rs 8, to Y - Rs 4
From B to W - Rs 4, to X- Rs 6, to Y - Rs 8
From D to W - Rs 8, to X - RS 4 , to Y - Rs 3
Solve the transportation problem.
(10 marks)
5 (a) A textile mill buys its raw material from a vendor. The annual demand of the raw material is 9000 units. The ordering cost is Rs.100 per order and the carrying cost is 20% of the purchase price per month, where the purchase price per unit is Re.1. Find the following :
Economic order quantity (EOQ)
(b) Total cost w.r.t. EOQ
(c) Number of orders per year
(d) Time between consecutive two orders.
(10 marks)
5 (b) Use graphical method to minimise the time needed to process the following jobs on Machines A, B, C, D and E. Find the total time lapsed to complete both jobs. Also find for job, the machines on which it should be processed first.
<colgroup width="162"> </colgroup> <colgroup width="138"> </colgroup> <colgroup width="143"> </colgroup> <colgroup width="131"> </colgroup> <colgroup width="101"> </colgroup> <colgroup width="85"> </colgroup> <colgroup width="125"> </colgroup>
 Job 1 Sequence A B C D E Time (Hrs) 2 3 5 2 1 Job 2 Sequence D C A B E Time (Hrs) 6 2 3 1 3
(10 marks)
6 (a) Consider the following data for the activities of a project :
<colgroup width="162"> </colgroup> <colgroup width="138"> </colgroup> <colgroup width="143"> </colgroup> <colgroup width="131"> </colgroup> <colgroup width="101"> </colgroup> <colgroup width="85"> </colgroup> <colgroup width="125"> </colgroup> <colgroup span="7" width="85"> </colgroup>
 Activity A B C D E F G H I J K L M Immediate Predecessors - - B C A,D D A,D E G,H I G J,K L Duration (Days) 6 5 2 2 2 1 6 5 6 2 4 3 1

i) Draw a network diagram for this project
ii) Find the critical path and duration of the project
iii) Find the total, independent floats of various activities
(12 marks)
6 (b) Explain JIT concept? Also explain JIT purchasing in detail with diagram.(8 marks) 7 (a) What are the various strategies for Aggregate planning? Explain(5 marks) 7 (b) Construct the dual of the problem
Maximize : z=4x1+2x2
x1 - 2x2 ≥ 2
x1+2x2=8
x1-x2≤ 10
x1 ≥ 0, x2 Unrestricted in sign
(5 marks)
7 (c) Use graphical method to solve following L.P.P.
Maximize : z=2x1+3x2
Subject to the constraints x1+x<sub.2&lt; sub="">≤ 30
x2 ≥ 3
0 ≤ x2 ≤ 12
0 ≤ x1 ≤ 20
x1 - x2 ≥ 0
x1 , x2 ≥ 0</sub.2&lt;&gt;<>(10 marks)