## Production Planning and Control - Dec 2013

### 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.
**1 (a)** What is the role of capacity planning in MPC(5 marks)
**1 (b)** Write short note on MRP and MRP-Il(5 marks)
**1 (c)** Explain the functions of MPS(5 marks)
**1 (d)** From the dual of the following primal problem:

Minimize Z=2x_{1}+6x_{2}

S.T. 9x_{1}+3x_{2}≥20

2x_{1}+7x_{2}=40

x_{1} & x_{2}≥0(5 marks)
**2 (a)** What are the key features of JIT and how does it affect MPC system. Explain in detail.(10 marks)
**2 (b)** The standard weight of a special purpose brick is 5kg and it contains two basic ingredients B_{1} and B_{2}, B_{1} cost Rs.5 per kg and B_{2} cost Rs.8 per kg. Strength consideration dictate that the brick contains not more than 4 kg of B_{1} and a minimum of 2kg of B_{2}. Since the demand for the product is likely to be related to the price of the brick, find graphically the minimum cost of the brick satisfying the above conditions(10 marks)
**3 (a)** Write short note on the following

i) MPC routing and scheduling

ii) Shop floor control.(10 marks)
**3 (b)** Find an optimal sequence for processing nine jobs through the machines A,B,C in the order ABC. Processing times are given below in hours. Find the total elapsed time for the optimal sequence and idle time for each machine.

Job | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

Machine A | 4 | 9 | 5 | 10 | 6 | 12 | 8 | 3 | 8 |

Machine B | 6 | 4 | 8 | 9 | 4 | 6 | 2 | 6 | 4 |

Machine C | 10 | 12 | 9 | 11 | 14 | 15 | 10 | 14 | 12 |

**4 (a)**The sales of a company are given below:

<colgroup span="11" width="85"> </colgroup>

Year | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 |

Sales | 240 | 280 | 300 | 330 | 380 | 410 | 490 | 560 | 680 | 800 |

Fit a straight line to data and find :

i) Forecast for the year 2013

ii) Coefficient of correlation

iii) Standard error of estimate

iv) Limits of forecast(10 marks)

**4 (b)**Solve the following LP problem using simplex method :

Maximize z=10x

_{1}+15x

_{2}+20x

_{3}

S.T. 2x

_{1}+4x

_{2}+6x

_{3}≤24

3x

_{1}+9x

_{2}+6x

_{3}≤30

x

_{1},x

_{2}&x

_{3}≥0.(10 marks)

**5 (a)**An airline company ha drawn up a new flight schedule involving five flights. To assist in allocating five pilots to the flights, it has asked them to state their preference scores by giving each flight a number out of 10. The higher the number. the greater is the preference. Certain of these flights are unsuitable to some pilots owing to domestic reasons. These have been marked with a 'X'.

<colgroup span="7" width="85"> </colgroup>

Flight Number | ||||||

1 | 2 | 3 | 4 | 5 | ||

Pilot | A | 8 | 2 | X | 5 | 4 |

B | 10 | 9 | 2 | 8 | 4 | |

C | 5 | 4 | 9 | 6 | X | |

D | 3 | 6 | 2 | 8 | 7 | |

E | 5 | 6 | 10 | 4 | 3 |

**5 (b)**The purchase manager currently follows EOQ policy of ordering for an item in the stores of his company. The annual demand of the item is 1,600 units. Its carrying cost is 40% of the unit cost where the unit cost is Rs.400. The ordering cost is ?500 per order. Recently, the vendor supplying that item has given a discount of 10% in its unit cost if the order size is minimum of 500 units.

(i) Find W and the corresponding total cost per year.

(ii) Greek whether the discount offer given by the vendor can be considered bv the purchase manager..(10 marks)

**6 (a)**Define the term 'Aggregate Plan'. What are its objectives, input and output?(10 marks)

**6 (b)**A bakery keeps stock of popular brand of cake. Previous experience shows the daily demand pattern for the item with associated probabilities as given below:

<colgroup span="7" width="85"> </colgroup>

Daily demand | 0 | 10 | 20 | 30 | 40 | 50 |

Probability | 0.01 | 0.2 | 0.15 | 0.5 | 0.12 | 0.02 |

Use the following sequence of random number to simulate the demand for the next 10 days.

Random numbers: 25,39,65,76,12,05,73,89,19,49.

Also estimate the daily average the daily average demand for the cakes on the basis of simulated data.(10 marks)

**7 (a)**A product is produced by four factories F

_{1},F

_{2},F

_{3}and F

_{4}. Their unit production costs are Rs.2,3,1 and 5 respectively. Production capacity of the factories are 50,70,30 and 50 units respectively. The product is supplied to four stores S

_{1},S

_{2},S

_{3}and S

_{4}the requirements of which are 25,35,105 and 20 respectively. Unit cost if transportation given below:

<colgroup span="6" width="85"> </colgroup>

Destination | |||||

S1 | S2 | S3 | S4 | ||

Factory | F1 | 2 | 4 | 6 | 11 |

F2 | 10 | 8 | 7 | 5 | |

F3 | 13 | 3 | 9 | 12 | |

F4 | 4 | 6 | 8 | 3 |

Find the transportation plan such that the total production and transportation cost is minimum.(10 marks)

**7 (b)**The following information is available regarding a project implementation:

<colgroup span="3" width="85"> </colgroup>

Activity | Preceding activity | Duration (days) |

A | - | 3 |

B | - | 4 |

C | - | 2 |

D | AB | 5 |

E | B | 1 |

F | B | 3 |

G | F,C | 6 |

H | B | 4 |

I | E,H | 4 |

J | E,H | 4 |

K | C,B,F,J | 1 |

L | K | 5 |

i) Draw the network for the above project

ii) Determine the critical path anad duration of the project.(10 marks)