Production Planning and Control  May 2015
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.
Solve any four of the following:
1 (a) Master Production Schedule. (5 marks)
1 (b) Kanban (5 marks)
1 (c) MRP II (5 marks)
1 (d) Capacity Planning (5 marks)
1 (e) Shop Floor Control (5 marks)
1 (f) Framework of MPC System with function of each Module. (5 marks)
2 (a) Seven jobs, each of which has to through the machines M_{1} and M_{2} in the order M_{2}M_{1}, have the following processing times in hours:
Job  A  B  C  D  E  F  G 
Machine M_{1}  3  12  15  6  10  11  9 
Machine M_{2}  8  10  10  6  12  1  3 
i) Determine the optimal sequence that will minimize the total elapsed time. Also find the idle time of each machine.
ii) If the oder is reversed to M_{1}M_{2}, what difference will it make to the calculated result and idle times. (10 marks)
2 (b) Find the optimal assignment (Effectiveness matrix in manhor needed):
Worker  Job  
A  B  C  D  
1.  5  3  2  8 
2.  7  9  2  6 
3.  6  4  5  7 
4.  5  7  7  8 
3 (a) Solve the following problem by Simplex Method: Z_{max}=2x_{i}+3x_{2}.
Subjected to: x_{1}+x_{2}≤10; 2x_{1}+3x_{2}≤5; x_{1}x_{2}≥10. (5 marks)
3 (b) A firm manufactures three products A, B and C, Time to manufacture product A is twice that for B and thrice that for C and theyare to be produced in the ratio 3:4:5. The relevant data is given in the following table:
Raw Material  Requirement per unit of product (kg)  Total Availability (kg)  
A  B  C  
P  6  5  9  5,000 
Q  4  7  8  6,000 
If the entire labour is engaged in manufacturing product A, 1,600 unit of this product can be produced. There is demand for at least 300, 250 and 200 units of product A, B and C and the profit earned per unit is Rs. 50, Rs. 40 and Rs. 70 respectively.
Formulate the problem as Linear Programming problem. (10 marks)
4 (a) The demand for an item is Rs. 18,000 per year. Production rate is 3000 unit / month. The carrying cost is Rs. 0.15 / unit / month and the setup cost is Rs. 500 per setup. The shortage cost is Rs. 20.00 per unit per year. Find the following parameters:
i) Economic Batch Quantity
ii) Maximum Inventory
iii) Maximum Stockout
iv) Cycle Time
v) Inventory Period
vi) Shortage Period. (10 marks)
4 (b) Estimate the sales forecast for the year 2000, using exponential smoothing forecastor. Take α=0.5 and the forecast for hea year 1995 as 160 × 10^{5} units. Compare the forecast with least square method.
Year  1995  1996  1997  1998  1999 
Sales Rs. (×10^{5})  180  168  159  170  188 
5 (a) The activities involved in a small project are given below along with relevant information. Construct the network diagram and find the critical path and floats for each activity.
Activity  12  13  23  24  34  45 
Duration  20  25  10  12  6  10 
5 (b) The time estimate (in weeks) for activities of a P.E.R.T. network are given below:
i) Draw the network and identify all the paths
ii) Determine the expected project length
ii) Calculate the standard deviation and variance of the project in Tabular form.
Activity  Optimistic Time t_{0}  Most Likely TIme t_{m}  Pessimistic Time t_{p} 
12  1  1  7 
13  1  4  7 
14  2  2  8 
25  1  1  1 
35  2  5  14 
46  2  5  8 
56  3  6  15 
6 (a) Complete the MRP plan for the component shown below. Use lot size=60 and lead time of 1 weeks and safety stock=10:
If the lot size is changed to 80 units, redraw the MRP plan and recalculate the table.
Component  1  2  3  4  5  6  7  8  
Gross Requirements  60  140  30  130  
Scheduled Receipts  50  50  50  
On hand at the end of period  20  
Planned Order Realease 
Explain the following:
6 (b) (i) Purchasing and EDI in MPC. (5 marks)
6 (b) (ii) CRP with flow diagram. (5 marks)
7 (a) "A company has three factories X,Y, Z. It supplies good to four warehouse W1, W2, W3 and W4. The production of the factories and demand of the warehouse are shown in the table. Determine the optimal solution of the problem.

Warehouse  
W1  W2  W3  W4 
Production Capacity 

Factory  X  19  30  50  12  7 
Y  70  30  40  60  10  
Z  40  10  60  20  18  
Demand  5  8  7  15 
7 (b) Discuss the advantages and limitations of Simulation. (5 marks)
7 (c) Explain lean and Agile Manufacturing in detail. (5 marks)