MRP-CaseStudies2008 (1)
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Transcript of MRP-CaseStudies2008 (1)
MRP Case studies by Prof Girish Phatak
Section A
Q.1 A firm has 4 work centres a, b, c and d in series with individual capacities in units
per day shown in the figure below. The actual output is also shown in the figure:
A B C D
Actual
output
310/day
(i) What is the system capacity,
(ii) What is the system efficiency.
Q.2. A work centre operates 5 days a week on a 2 shifts per day basis, each shift of 8
hours duration. There are five machines of the same capacity in this work centre. If the
machines are utilized 80% of the time at a system efficiency of 90%, what is the rated output in
standard hours per week.
Q.3. The following is a tentative master schedule for four weeks:
Product Week
1 2 3 4
A
B
C
3000
2000
1200
4000
1500
1800
1200
3000
2500
2500
3500
2000
The bill of labour in key centres for the company’s three major products A, B &c is as
below:
Department Product
A B C
X
Y
Z
0.20 hr
0.08hr
0.11hr.
0.05 hr
0.15 hr
0.08hr
0.10hr
0.20 hr,
0.05hr.
Determine the load on department x, y & z over the next 4 weeks
Q.4 Why Master Production Schedule is prepared ? Explain with suitable examples
A firm produces two products P and Q on produce-to-order basis. The demand for the products
come from several sources. The estimated demand for the two products over the next 5 weeks
are given below:
Sources of demand Product P Product Q
430 380 350 410
Week Week
1 2 3 4 5 1 2 3 4 5
Intra company
orders
- - 20 10 10 - - 10 - 10
Branch warehouse
orders
- 20 - - - - - - 20 -
R & D orders - 10 10 - - - - - 10 10
Customer demand
(forecast + on
hand order)
25 25 20 25 20 30 30 25 25 20
The safety stock for product P is 25 and for Q is 30. The lot size for P is 60 and for Q is
70. The beginning inventory for P is 50 and for Q is 60. Prepare a master production schedule for
these two products.
Q.5 What do you mean by Master Production Schedule ? Explain with suitable examples
A firm has developed a MPS for 5 weeks for the products P and Q as shown below:
MPS for 5 weeks
Product Qty. to be produced per week
1 2 3 4 5
P - 60 60 60 -
Q - 70 - 70 70
Determine whether the above MPS underloads or overloads the final assembly line
that produces products P and Q. The final assembly line has an available weekly capacity of
200 hours. Each of product ‘P’ requires 2 hours and each of product ‘Q’ requires 3 hours of
final assembly capacity:
(a) Compute the actual final assembly capacity required to produce the MPS for both
products.
(b) Compare the load with the final assembly capacity available in each week and for the
total 5 weeks.
(b) Does sufficient final assembly capacity exist to produce the MPS ?
(c) What changes to the MPS would you recommend ?
Q.6 What do you mean by level output capacity plan ? Explain
The following information is available regarding a product:
Regular time production capacity = 2500 units per month
Overtime production costs = Rs 10 per unit
Inventory carrying cost = Rs 3 per unit per month
Backlog costs = Rs 5 per unit per month
Beginning inventory = 400 units
Demand in units for four months is 4000, 3500, 2500 and 2800 respectively.
Develop a level output capacity plan that yields zero inventory at the end of 4th month.
What is the total cost that will result from this plan ?
Q.7 Recommend the inventory strategy while launching new product.
A firm has developed the following demand forecast in units for a product:
Month Demand (Units) Month Demand (units)
Jan. 210 July 400
Feb. 100 Aug 220
Mar. 200 Sept 200
April 400 Oct 120
May 600 Nov 100
June 700 Dec 250
(a) Determine the production rate required to meet the average demand if the
available working days are as below:
Month Working Days Available Month Working Days Available
Jan 22 July 21
Feb 18 Aug 22
Mar 21 Sept 20
April 22 Oct 23
May 22 Nov 19
June 20 Dec 20
(b) Determine the monthly inventory balance required to follow a plan of letting the
inventory absorb all fluctuations in demand. Assuming a constant workforce, no idle time or
overtime, no back orders, no use of sub-contractors and -no capacity adjustment, and no safety
stock, determine the beginning inventory to avoid backlogging of order during any month
(i.e., no negative inventory).
Q,8 Why aggregate planning strategies are necessary?
XYZ Manufacturing company produces a product which has a 6 months demand cycle as below:
Month Forecast demand (units) Work days / month
Jan 300 22
Feb 500 19
Mar 400 21
April
May
100
200
21
22
June 300 20
The company works on a single shift basis of 8 hours per shift. Each unit requires 10
labour-hours to be produced at a labour cost of Rs.6 per hour (regular rate) or Rs.9 per hour
(overtime rate). Units can be sub-contracted at a cost of Rs.208 per unit where as the in-
house manufacturing cost is estimated at Rs.200/- per unit. There are currently 20 workers
employed. The hiring and training costs of additional workers are Rs.300/-per person
whereas the lay-off costs are Rs.400/- per person. Company’s policy is to retain a safety stock
of 20% of monthly forecast and each month’s safety stock becomes the beginning
inventory for the next month. The beginning inventory in January is 50 units and the
inventory carrying cost is estimated to be Rs.2 per unit per month, Stock out cost is estimated as
Rs 20 per unit per month. Three aggregate plans arc proposed.
Plan 1:Vary the workforce size to accommodate demand.
Plan 2:Maintain a constant workforce of 20 and use overtime and allow idle time to meet
demands.
Plan 3:Maintain a constant workforce of 20 and build inventory or incur stock-out cost.
Plan 4: Maintain a constant workforce of 20 and allow subcontracting and idle time to
meet demand
Plan 5: Maintain a constant workforce of 20 and build inventory or incur subcontracting
cost
Compare the cost of these 3 plans and choose the best plan.
Q.9 What do you mean by Hire and Fire strategy ? Explain
The monthly production requirements of an item for a six-month period was arrived at, keeping
in view the opening stock, forecast demand and safety stock etc. as below.
Month Production
Requirement (units)
Working days
July
August
Sept.
Oct.
Nov.
Dec.
1850
1425
1000.
850
1150
1850
22
19
21
21
22
20
The information relating to the cost is as follows: Manufacturing cost per unit = Rs 100/-
Storage cost (obsolescence, opportunity cost etc.) = 1.5% per month of the
manufacturing cost.
Marginal cost of stockout = Rs 5 per unit per month.
Marginal cost of sub-contracting = Rs.2 per unit (sub-contracting cost of Rs.102 less
mfg. cost of Rs. 100/- per unit).
Man hours required per unit = 5 hours.
The company wants to meet the production requirements by adopting one of the two
levels of manning as mentioned below:
Strategy I: maintain a constant work force level based on average production
requirements during the 6 months, allow inventory to accumulate and fill shortages from
next month’s production.
Strategy II: fix the constant workforce level at the minimum necessary to meet the low
October demand (i.e., it is assumed that workers required = 850 6 5 125 days
8 hrs per day = 25 workers) and sub-contract any monthly difference between
requirements and production. Which strategy should the firm adopt ?
Q.10 What are the advantages and disadvantages of various aggregate planning strategies?
A company adopts a counter seasonal product strategy to smooth production requirements. It
manufacturers its spring product line during the first four months of the year and would like to
employ a strategy that minimises production costs while meeting the demand during these four
months. The company presently has on its rolls, 30 employees with an average wage of Rs 1000
per month. Each unit of the product requires 8 man hours. The company works on single shift
basis (8 hours shift/day) Hiring an employee costs Rs 400 per employee per occasion and
discharging an employee costs Rs 500 per person per occasion. Inventory carrying costs are Rs.
5 per unit per month and shortage costs are Rs.100 per unit per month. The company forecasts
the demand for the next four months:
Month Demand (Unit) No. of working days
in the Month
January
February
March
April
500
600
800
400
22
19
21
21
The company is thinking of adopting one of the following pure strategies:
Plan I: Vary workforce levels to meet demand
Plan II: Maintain 30 employees and use inventory and stock outs to absorb demand
fluctuations. Which strategy would you recommend?
You may assume nil inventory at the start.
Q.11 Discuss the importance of aggregate planning ?
The order position (i.e, requirements of despatch) for the next 12 months in respect of a
particular product is as under
Month Required units Month Required Units
1 13000 7 11000
2 12000 8 7000
3 10000 9 15000
4 9000 10 13000
5 11000 11 12000
6 13000 12 10000
The production capacity of the shop is 10,000 units per month on regular basis and 3000 units
per month on overtime basis. Subcontracting can be relied up on upto a capacity of 3000 units
per month after giving a lead time of 3 months.
Cost data reveal as under
Rs.5 per piece on regular basis;
Rs.9 per piece on over-time basis;
Rs.7 per piece on sub-contract basis.
Cost of carrying inventory is Re.1.00 per unit per month. Assuming an initial inventory of 1000
units and that no back logging of order is permissible. Suggest an optimal production schedule.
Also, workout the total cost on the basis of the suggested schedule.
Q.12. What do you mean by aggregate planning?
The demand forecast for a particular product of ABC company for a demand cycle of 10 weeks
is as below. The demand cycle is expected to repeal for the future period,
Week Forecast Week Forecast
1 500 6 1000
2 500 7 600
3 600 8 200
4 800 9 200
5 1200 10 500
Five aggregate planning strategies arc- considered.
Strategy 1: Vary the labour force from an initial capability of 400 units / week to whatever
capacity is required to meet the demand. The incremental cost to change labour
force is as given below.
Amount of change / week Incremental cost to change labour force
200 units
400 units
600 units
Increase
Rs 10,000
Rs. 15,000
Rs. 18,000
Decrease
Rs.10,000
Rs, 18,000
Rs.30.000
Strategy 2: Maintain a stable workforce capable of producing 600 units per week and meet demand by overtime at a
premium of Rs.50 per unit. Idle time costs are equivalent to Rs.60 per unit.
Strategy 3: Vary inventory levels, but maintain a stable workforce producing at an average demand rate with no
overtime or idle time. The carrying cost per unit per week is Rs. 20. (Assume that the company can
arrange to have whatever inventory level is required before week 1 at no additional cost
Strategy 4: Produce at a steady rate of 400 units per week and accept a limited number of back orders during weeks,
when demand exceeds 400 units. The stock out. cost of lost sale is Rs.100 per unit.
Strategy 5: Produce at a steady rate of 200 units per week and sub contract for excess demand at a marginal cost of
Rs,50 per unit
Which strategy do you recommend?
Section B
Q.13 The lead times needed to produce or procure the items were given. Suppose, now we complete the product structure tree by writing the lead time for any item next to it as shown in Fig. below
P, LT = 2
Q (3), LT = 1 R (1), LT = 3 S (2), LT = 2
LT = 3, R (2) T(2), LT = 3 T(3), LT = 3 U (4), LT = 1
Fig. Product Structure
( Note : Lead times (LT) are in days.)
Based on the above, find out the time-schedule of the requirements of the various items involved if 50 units of the end product P are required to be shipped out on day 8. Specify as to when an item is required and when an order for its production/procurement is to be placed in what quantities.
Q.14 The lead time to procure Paracetamol from a supplier is four
weeks. At present, 54 kg of the drug is available with us. There is also a
scheduled receipt of 45 kg of it in four weeks. The production
requirements of paracetamol over the next nine weeks are as :
Week 1 2 3 4 5 6 7 8 9
Amount in kg 24 - 29 11 - 5 19 27 18
If we use an order quantity of 45 kg, when shall we release the orders for
Paracetamol?
Q.15 Given the following information, how many units are on hand at the end of week 9?
Which are the weeks in which the orders may be placed?
Order Quantity = 200
Lead Time = 2 weeks Week 1 2 3 4 5 6 7 8 9
Requirements
90
10
140
55
5
15
115
95
100
Scheduled Receipts
On Hand at the
End of the Period
110
Planned Order Release
Q.16. Geetha Industries uses MRP for its production materials planning. The table below
provides the information about a particular component X. The demand for this component
is somewhat uncertain and in order to take care of a sudden spurt in the demand, a safety
stock of 50 items is recommended.
Order Quantity = 250
Lead Time = 3 weeks Week
1 2 3 4 5 6 7 8 9
Requirements
40
100
70
150
20
20
50
100
70
Scheduled Receipts
250
On Hand at the
End of the Period
150
Planned Order
Release
During which week/weeks should the receipts be planned? When should the orders be
placed? What is the expected on hand position at the end of week 9?
Q.17. Jayanagar Chair Co., (JCC) makes office chairs mainly with a steel frame, plastic-thread work and two beautifully carved wooden arm-rests. The latter are procured from a wood-turning shop which supplies JCC with a lead time of five weeks and in a lotsize of 2000 arm-rests.
As per JCC's customers' requirements, the delivery schedule for completed chairs is: Week No. 1 2 3 4 5 6 7 8 9 No. of Chairs required 200 200 500 700 300 The wooden chair handles are almost the last item to go in to JCC's chairs and
the lead time for the final assembly of the chair can be taken as one week. There are 50completed chairs in stock in JCC's finished goods' warehouse and 800 wooden handles in the plant's store. Due to the orders placed earlier, 2000 wooden handles are scheduled to arrive in week 4. Draw a MRP for the wooden handles.
Q.18 What do you mean by Bill Of Material ?
The manufacture of product x, requires the assembly of modules a, b, and c. Two
modules, each of a and c and only one module of b is needed to make one unit of x.
Module a is made from the sub-assemblies d (2 needed), e(1 needed) and f(2 needed). d is
made from components i, j and k. To make one sub-assembly of d, two components each
of i and j are required and 1 of component k. Sub-assembly f needs components l and m
(one each) . Module c needs sub-modules of g and h in quantities of two units and one
unit, respectively.
Sub-module g is, in turn, assembled from five units each of components i and j. Item i is
made from 1 unit each of components n and o.
(1) Draw the product structure based on the above information.
(2) If 100 units of x are to be produced, what are the requirements at the various
levels of the product? Write an indented Bill of Materials and calculate the
requirement of materials at the various levels.
(3) Calculate the net requirements if the quantities on hand and/or on order are as
shown below. A safety stock of i of 400 is seen as essential as it is used
sometimes in another product y whose demand is not all that predictable.
Item On Hand On Order
d 70
e 100
f 50 100
i 500 500
Q.19 Discuss the importance of MRP.
Bhagyadeep Industries is a small scale unit which assembles decorative lamps. These are
available in two models, Lakshmi (L) and Saraswati (S). The lampbase assembly (A) consisting
of the base (B), the Holder (H) and Wirecoil (W) is common to both the models; however, the
shades or covers (C) for the two models of lamps are different. The lead times are as given in
Figure below.
L,LT = 1 S,LT = 1
CL (1), LT = 3 A (1), LT = 1 CS (1), LT = 1 A (1), LT = 1
B(1) H(1) W(1) B(1) H(1) W(1)
LT=2 LT=2 LT=1 LT=2 LT=2 LT=1
Product Structures for Lamps
At the beginning of week 1, the materials position is as :
On Hand Scheduled Receipts
Base : 25 Units Cover ( Saraswati ) : During Week 2,
Holders : 100 Units 50 Units
Wire-coil : (During week 3), 100 units.
If an order of 100 Lakshmi is and 50 Saraswati is to be filled by the sixth week, calculate
the materials requirement plan. Assume that the items are ordered as required (there is no fixed
lot size).
Q.20 What is MRP ?
Stick- fast Adhesive Ltd makes adhesive plasters, cellophane tapes, plastic-coated adhesive
tapes, etc all of which need the basic ingredients of a special rubber (Code; RB 342) and a resin
(Code: Rs 108) in addition to various other ingredients. The requirements as per the formula are
as follows:
(a) Adhesive Hospital Tape (AHT)
RB 342; 100 Kg per 1000 m
Rs 108: 90 Kg per 1000 m
(b) Cellotape (CT)
Transparent (CTT)
RB 342: 50 Kg per 1000 m
Rs 108: 60 Kg per 1000 m
Coloured (CTC)
RB 342; 60 Kg per 1000 m
Rs 108: 72 Kg per 1000 m
(c) Plastic-coated Tape (PCT)
RB 342; 40 Kg per 1000 m
Rs 108: 40 Kg per 1000 m
(d) Water-Proof Sticking Tape (WPT)
RB 342; 80 Kg per 1000 m
Rs 108: 75 Kg per 1000 m
The RB 342 needs to be masticated and cured before it can be incorporated into the tapes. The
mastication and curing time is roughly two weeks. There is no loss of rubber during the
mastication and curing process. RS 108 is procured from another plant of the same company
located elsewhere and usual notice needed by that plant is about 4 weeks. RB 342 (Raw) is
supplied in batches of 4000 Kg with a lead time of four weeks.
The process of manufacture of these tapes consists of:
(a) Masticating and curing the rubber
(b) Mixing the masticated rubber, resin (RS 108) and other ingredients with n-Hexane in a mixer
(c) Coating the solution , thus prepared, onto the cello-paper or clot (as the case may be) and
simultaneously curing the coated sheet in heated chambers.
(d) Slitting the tapes into standard sizes such as 1 inch, ½ inch, etc. and packing in containers.
The manufacturing time for all the tapes (inclusive of packaging) is approximately two weeks
before the product can be shipped out.
Orders committed and forecasted are as follows:
Week from Now 1 5 9 13 17 21 25
Orders in thousand
meters for
AHT
CTT
CTC
PCT
WPT
5
25
-
-
-
10
-
-
5
-
5
25
15
-
-
15
15
-
8
-
20
-
-
-
10
18
-
10
8
10
15
30
-
-
10
The resin is supplied in batches of 5000 Kg.
The inventory position at the plant, as of now, is
RB 342 (raw) : 4500 Kg
RB 342 (Masticated) : 1800 Kg
RS 108 : 3000 Kg
RS 108 is in order, with 5,000 kg expected to arrive in week 5.
Draw a materials Requirement Plan for the above example.
Q.21 What do you mean by MRP ?
Develop product structure for Item A and Item B based on following data:
To make one unit of A, it requires 1 unit of D ,1 unit of C and 2 units of E.
To make one unit of B, it requires 1 unit of E,1 unit of C and 2 units of F.
To make one unit of C, it requires 1 unit of D and 2 units of F.
To make one unit of D, it requires 1 unit of E and 1 unit of F.
Following information is given with respect to on hand inventory and lead time.
Item On-Hand-Inventory Lead-time(Weeks)
A 50 2
B 60 2
C 40 1
D 30 1
E 30 1
F 40 1
Gross requirement of Item A is 1250 units in the week 9 as well as Gross
requirement of Item B is 460 units in week 9 . Also there is independent requirement of 270 units
for Item D and 380 units for Item E in week9.
Prepare MRP schedule based on above information.
Section C
Q.22 The precedence diagram for assembly activities A to G is shown below. The element times
required for the activities are shown in the diagram in the minutes. The line operates for 7 hours
per day and an output of 550 units per day is desired.
(a) Calculate (i) The cycle time. And
(ii) The theoretical minimum number of workers
(b) Group the task into an appropriate number of workstations.
(c) Calculate the balance efficiency.
Q.23 A producer of electronic equipment needs to add a component sub-assembly operation that
can produce 80 units during 8 hours shift. The operation have been designed for 3 activities as
shown
Operation Activity Standard time (minutes)
A
B
Mechanical Assembly
Electric wiring
12
16
C
Testing 3
(a) How many workers will be required for each activity?
(b)Assuming that the workers at each station cannot be used for other activities in the plant,
what is the approximate percentage of idle time for this assembly operation?
(c) Compute the balance efficiency.
Q.24 Balance the line for the following
Only 4 workstation are available.
Find the idle time and efficiency of balancing.
Q.25 The sequence of manufacture for a product is as given below
a) What is the most efficient number of workstations to produce this product at a rate of 40 units
per day? How many workers are required?
b) What is the most efficient and best-balanced operations assignment for 10 workers? What is
the rate of production?
c) The total direct labour cost is Rs. 40 per hour. What is the idle time cost per unit? Assume 8
hours work per day.
Section D
Q.26 PQR company has kept records of break-downs of its machines for 300 day work year as
shown below:
No. of break-
down
Frequency in days
0 40
1 150
2 70
3 30
4 10
300
The firm estimates that each break-down costs Rs.650/- and is considering adopting a
preventive maintenance program which would cost Rs.200 per day and limit the number of
break-down to an average of one per day . What is the expected annual savings from
preventive maintenance programme?
Q. 27. In a simulated operation, a firm’s maintenance crew received requests for service and
provide service during an 8 hour period as shown below:
Request arrival (clock) time Service time (hours)
0.00 1.5
1.00 0.5
3.30 2.0
4.0 0.5
7.0 1.0
The maintenance labour cost is Rs.140 per hour and the delay time cost is Rs.450 per hour .
a) Find the idle time cost for the maintenance crew.
b) Find the delay time cost for the machinery .
Q.28 The breakdowns of equipment over the past 2 years is as below:
No. of break-downs No . of month this
occurred
0 3
1 7
2 9
3 3
4 2
Total 24
Each break down costs an average of Rs. 300/- . Preventive maintenance service can be hired
at a cost of Rs . 150 per month and it will limit the break downs to an average of one per month.
Which maintenance arrangement is preferable , the current break down maintenance policy or a
preventive maintenance service contract?
Q.29 Request for maintenance service made upon a centralized maintenance facility have been
simulated for a typical 8 hours shift with arrival and service pattern as shown below :
Request arrival (clock) time Repair service time
1:30 60 mins.
2:00 20 mins.
4:15 45 mins.
4:30 120 mins.
5:30 30 mins.
7:00 10 mins.
The labour charges of maintenance crew is Rs.40 per hour, whether working or idle . the waiting
time of operators and machinery that has broken down is costed at Rs. 70 per hour .
a) Find the idle time cost of maintenance facility.
b) Find the waiting time cost of operators and machinery (not including repair time).
c) Find the total facility idle time and machinery waiting time cost .
d) Assuming that for an additional cost of Rs.10 per hour , the maintenance center could add
another crew and decrease the repair time by one third , would the additional cost be
justified.
Q.30 The probabilities of failure after maintenance for a machine is given in the table below:
Years after
maintenance
1 2 3 4 5
Probabilities of
break downs
0.2 0.4 0.2 0.1 0.1
If there are 50 machines in the facility , what is the expected number of break-downs in the 3rd
year?
Q.31 It costs Rs.4,000 to perform preventive maintenance on a group of 10 machines . If one of
the machine breaks down between preventive maintenance inspection, the break-down
maintenance costs Rs.8,000/- . The break down history on the machines is given below:
Weeks between preventive maintenance
(n)
Probability of break-down
1 0.1
2 0.2
3 0.3
4 0.4
If only costs are considered, how often should preventive maintenance de performed to minimize
the total maintenance cost (i.e. ,cost of preventive maintenance + cost of break-down
maintenance).
Q.32 CCS company has 10 regional computer centers. A preventive maintenance inspection
and repair costs a total of Rs.7000 on the average in all 10 centres. If a break –down occurs at
any centre, and average cost of Rs.10,000 is incurred for break-down maintenance. The break –
down history is as below :
Weeks between preventive maintenance
(n)
Average no. of break-downs between
PM inspections
1 0.6
2 1.8
3 3.0
4 7.0
Recommend how often preventive maintenance should be performed for minimising the total
maintenance cost.
Q.33 Aworkshop has 20nos. of identical machines. The failure pattern of machines is given in
the following table:
Estimated time after maintenance
attention (in month)
1 2 3 4 5 6
Probability of failure 0.20 0.15 0.15 0.15 0.15 0.20
It costs Rs.150/- to attend a failed machine and rectify the same. Compute the yearly cost of
servicing the broken down machines.
Q.34 The probability of failure Pn of an equipment in the nth
period after maintenance has been
estimated as follows :
N 1 2 3 4
Pn 0.1 0.2 0.4 0.3
Cost of preventive maintenance =Rs.150/-
Cost of break-down maintenance =Rs.1000/-
Determine the optimum frequency of preventive maintenance .
Q.35 A work shop has 65 nos. of machines which are identical. The failure pattern of the
machine has been observed as follows over a year :
Elapsed
time after
last
maintenan
ce in
months
1 2 3 4 5 6 7 8 9 10 11 12
Probabilit
y of
failure
0.0
5
0.0
5
0.1
0
0.1
0
0.1
0
0.1
0
0.1
0
0.1
0
0.1
0
0.1
0
0.0
5
0.0
5
If the yearly cost of servicing the failed machine is Rs. 24,000. What is the average cost of
repairs per machine per occasion.
Q.36 The break-down probability of an equipment is given below:
Month 1 2 3 4 5
Probability 0.05 0.15 0.30 0.30 0.20
There are 50 equipments in the plant . The cost of individual preventive replacement is Rs. 15
per equipment and the cost of individual break-down replacement is Rs.30 per equipment. Find
out the average break-down maintenance cost per month.
Q.37 Product A has a mean time between failure (MTBF) of 30 hrs. and has a mean time to
repairs(MTTR) of 5hrs. Product B has an M.T.B.F. of 40 hrs and has at MTTR of 2 hrs.
a) Which product has the higher reliability?
b) Which product has greater maintainability ?
c) Which product has greater availability?
Q.38 An electrical circuit board in the main control panel of a machine has four components
A,B,C and D 200 Nos.of the circuit board were subjected to accelerated operation tests which
have been equivalent to 3000 hrs of normal operation. The following data is available from the
tests..
Components
No. of failures
A 3
B 2
C 24
D 5
a) Determine the reliability of the circuit board .
b) Calculate the MTBF for the four components.
Section E
Q. 39 Following is the manpower requirements for each activity in a software project.
Activity Normal time Manpower required
0-1 2 4
1-2 3 3
1-3 4 3
2-4 2 5
3-5 4 3
3-6 3 4
4-7 6 3
5-7 6 6
6-8 5 2
7-9 4 2
8-9 4 9
A) Draw the network diagram of the project activities.
B) Rearrange the activities suitably for reducing the existing total manpower
requirement.
C) If only 9 men are available for the execution of the project then rearrange the
activities suitably for leveling the manpower resource.
Q.40 Following the manpower requirements for each in a project.
Activity Normal time(days) Manpower Required / Day
1-2 10 2
1-3 11 3
2-4 13 4
2-6 14 3
3-4 10 1
4-5 7 3
4-6 17 3
5-7 13 5
6-7 9 8
7-8 1 11
a) Draw a network and find out total and free float for each activity.
b) The contractor stipulates that during the first 26 days only 4 to 5 men and
during remaining days 8 to 11 men only can be made available. Rearrange
activities suitably for levelling the manpower sources, satisfying the above
condition.
Section F
Q.41 The information regarding jobs to be scheduled through one machine is given below
Job A B C D E F G
Processing Time (
days)
4 12 2 11 10 3 6
Due date ( days ) 20 30 15 16 18 5 9
a. What is the First Cum First Served Schedule ( FCFS ) ?
b. What is the Shortest Processing Time ( SPT ) schedule ?
c. What is the Slack Time Remaining ( STR ) schedule ?
d. What is the Earliest Due Date ( EDD ) schedule ?
e. What are the Mean Flow Times for each of the above
Q.42 Eight jobs are to be processed on a single machine . The processing times, due dates and
importance weights of the jobs are as shown in the table.
Job 1 2 3 4 5 6 7 8
Processing Time (
days)
5 8 6 3 10 14 7 3
Due date ( days ) 15 10 15 25 20 40 45 50
Importance
Weights
1 2 3 1 2 3 2 1
Assuming no new jobs arrive thereafter, determine using SPT rule and WSPT rule
a. Optimal Sequence
b. Completion time of the jobs
c. Mean flow time as well as Weighted Mean flow time
d. Average in process inventory
e. Lateness, Mean lateness, and Maximum lateness
f. Number of jobs actually late
Q.43 The process times for the five jobs A, B, C, D and E and the due dates of the jobs are given in table below. Job Process Time Due Date (Days) (Days from now) A 9 16 B 7 20 C 5 25 D 11 15 E 6 40 The jobs may be sequenced according to any of the following rules:
a) Minimum Process Time ( MINPRT) b) First Come First Served (FCFS) c) Longest Process Time (LPT) d) Due Date (DD)
For the above set of jobs, compute the following resultant characteristics of he priority rules (sequencing rules):
i) Total completion time ii) Average completion time iii) Average number of jobs in the system iv) Average job lateness
Compare the above characteristics for the given four sequencing rules. Q.44 A machine operator has to perform two operations turning and threading, on a number of
different jobs. The time required to perform these operations for each job is known. Determine
the order in which the jobs should be processed in order to minimize the total time required to
turn out all the jobs.
Job Time for Turning Minutes Time for Threading Minutes
1 3 8
2 12 10
3 5 9
4 2 6
5 9 3
6 11 1
Also find the total processing time and idle time for turning and threading operations
Q.45 There are seven jobs, each of which has to go through the machines A and B in the order
AB. Processing time in hours is as given below.
Job 1 2 3 4 5 6 7
M/C A 3 12 15 6 10 11 9
M/C B 8 10 10 6 12 1 3
Determine a sequence of these jobs that will minimize the total elapsed time T. Also find T and
idle time for machine A and B.
Q.46 A refrigeration company has six plants located in different parts of a city. Every year it is
necessary for each plant to be completely overhauled. The overhauling is carried out in two
stages A and B, and each stage requires a crew of workmen with completely different skills. The
work on stage B can start only when stage A has been completed. The plant has to be closed for
the entire period of the overhauling. The company, at present is following the schedule of the
overhaul of the six plants as given below:
Time required by the crew in days
Plant P1 P2 P3 P4 P5 P6
Crew A 12 9 10 8 10 10
Crew B 10 7 9 14 6 8
a. Determine the optimal sequence
b. If downtime of any of the six plants costs Rs.5000/day, idle time for crew A costs Rs.
1500/day and idle time for crew B costs Rs.2500 / day, which of the two schedules, the
present one or the one determined in part (a), will be more economical? What are their
respective costs?
Q.47 Four jobs 1,2,3 and 4 are to be processed on each of the five m/cs A,B,C,D and E in the order of ABCDE. Find the minimum total elapsed time if no passing of jobs is permitted. Also determine idle time for each m/c
m/c A m/c B m/c C m/c D m/c E
Job 1 7 5 2 3 9
Job 2 6 6 4 5 10
Job 3 5 4 5 6 8
Job 4 8 3 3 2 6
Q.48 Four jobs 1,2,3 and 4 are to be processed on each of the four m/cs A,B,C, and D in the order of ABCD. Find the minimum total elapsed time if no passing of jobs is permitted. Also determine idle time for each m/c
m/c A m/c B m/c C m/c D
Job 1 58 14 14 48
Job 2 30 10 18 32
Job 3 28 12 16 44
Job 4 64 16 12 42