DEPARTMENT OF MECHANICAL...
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DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK VIII SEMESTER ME6015– OPERATIONS RESEARCH Regulation – 2013 Academic Year 2016 – 17
Transcript of DEPARTMENT OF MECHANICAL...
DEPARTMENT OF
MECHANICAL ENGINEERING
QUESTION BANK
VIII SEMESTER
ME6015– OPERATIONS RESEARCH
Regulation – 2013
Academic Year 2016 – 17
DEPARTMENT OF MECHANICAL ENGINEERING
QUESTION BANK
SUBJECT : ME6015 – OPERATIONS RESEARCH
SEM / YEAR : VIII Semester / IV Year MECH
UNIT I LINEAR MODELS
The phase of an operation research study – Linear programming – Graphical method– Simplex algorithm – Duality
formulation – Sensitivity analysis..
PART - A
Q.No Questions BT Level Competence
1. Define Operations Research (OR). 1 Remember
2. Define Linear Programming problem. 1 Remember
3. List the four assumptions in Linear programming 1 Remember
4. Define Big M method. 1 Remember
5. Differentiate between simplex and Big M Method. 2 Understand
6. What is Two phase method? 1 Remember
7. What do you mean by Duality? List the Rules for primal and dual. 1 Remember
8. Compare Slack variable and Surplus Variable. 2 Understand
9. Distinguish between Feasible and Optimal solution. 2 Understand
10. Summarize the Graphical method procedure. 2 Understand
11. Discuss about sensitivity analysis. 2 Understand
12. Give some example for usage of Surplus variable & Slack Variable. 3 Apply
13. Point out the application areas of LPP 4 Analyze
14. Give two examples for objective solutions 3 Apply
15. Demonstrate the unbounded solution of LP problems graphically. 3 Apply
16. Explain the limitations of LPP. 4 Analyze
17. What do you think about Infeasible solution? 4 Analyze
18. Criticize why the two phase method is better than big M method? 5 Evaluate
19. Analyze the difference between unrestricted and artificial variables. 4 Analyze
20. Generalize the maximization LPP with an example. 6 Create
PART - B
1. Maximise Z=3x+4y subject to
2x+5y ≤ 60,
4x+2y ≤ 40.
x, y >=0. Solve by Graphical Method and find the optimal solution. (16)
1
Remember
2. Write the dual of the following LPP and solve it. Find the best value for x & y.
Maximize Z = 4 X1 +2 X2
Subject to the constraints - X1 – X2 ≤-3
- X1 + X2 ≥ -2 , X1, X2 ≥ 0
(16)
1
Remember
3. i) List out the graphical method Procedure to solve simple linear programming
problems of two decision variables. (4)
ii) Examine the following LP problem using graphical method
Minimize Z = 2 X1 + 3 X2
Subject to
X1 + X2 ≥6,
7 X1 + X2 ≥14
X1 and X2 ≥ 0. (12)
1
1
Remember
Remember
4. i) Compare minimization problem and maximization problem in LPP. (4)
ii) Analyze the following LPP by Simplex Method:
Max Z= 3x1+2x2
Subject to 2x1+x2 ≤ 2,
3x1+4x2 ≥ 12,
3x1+4x2 ≤ 0 &
x1,x2 ≥ 0. (12)
4
4
Analyze
Analyze
5. Evaluate by using dual simplex method solve the LPP.
Minimize Z=2x+y
Subject to 3x+2y ≥ 3
4x+3y ≥ 6
x+y ≤ 5 & x , y ≥ 0 (16)
5
Evaluate
6. A company manufactures two types of products P1, P2.Each product uses lathe
and Milling machine. The processing time per unit of P1 on the lathe is 5 hours
and on the milling machine is 4 hours. The processing time per unit of P2 on the
lathe is 10 hours and on the milling machine, 4 hours. The maximum number of
hours available per week on the lathe and the milling machine are 60 hours and
40 hours, respectively. Also the profit per unit of selling P1 and P2 are Rs.6.00
and Rs.8.00, respectively. Create a linear programming model to determine the
production volume of each of the products such that the total profit is maximized.
and also solved by simplex method. (16)
6
Create
7. Use simplex method to calculate X1 and X2 in the LPP.
Maximize Z = 4X1 + 10X2
Subject to the constraints
2X1 + X2 ≤ 50
2X1 + 5X2 ≤ 100
3
Apply
2X1 + 3X2 ≤ 90 and
X1, X2 ≥ 0. (16)
8. Analyze the dual of the following LPP and solve it. Find the value of x1 & x2.
Maximize Z = 4x1+2x2
Subject to the constraints -x1-x2 ≤-3
-x2+x2 ≥-2 , x1, x2 ≥ 0 (16)
4
Analyze
9. A company produces 2 types of hats A & B. Every hat B requires twice as much
as labour time as hat A. The company can produce a total of 500 hats a day. The
market limits daily sales of the A & B to 150 and 250 hats respectively. The
Profits on hats A & B are Rs..8 & Rs.5 respectively. Construct a Simplex table
and solve it. (16)
2
Understand
10. a) Explain slack variable and surplus variable. (4)
b) Develop a Simplex Table and Solve
Max Z = 3 x1+2 x2, Subject to x1+ x2 ≤4,
x1- x2 ≤ 2; x1, x2 ≥0.. (12)
4
6
Analyze
Create
11. An animal feed company must produce 200 Kg of a mixture consisting of
ingredients x1 & x2 respectively x1 cost Rs.3 per kg and x2 cost Rs.8 per kg. not
more than 80 Kg of x1 can be used and atleast 60 Kg of x2 must be used.
Determine how much of each ingredient must be used to minimize cost.
3
Apply
12. i) What is meant by linear programming problem? Give brief description of the
problem with illustrations. How the same can be solved graphically. What are the
basic characteristics of a linear programming problem? (8)
ii) Solve the following LPP Graphically:
Minimize Z = 4X1 + 3X2
Subject to the constraints
X1 + 3X2 ≥ 9
2X1 + 3X2 ≥ 12
X1 + X2 ≥ 5
X1, X2 ≥ 0. (8)
2
3
Understand
Apply
13. A company produces refrigerator in Unit I and heater in Unit II. The two products
are produced and sold on a weekly basis. The weekly production cannot exceed
25 in unit I and 36 in Unit II, due to constraints 60 workers are employed. A
refrigerator requires 2 man week of labour, while a heater requires 1 man week of
labour, the profit available is Rs. 600 per refrigerator and Rs. 400 per heater.
Formulate the LPP problem and solve by any method. (16)
5
3
Evaluate
Apply
14. Formulate the dual of the following primal problem and Examine this problem.
Maximize Z = 4x1 + 10x2 + 25x3
Subject to
2x1 + 4x2 + 8x3 ≤ 25,
4x1 + 9x2 + 8x3 ≤ 30
6x1 + 8x2 + 2x3 ≤ 40
x1, x2, and x3 ≥ 0. (16)
6
Create
UNIT II - TRANSPORTATION MODELS AND NETWORK MODELS
Transportation Assignment Models –Traveling Salesman problem-Networks models – Shortest route – Minimal spanning tree
– Maximum flow models –Project network – CPM and PERT networks – Critical path scheduling – Sequencing models.
PART - A
Q.No Questions BT Level Competence
1. List out the common methods to obtain an initial basic feasible solution for a
transportation problem.
1 Remember
2. Define optimality test in a transportation problem. 1 Remember
3. Quote the differences between North west corner rule and minimum matrix
method.
1 Remember
4. Differentiate balanced transportation problem from unbalanced transportation
problem.
2 Understand
5. Describe unbounded assignment problem. 1 Remember
6. Define transshipment problem. 1 Remember
7. What difference exist between Transportation & Transshipment Problems? 2 Understand
8. Where assignment problems are used? 1 Remember
9. Describe how a maximization problem is solved using assignment model. 1 Remember
10. Illustrate the traveling salesman problem. 3 Apply
11. Distinguish between CPM and PERT. 2 Understand
12. Give the mathematical formulation of assignment problem. 2 Understand
13. Describe the method of processing ‘n’ jobs through two machines. 1 Remember
14. Illustrate any sequencing model with your own example. 3 Apply
15. Compare pessimistic time with optimistic time. 4 Analyze
16. How to measure the free float of an activity in a network. 5 Evaluate
17. Compare Vogel approximation method (VAM) & Least Cost Method. 4 Analyze
18. Explain the purpose of using dummy activities in a network with an example. 5 Evaluate
19. Summarize the assumptions, based on which PERT/CPM analysis is done for a
project.
5 Evaluate
20. Generalize the mathematical formulation of transportation problem. 6 Create
PART - B
1. i) Write the steps involved for solving Transportation problem using Vogel’s
Approximation method. (8)
ii) Obtain the Initial Basic Feasible Solution for the following TP using North
West Corner method.
I II III Supply
S1 8 5 6 120
S2 15 10 12 80
S3 3 9 10 150
Demand 150 80 50
(8)
1
3
Remember
Apply
2. Solve the following assignments problem
I II III IV V
A 10 5 9 18 11
B 13 19 6 12 14
C 3 2 4 4 5
D 18 9 12 17 15
E 11 6 14 19 10
(16)
3
Apply
3. Solve the TP where cell entries are unit costs. Use vogel’s approximate method to
find the initial basic solution
D1 D2 D3 D4 D5 AVAIL
ABLE
O1 68 35 4 74 15 18
O2 57 88 91 3 8 17
O3 91 60 75 45 60 19
O4 52 53 24 7 82 13
O5 51 18 82 13 7 15
REQUI
RED 16 18 20 14 14
(16)
4
Analyze
4. Solve the following travelling salesman problem so as to minimize the cost per
cycle. Determine whether path is satisfied.
TO
A B C D E
A - 3 6 2 3
B 3 - 5 2 3
FROM C 6 5 - 6 4
D 2 2 6 - 6
E 3 3 4 6 -
(16)
5
Evaluate
5. Solve the following transportation problem to maximize the profit.
(16)
2
Understand
6. Five workers are available to work with the machines and respective cost
associated with each worker –machine assignments is given below. A sixth
machine is available to replace one of the existing machines and the associated
costs are also given below.
Determine whether the new machine can be accept and also determine optimal
assignments and the associated saving in cost. (16)
5
Evaluate
7. Solve the assignment problem given below.
(16)
2
5
Understand
Evaluate
8. A small project is composed of seven activities whose time estimates are listed in
the table as follows
Activity Preceding
activities Duration
A --- 4
B --- 7
C --- 6
D A,B 5
E A,B 7
F C,D,E 6
G C,D,E 5
i) Draw the network and find the project completion time. (8)
ii) Calculate the three floats for each activity. (8)
5
Evaluate
9. Calculate the
total float, (4)
free float and (4)
independent float for the project whose activities are given below: (4)
Activity 1-2 1-3 1-5 2-3 2-4 3-4 3-5 3-6 4-6 5-6
Time
(mins) 8 7 12 4 10 3 5 10 7 4
Find the critical path also. (4)
4
Analyze
10. A small project is composed of 7 activities, whose time estimates are listed in the
table below. Activities are identified by their beginning (i) and (j) node numbers.
i) Draw the project network and identify all the paths through it. (4)
ii) Find the expected duration and variance for each activity. What is the
expected project length? (4)
iii) Calculate the variance and standard deviation of the project length. What
is the probability that the project will be completed at least 4 weeks earlier
than expected time? (8)
2
Understand
11. The following table lists the jobs of a network along with their time estimates.
Draw the network. Calculate the length and variance of the critical path and find
the probability that the project will be completed within 30 days. (16)
5
Evaluate
12.
Use graphical method to minimize the time needed to process the following jobs
on machines A, B, C and D. Find the total time to complete the jobs.
JOB1 Sequence A B C D
Time (hrs) 2 3 5 2
JOB2 Sequence D C A B
Time (hrs) 6 2 3 1
(16)
6
Create
13.
Develop the optimal sequence of jobs that minimizes the total elapsed time
required to complete the following jobs and find the total elapsed time. The jobs
are to be processed on three machines M1, M2 and M3 in the order M1 – M2 –
M3.
JOB M1 M2 M3
A 3 4 6
B 8 7 3
C 7 2 5
D 4 5 11
E 9 1 5
F 8 4 6
G 7 3 12
(16)
6
Create
14. Evaluate the sequence that minimizes the total elapsed time (hours) to complete
the following jobs on two machines M1 and M2 in the order M1 – M2. Find also
the idle time.
JOB M1 M2
A 5 2
B 1 6
C 9 7
D 3 8
E 10 4
(16)
5
Evaluate
UNIT III - INVENTORY MODELS
Inventory models – Economic order quantity models – Quantity discount models – Stochastic inventory models – Multi
product models – Inventory control models in practice.
PART - A
Q.No. Questions BT Level Competence
1. Define inventory. 1 Remember
2. List out the basic inventory models. 1 Remember
3. Name the various costs involved in inventory problems. 1 Remember
4. Define safety stock. 1 Remember
5. When the inventory can be increased? Why? 1 Remember
6. Express the disadvantages of increased inventory. 2 Understand
7. Differentiate direct inventory from indirect inventory. 2 Understand
8. Summarize the causes of poor inventory control. 2 Understand
9. Give explanation for lead time and reorder point. 2 Understand
10. Classify types of Inventories. 3 Apply
11. Show the economic order quantity graphically. 3 Apply
12. Identify when shortage cost and stock out cost arises. 3 Apply
13. Highlight the importance of Reorder level. 4 Analyze
14. What inference can you make about holding cost? 4 Analyze
15. Discuss the concept of Quantity Discount Model 5 Evaluate
16. Contrast EOQ and EBQ. 4 Analyze
17. Explain the Monte Carlo Method. 5 Evaluate
18. Compare Ordering Cost and Carrying Cost. 5 Evaluate
19. Summarize the objectives of inventory control. 5 Evaluate
20. Interpret the meaning of EOQ 6 Create
PART - B
1. Alpha industry needs 5400 units per year of a bought out component which will
be used in its main product. The ordering cost is Rs.250 per order and the
carrying cost per unit per year is Rs.30. Which is the best order quantity and
Number of order per year and Frequency of orders? (16)
1
Remember
2. A stockiest has to supply 12000 units of a product per year to his customer.
Demand is fixed and known. Shortage cost is assumed to be infinite. Inventory
holding cost is 20 paise per unit per month. Ordering Cost is Rs. 250 and
purchase price is Rs.10 per unit. Develop EOQ & Frequency of orders and total
inventory cost. (16)
2
Understand
3. Demand for an item in a company is 18,000 units per year. The company can
produce the items at a rate of 3000 units per month. The Cost of one setup is
Rs.500 and the holding cost of one unit per month is 15 paise. Shortage cost of
one unit is Rs.20 per year. Analyze and find the optimum manufacturing quantity
and number of shortage, frequency of Production run. (16)
4
Analyze
4. A company has a demand of 12000 units per year for an item and it can produce
2000 such items per month. The cost of one setup is Rs400 and holding
cost/unit/month is Rs.0.15. Find the optimum lot size and total cost per year,
assuming the cost of one unit as Rs.4. Also find the maximum inventory,
manufacturing time and total time. (16)
3
Apply
5. A contractor has to supply 10000 bearings per day to an automobile
manufacturer. He finds that when he starts a production run he can produce 25000
bearings per day. The cost of holding a bearing in stock for one year is 2 paise
and the set up cost of the production run is Rs.18. How frequently should
production run be made and which is the Best Economic Batch Quantity? How
much would be the No. of Setup and Total Inventory Cost. (16)
4
Analyze
6. A stockiest has to supply 400 units of a product every Monday to his customer.
He gets the product at Rs.50 per unit from the manufacturer. The cost of ordering
and transportation from the manufacturer is Rs.75 per order. The cost of carrying
inventory is 7.5% per year of the cost of product. Predict EOQ, Frequency of
orders and Number of Orders, Total Incremental cost and Total Cost. (16)
4
Analyze
7. A company uses annually 50000 units of an item each costing Rs1.20. Each order
costs Rs.45 and inventory carrying cost are 15 % of average annual inventory
value.
i) Find the Economic order quantity. (4)
2
2
Understand
Understand
ii) If the company operates 250 days an year, the procurement time is 10
days and safety stock is 500 units, find the reorder level, maximum,
minimum and average inventory. (12)
8. i) Explain the inventory model with price break. (4)
ii) A company requires 200 casting per month. The requirement is assumed
to be fixed and known. The set up cost per procurement is Rs. 350. The
holding cost is 2% of the cost of the item. The price break details are as
follows.
K11 = Rs. 10 /- 0 < q < 500
K12 = Rs 9.50 /- q >=500
Find the optimal purchase quantity. (12)
4
5
Analyze
Evaluate
9. i) Explain the inventory models with probabilistic demand. (6)
ii) Find the various results for the following inventory model.
Demand rate = 10000 units/year
Production rate = 20000 units/year
Setup cost = Rs. 400/-
Holding cost = Rs 1.60/- per unit/year
Shortage cost = Rs 18/- per unit/year. (10)
4
5
Analyze
Evaluate
10. i) ABC manufacturing company purchases 9000 parts of a machine for its
annual requirement. Each part costs Rs.20. The ordering cost per order
is Rs.15 and the carrying charges are 15% of the average inventory per
year. Apply EOQ formulae and find out the Total Inventory Cost. (8)
ii) A company has a demand of 12000 units/year for an item and it can
produce 2000 units per month. The cost of one setup is Rs.400 and the
holding cost/unit/month is 15 paise. Select the optimum lot size and total
cost per year assuming the cost of 1 unit as Rs.4. Find EBQ (8)
4
Analyze
11. i) Classify and explain various inventory models. (6)
ii) An air craft company uses a certain part at a constant rate of 2500 units
per year. Each unit costs Rs 30/- and the company personnel estimate
that it costs Rs.130/- to place an order and carrying cost is 10% per year.
How frequently should orders be placed? Determine the optimum size of
each order. (10)
4
5
Analyze
Evaluate
12. A textile industry has a demand of 8000 drive pulleys per year. The cost of one
procurement is Rs. 100/- and the holding cost per unit is Rs. 2.25 per year. The
replacement is instantaneous and no shortages are allowed. Evaluate
i) The EOQ (4)
ii) The number of orders per year (4)
iii) The time between orders (4)
iv) The total cost per year if the cost of one unit is Rs 1.50. (4)
5
Evaluate
13. i) Derive the simplest economic order quantity formula. State all the
assumptions. (6)
ii) A company uses 25000 units of an item each costing Rs 2/-. Each order
2
Understand
cost Rs.120/- and inventory carrying cost are 12% of the average annual
inventory value. Find EOQ. If the company operates 300 days an year,
the procurement time is 15 days and safety stock is 350 units, find the
reorder level, maximum, minimum and average stock. (10)
3
Apply
14. Find the optimal order quantity for a product for which the price breaks are as
follows.
K11 = Rs. 12.50 0 < q < 750
K12 = Rs. 11.75 750 <= q < 1500
K13 = Rs. 11.00 q >= 1500 (16)
5
Evaluate
UNIT IV - QUEUEING MODELS
Queueing models - Queueing systems and structures – Notation parameter – Single server and multi server models – Poisson
input – Exponential service – Constant rate service – Infinite population – Simulation.
PART - A
Q.No Questions BT Level Competence
1. Define Kendal’s notation for representing queuing models. 1 Remember
2. How would you explain consumer behaviour? 1 Remember
3. List out the basic elements of queue. 1 Remember
4. Define a queue. Give example. 1 Remember
5. Distinguish between transient and steady state queuing system 4 Analyze
6. What are the assumptions in m/m/1 model? 3 Apply
7. Give the formula for the problem for a customer to wait in the system under
(m/m/1 : N/FCFS)?
2 Understand
8. Identify the properties of Poisson process. 4 Analyze
9. Categorize Queue Discipline. 3 Apply
10. Compare Serial and parallel Queue with Examples. 2 Understand
11. Classify the service disciplines. 3 Apply
12. Differentiate single channel queue and multi-channel queue. 3 Apply
13. Interpret the terms arrival rate and service rate in queuing models. 6 Create
14. Give the formulae for expected number of customers in the queue and the system
for (M/M/1): (FCFS/∞/∞)
4 Analyze
15. Write down the postulates of birth and death process? 3 Apply
16. Describe Kendall’s Notation for identifying a Queue Model with two channels,
Poisson arrivals, exponential service and infinite calling population.
1 Remember
17. In a super market, the average arrival rate of customer is 5 in every 30 minutes
following Poisson process. The average time is taken by the cashier to list and
calculate the customer’s purchase is 4.5 minutes; following exponential
distribution. What is the probability that the queue length exceeds 5?
5 Evaluate
18. If traffic intensity of M/M/I system is given to be 0.76, what percent of time the
system would be idle?
5 Evaluate
19. Interpret the Characteristics Of Queuing Models. 6 Create
20. Customer arrives at a one-man barber shop according to a Poisson process with
an mean inter arrival time of 12 minutes. Customers spend a average of 10
minutes in the barber’s chain.What is the expected no of customers in the barber
shop and in the queue?
6 Create
PART - B
1. A self-service store employs one cashier at its counter. 9 Customers arrive on an
average every 5 minutes. While the cashier can serve 10 customer in 5 minutes.
Assuming Poisson Distribution for arrival rate and exponential distribution for
service
rate Find the following:
(i) Average number of customer in the system
(ii) Average Number of customer in Queue.
(iii) Average time a customer spend in the system
(iv) Average time a customer wait before being Served. (16)
4
Analyze
2. A super market has 2 girls running up sales at the counters. If the service time for
each customer is exponential with mean of 4 minutes and if people arrive in a
Poisson fashion at the rate of 10 an hour. Infer the following:
(i) What is the average waiting time a customer spends in the system?
(ii) What is the expected percentage of Idle time for each girl? (16)
4
Analyze
3. A two – person barber shop has five chairs to accommodate waiting customers.
Potential customers who arrive when all five chairs are full leave without entering
the barbershop. Customers arrive at the average rate of 3.7674 per hour and spend
an average of 15 minutes is the barber chair. Apply Kendall’s Notation and Solve.
i) What is the probability a customer can get directly into the barber chair upon
arrival?
ii) What is the effective arrival rate?
iii) How much time can a customer expect to spend in the barber shop?
iv) How much time can a customer expect to spend in the barber shop? (16)
5
Evaluate
4. In a reservation counter with a single server, customer arrive with the inter-arrival
time as the exponential distribution with mean 10 minutes. The service time is
also assumed to be exponential with mean 8 minutes. Find
i) the idle time of the server
ii) the average length of the Queue.
iii) Expected time that a customer spends in the system. (16)
2
Understand
5. Ships arrive at a port at the rate of one in every 4 hours with exponential
distribution of inter arrival times. The time a ship occupies a berth for unloading
has exponential distribution with an average of 10 hours. If the average delay of
ships waiting for berths is to be kept below 14 hours. How many berths should be
provided at the port?
3
Apply
6. A branch of a national bank has only one typist. Since the typing work varies in
length, the typing rate is randomly distributed approximating Poisson distribution
with mean rate of 8 letters per hour. The letter arrives at a rate of 5 per hour
during the entire 8 hour work day. If the typewrite is valued at Rs.1.50 per hour.
Determine equipment utilization, the percent time an arriving letter has to wait,
average system time and average idle time cost of the typewriter per day. (16)
3 Apply
7. i) Explain any two queuing models with example. (4)
ii) If, for a period of 2 hours in a day trains arrive at the yard every
20minutes but the service time continues to remain 36 minutes.
Calculate the probability that the yard is empty and average queue
length on the assumption that the time capacity of the yard is limited to
4 trains only. (12)
4
5
Analyze
Evaluate
8. i) Write a short note on M/M/1 models and their applications. (4)
ii) Patients arrive at a clinic according to poissons distribution at the rate of
30 per hour. The waiting room does not accommodates more than 14
patients. Examination time per patient is exponential with mean rate of
20 per hour. Find the effective arrival rate at the clinic. What is the
expected waiting time of a patient until he is discharged? (12)
2
3
Understand
Apply
9. Arrivals of a telephone booth are considered to be poisson with an average time
of 10 minutes between one arrival and the next. The length of phone call is
assumed to be distributed exponentially, with mean 3 minutes.
i). What is the probability that a person arriving at the booth will have to wait? (6)
ii). The telephone department will install a second booth when convinced that an
arrival would expect waiting for atleast 3 minutes for a phone call. By how much
should the flow of arrivals increase in order to justify a second booth? (6)
iii). What is the average length of the queue that forms from time to time? (4)
3
Apply
10. An airport emergency medical facility has a single paramedic and room for a total
of three patients, including the one being treated. Patients arrive with an
exponentially distributed inter arrival time with a mean of one hour. Service time
is exponentially distribute with a mean of 30 minutes.
i). What percentage of the time is the paramedic busy? (8)
ii). How many patients on average are refused entry in a 24 hour day? (4)
iii). What is the average number of patients in the facility at any given time? (4)
4
Analyze
11. An insurance company has three claims adjusters in its branch office. People with
claims against the company are found to arrive in a Poisson fashion, at an average
rate of 20 per 8 hour day. The amount of time that an adjuster with a claimant is
found to have an exponential distribution, with mean service time 40 minutes.
Claimants are processed in the order of their appearance.
i). How many hours a week an adjuster expected to spend with claimants? (8)
ii). How much time, on the average, does a claimant spend in the branch office?
(8)
5
Evaluate
12. A bank has two tellers working on savings accounts. The first teller handles
withdrawals only. The second teller handles depositors only. It has been found
that the service time distributions of both depositors and withdrawals are
exponential with a mean service time of 3 minutes per customer. Depositors and
withdrawers are found to arrive in a Poisson fashion throughout the day with
mean arrival rate of 16 and 14 per hour.
i). What would be the effect on the average waiting time for depositors and
withdrawers if each teller could handle both withdrawals and deposits? (8)
ii). What would be the effect if this could only be accomplished by increasing the
service time to 3.5 minutes. (8)
5
Evaluate
13. A departmental store has a single cashier. During the rush hours customers arrive
at a rate of 20 customers per hour. The average number of customers that can be
processed by the cashier is 24 per hour. Assume that the conditions for use of the
single channel queuing model apply.
i). What is the probability that the cashier is idle? (4)
ii). What is the average number of customers in the queuing system? (4)
iii). What is the average time a customer spends in the system? (4)
iv). What is the average number of customers in the queue? (4)
4
Analyze
14. At a certain filling station, customers arrive in a Poisson process with an average
time of 12 per hour. The time intervals between services follow exponential
distribution and as such the mean time taken to service a unit is 2 minutes.
Evaluate:
i). the probability that there is no customer at the counter. (4)
ii). the probability that there are more than two customers at the counter. (4)
iii). the probability that there is no customer to be served. (4)
iv). the expected number of customers waiting in the system. (4)
5
Evaluate
UNIT V - DECISION MODELS
Decision models – Game theory – Two person zero sum games – Graphical solution- Algebraic solution– Linear
Programming solution – Replacement models – Models based on service life – Economic life– Single / Multi variable search
technique – Dynamic Programming – Simple Problem.
PART - A
Q.No Questions BT Level Competence
1. Compile the Characteristics of game. 1 Remember
2. How would you make use of the concept of Game theory in Managerial Decision
Making?
3 Apply
3. Interpret the concept of two person zero sum game. 6 Create
4. How decision Tree analysis is related to improve the decision-making process? 1 Remember
5. Identify the basic assumptions of the Game. 3 Apply
6. Conclude the advantages of Game theory. 4 Analyze
7. Summarize how graphs and LP solution are used in Game theory. 2 Understand
8. What is a Decision Tree? 1 Remember
9. Define Dominance principle. 1 Remember
10. Classify the different types of strategy. 4 Analyze
11. Classify the types of Replacement model. 4 Analyze
12. Explain saddle point and value of game shortly. 4 Analyze
13. Point out the limitations of game theory. 4 Analyze
14. Compare competitive game and rectangular game. 4 Analyze
15. Point out the situations which make replacement necessary. 1 Remember
16. Define group replacement. Give example. 1 Remember
17. Explain dynamic programming problem. 4 Analyze
18. Differentiate linear programming from dynamic programming. 4 Analyze
19. Give the applications of dynamic programming. 2 Understand
20. Compare single and multi-variable search techniques. 4 Analyze
PART - B
1. The cost of machine is Rs.16,100 and scrap value is Rs.1,100. Maintenance Cost
form for machine are as follows:
Year 1 2 3 4 5 6 7 8
Cost 300 450 600 800 100 1200 1500 2000
When should the machine be the replaced? (16)
1
Remember
2. The following table gives to cost of spares per year, overhead cost of maintenance
per year and resale value of certain equipment whose purchase price is Rs.
50,000: Illustrate when the machine can be replaced.
Year 1 2 3 4 5
Cost of spares 10000 12000 14000 15000 17000
Overhead
cost 5000 5000 6000 6000 8000
Resale value 40000 32000 28000 25000 22000
(16)
3
Apply
3. A Taxi owner estimates from his past records that the cost per year for operating a
taxi whose purchase price when new is Rs.60,000 are as follows.
Age 1 2 3 4 5
Operating
cost 10000 12000 15000 18000 20000
After 5 years the operating cost is Rs.6000 x K, Where “k” is 6,7,8,9,10(age). If
the resale value decreases by 10% of purchase price each year, what is the best
replacement policy if time value is not implemented? (16)
3
Apply
4. i) Deduce an expression for the average annual cost of an item over a
period of n years, when the money value remains constant. (6)
ii) A truck has been purchased at a cost of Rs.1,60,000. The value of the
truck is depreciated in the first 3 years by Rs 20,000 each year and Rs
16,000 per year thereafter. Its maintenance and operating cost for the
first 3 years are Rs 16000, 18000 and 20000 in that order and then
increase by Rs 4000 every year. Assuming an interest rate of 10% find
the economic life of the truck. (10)
6
4
Create
Evaluate
5. Machine A Costs Rs.9000. Annual Operating Cost is Rs.200 for the 1st year and
then increases by 2000 every year. Determine the best age at which to replace the
machine. Assume the machine has no resale value.
Machine B Costs Rs.10,000 . Annual operating cost is Rs.400 for the 1st year and
then increases by 800 every year. No resale value. You have now a machine of
type A which is one year old. Conclude if M/c A can be replaced by M/c B. Is so,
When? (16)
1
Remember
6. i) Explain Bellman’s principle of optimality and give classical formulation
and the dynamic programing formulation of any problem. (8)
ii) State the principle of optimality in dynamic programming. Explain the
basic features which characterize a dynamic programming problem. (8)
4
Analyze
7. i) Explain decision tree analysis with example. (6)
ii) In a game of matching coins with 2 players, A wins 1 unit value when
there are 2 heads, wins nothing when there are 2 tails and closes ½ unit
value when there are one head and one tail. Determine Pay Off matrix
and value of the game. (10)
5
Evaluate
8. i) Two players A&B match coins. If the coins match then A wins one unit
value, if the coins do not match then B wins one unit of value.
Determine pay-off matrix which strategy is to be chosen and find the
value of game. (8)
ii) A and B play a Match(Game) in which each has 3 coins 5 paise, 10 paise
and 20 paise. Each player selects a coin without the knowledge of others
choice. IF the sum is even, B wins A’s Coin. Find the Best Strategy &
value of the Game. (8)
2
Understand
9. i) Using dominance rule solve the following game.
(8)
ii) Solve the following 3 x 3 game by the method of matrices.
1 -1 -1
-1 -1 3
-1 2 -1
(8)
3 2 4 0
3 4 2 4
4 2 4 0
0 4 0 8
3
Apply
10. Solve the following game
Player B
Pla
yer
A
1 2 3 4 5
1 3 5 4 9 6
2 5 6 3 7 8
3 8 7 9 8 7
4 4 2 8 5 3
(16)
3
Apply
11. i) Differentiate the decision making under risk and under uncertainty in
statistical decision theory. (4)
ii) Using graphical method, solve the following game and evaluate the
game value.
B1 B2 B3 B4
A1 2 2 3 -2
A2 4 3 2 6
(12)
2
5
Understand
Evaluate
12. An electro mechanical equipment has a purchase price of Rs 7000/-. Its resale
value and running cost are given here.
Year 1 2 3 4 5 6 7 8
Running
cost 2000 2100 2300 2600 3000 3500 4100 4600
Resale
value 4000 3000 2200 1600 1400 700 700 700
When to replace the machine? (16)
1
Remember
13. The cost of a machine is Rs.6100/- and its scrap value is Rs 100/-. The
maintenance costs found from experience are as follows.
Year 1 2 3 4 5 6 7 8
Maintenance
cost 100 250 400 600 900 1200 1600 2000
When should the machine be replaced? (16)
1
Remember
14. Write short notes on
i) Economic life (4)
ii) Decision models (4)
iii) Dynamic programming (4)
iv) Two persons zero sum games (4)
2
Understand
