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Bcom 371: Operations Research Ii Question Paper
Bcom 371: Operations Research Ii
Course:Bachelor Of Commerce
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
THIRD YEAR EXAMINATION FOR THE AWARD OF DEGREE OF
BACHELOR OF COMMERCE
BCOM 371: OPERATIONS RESEARCH II
STREAMS: BCOM Y3S1 TIME: 2 HOURS
DAY/DATE: TUESDAY 13/8/2013 2.30 P.M. – 4.30 P.M.
INSTRUCTIONS:
ANSWER QUESTION ONE AND ANY OTHER TWO QUESTIONS.
DO NOT WRITE ON THE QUESTION PAPER.
(a) Discuss the steps in the simulation process. [4 marks]
(b) Using suitable examples, distinguish between gradual failure and sudden failure as used in replacement theory. [4 marks]
(c) Discuss the assumptions of the first order Markov process. [4 marks]
(d) Discuss anyFive management applications of dynamic programming. [4 marks]
(e) A company has three factories I, II and III which make weekly dispatches of four depots A, B, C and D. The transport cost per crate of goods dispatched along each route is as follows:
Cost per Crate Quantity available
Depot A B C D
Factory I 4 7 9 2 200
II 1 8 3 9 200
III 4¬_ 6_ 3 _ 5 _ 400
Quantity required 250
=== 250
=== 420
===
80
=== 1000
====
Using Vogel’s approximation method (VAM) determine the number of crates to be sent along each of the routes to minimize the transportation cost. [10 marks]
(f) Discuss the types of Integer programming problems. [4 marks]
(a) Discuss the steps in using the stepping stone method in transportation problems.
[8 marks]
(b) The inter-arrival times of customers in a single channel Automated Teller Machines (ATM) is as follows:
Inter arrival times
(minutes) Probability
10 0.10
15 0.25
20 0.30
25 0.25
10 0.10
The ATM’s service time is as follows:
Service Time
(minutes)
Probability
5 0.08
10 0.14
15 0.18
20 0.24
25 0.22
30 0.14
The management is concerned about the waiting time and the service time spent in the ATM system.
Required:
Simulate the 1stTen customers arriving for the service and estimate the waiting time and the time spent in the ATM system using the following Random Number’s.
74 97 30 98 48 15 34 78 88 20
52 99 96 91 14 13 01 50 62 37
[12 marks]
(a) Discuss the term queue discipline as used in queuing theory. [4 marks]
(b) A Chinese investor has approached the Jubilee government to be allowed to do business in Kenya. The investor intends to produce two competing products A and B and expects the products to share the available market in the same proportion initially. The Engineering and marketing research departments of the investing company have determined the state transition matrix of the products to be:-
To
A B
From ¦(A@B)(¦(0.8&0.2@0.6&0.4))
Assume that the conditions of a first order Markov process apply to this problem.
Required:
The expected market shares of the two products in the first four periods.
[8 marks]
The equilibrium market shares of the products. [4 marks]
(c) Discuss the term state transition matrix as used in Markov analysis. [4 marks]
(a) A microfinance company has a single cashier. During the normal working hours,
customers arrive at the rate of one customer in every three minutes. The average number of customers that can be processed by the cashier is 24 per hour.
Assume that the condition of single channel queuing model applies.
Calculate:
The customer utilization value
The number of customers in the queuing system
The average time that customers spend in the system
The average number of customers in the queue
The average time that customer spends in the queue waiting for service.
[10 marks]
(b) Discuss any Five primary considerations that lead to replacement of assets.
[5 marks]
(c) Using suitable examples, distinguish between a balanced and unbalanced transportation problem. [5 marks]
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