ISE 303 Operations Research 1 Exam 2 Sample
- Because of the rise in the number of accidents at
different intersections in the city, The
Khobar Traffic Department will
install cameras to monitor the traffic and issue electronic tickets for
traffic light violators. The map of Khobar is shown below and the
dangerous intersections are indicated with dark small circles.
The cameras get their power from solar cells, by converting sun light to electricity. Images captured by the cameras are transmitted through radio waves, where the energy required to send images is proportional to the distance.
The equivalent network with the distances in km is shown below:
Construct the minimum energy network of cameras by applying the minimum spanning tree algorithm.
- Zarief is a website design and
search-engine-optimization solution based company, with sole emphasis on
providing professional and quality web design, SEO consultancy, graphics
design, and multimedia solutions. The development of a website requires
the use of many graphics and html code generation software packages, and
the time needed to develop a website would be influenced by the sequence
by which these software packages will be used. Zarief is going to
develop a website for the National Hajj Department, Ministry of Hajj,
that will facilitate the national hajj seekers to get permits and pay
fees. The network below shows the different ways the website can be
developed, where each arc represents the time in days to develop a
component of the website using a particular software package.
Node 1 represents the start of the website development and node 7 represents the completion of the website. Zarief wants to determine the sequence of software packages that will minimize the time to develop the website. Use Dijkstra algorithm to solve the problem and indicate the number of days required to complete the site development.
- In SABB,
King Abdul Azziz St. branch, customers arrive to the teller windows
according to a Poisson process
with a rate of 20 customers per hour.
Customers of this SABB branch are usually managers, who expect to get
service fast. When the arriving customer finds 3 customers or less in
the bank, he is going to proceed to seek service. When the number of
customers in the bank is between four and seven, there is a probability
of 0.5 that he is going to leave without getting the service. If the
number of customers is between eight and eleven, the probability he is
going to seek service is only 0.2. The arriving customer is going to
leave un-serviced if the number of customers is twelve or more.
The management of the branch has given their tellers training on how to respond to high service volume. Tellers are able to adjust their service rate as the number of customers increases. In a specific day, there is only one teller and the service rate is exponential with a mean of 10 minutes. Because of the training he has been given, the average service time is 10 minutes if there is only one customer in the bank. The average service time is cut by half, i.e. 5 minutes, if there are two customers in the bank. The average service time is 10/3 if there are three customers in the bank, and so on.
- What is the effective arrival rate?
- What is the departure rate?
- Customers arrive to Dhahran Oil Change, where the
inter-arrival times have an exponential distribution with a rate of one
customer every 20 minutes. The time it takes to change the oil is
exponentially distributed with a mean time of 18 minutes. When
customers arrive to the oil change and find 9 cars waiting, they leave.
There is only one worker, and he can only handle one car at a time. The
owner of the oil change has determined that parking spaces are needed
for the waiting customers. In order to keep the cost of parking area
construction reasonable, the parking spaces that will be constructed
will be equal to the expected number of waiting cars. How many parking
spaces have to be constructed?
Use the appropriate method to find the best assignment and calculate the corresponding total cost.
2008
Industrial Engineering
King Fahd University of Petroleum and Minerals