The ‘‘traffic-assignment’’ model concerns minimizing travel time over a large network, where…

 The ‘‘traffic-assignment’’ model concerns minimizing travel time over a large network, where traffic enters the network at a number of origins and must flow to a number of different destinations. We can consider this model as a multicommodity-flow problem by defining a commodity as the traffic that must flow between a particular origin– destination pair. As an alternative to the usual node–arc formulation, consider chain flows. A chain is merely a directed path through a network from an origin to a destination. In particular, let

The ‘‘traffic-assignment’’ model concerns minimizing travel time over a large network, where traffic...-1

For example, the network in Fig. shows the arc flows of one of the commodities, those vehicles entering node 1 and flowing to node 5. The chains connecting the origin–destination pair 1–5 can be used to express the flow in this network as:

The ‘‘traffic-assignment’’ model concerns minimizing travel time over a large network, where traffic...-2

Frequently an upper bound ui is imposed upon the total flow on each arc i. These restrictions are modeled as:

The ‘‘traffic-assignment’’ model concerns minimizing travel time over a large network, where traffic...-3

The summation indices jk correspond to chains joining the kth origin–destination pair. The total number of arcs is I and the total number of origin–destination pairs is K. The requirement that certain levels of traffic must flow between origin–destination pairs can be formulated as follows:

The ‘‘traffic-assignment’’ model concerns minimizing travel time over a large network, where traffic...-4

Finally, suppose that the travel time over any arc is ti , so that, if xi units travel over arc i, the total travel time on arc on arc i is ti xi .

a) Complete the ‘‘arc–chain’’ formulation of the traffic-assignment problem by specifying an objective function that minimizes total travel time on the network. [Hint. Define the travel time over a chain, using the ai j data.]

b) In reality, generating all the chains of a network is very difficult computationally. Suppose enough chains have been generated to determine a basic feasible solution to the linear program formulated in part (a). Show how to compute the reduced cost of the next chain to enter the basis from those generated thus far.

c) Now consider the chains not yet generated. In order for the current solution to be optimal, the minimum reduced costs of these chains must be nonnegative. How would you find the chain with the minimum reduced cost for each ‘‘commodity’’? [Hint. The reduced costs are, in general,

The ‘‘traffic-assignment’’ model concerns minimizing travel time over a large network, where traffic...-2

where πi and uk are the shadow prices associated with the capacity restriction on the ith constraint and flow requirement between the kth origin–destination pair. What is the sign of πi ?] d) Give an economic interpretation of πi . In the reduced cost of part (c), do the values of πi depend on which commodity flows over arc i?

Calculate the price
Make an order in advance and get the best price
Pages (550 words)
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Upload your instructions
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with Online Academic Experts
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
Business and administrative studies
awesome work
Customer 453201, June 15th, 2022
thank you so much
Customer 452749, June 10th, 2021
Business Management
Awesome job, Thank you
Customer 453201, June 12th, 2022
English 101
very good paper thank you.
Customer 453083, February 18th, 2022
Human Resources Management (HRM)
I finished the first deliverable of a project presentation but had no time to finish my second deliverable. The writer revamped my first deliverable and made it much more appealing! Not only was I impressed with the content but I was so grateful for the time they took to redo the background. I have been under a lot of pressure at work and at home so this has been a great service when I have had little time! I appreciate the detail and help! Always on time and always exceeding expectations!
Customer 453077, April 5th, 2022
Thank you!
Customer 452545, February 6th, 2021
English 101
Thank you for this excellent analysis of the Alchemist.
Customer 453213, June 15th, 2022
Criminal Justice
This has been the greatest help while I am recovering from an illness. Thank your team so much.
Customer 452671, May 2nd, 2021
Social Work and Human Services
Although it took 2 revisions I am satisfied but I did receive it late because of that.
Customer 452603, March 25th, 2021
IT, Web
Awesome paper in such a short amount of time. Was in a jam with another service who didn't deliver, but Theresa did the job correctly. I will use her again to do my essays for sure!
Customer 452967, November 27th, 2021
Thank you!
Customer 453145, April 19th, 2022
Received before the deadline. Great job!
Customer 453027, January 15th, 2022
Customer reviews in total
Current satisfaction rate
3 pages
Average paper length
Customers referred by a friend
15% OFF your first order
Use a coupon FIRST15 and enjoy expert help with any task at the most affordable price.
Claim my 15% OFF Order in Chat
Live ChatWhatsApp