TB028A
Decision making in multi-modal transport systems
Lecturer : Yousef Maknoon 2021–2022
Midterm (I)
General Information
• You are allowed to submit the assignments in groups (up to 3 persons
in each group).
Note: if, for any reason, you are not willing to work with your group-
mate, you can also work on the assignment individually.
Attention
– No exchange between groups is allowed.
– The groups committed plagiarism is given 0 points.
– After you submit your assignments, there is a possibility of the
oral exam. If one student in a group performs poorly in the oral
exam, the entire group will receive 0 points for this assignment.
– In case of plagiarism, the case will be reported to the board of
examination.
• You are provided by question, Jupyter template for your report, and a
cover page.
• You can ask for feedback (at most 2 times per group) on your model
(by appointment only) up to 3 days before the deadline.
• For your report, please do the following steps:
1. Fill and sign the cover page (one page per group)
2. Write your answers in Jupyter template and e-mail it to me
• You MUST submit your answers and handle your cover page (on line)
by Tuesday 17th of December at 16h00 the latest. After that
time, the missing reports (Jupyter or cover page) are considered 0.
• This exam counts for 15% of the final grade.
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TB028A
Decision making in multi-modal transport systems
Lecturer : Yousef Maknoon 2021–2022
Midterm (I)
Cover page
By signing this page, I testify that
• I’ve carefully read the general information (page 1 of this document)
• I’ve contributed (equally with the other group members) to this exam.
• My group members have equally contributed to this exam.
• I have no exchange with other people outside my group.
Example of exchange: answering questions, sharing the code, study
together, etc.
1. Name: .......
student number: ......
signature: ..........
2. Name: .......
student number: ......
signature: ..........
3. Name: .......
student number: ......
signature: ..........
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TB028A
Decision making in multi-modal transport systems
Lecturer : Yousef Maknoon 2021–2022
Midterm (I)
Description
Due to the current travel restrictions, Delta Airlines has decided to re-design
its transportation network. The company aims to determine the location of
hubs and their connection to maximize profit. The demand is presented as
the number of passengers traveling between each pair of cities (nodes). To
achieve this goal, the company has to make two types of decisions. First, it
has to determine which set of origin-destination (O-D) pairs to serve. Second,
it has to decide on the movement of passengers into the network. The O-
D pair can remain unserved if it is not profitable. The is no restriction
on how hubs are connected. On the other hand, the company is interested
in investigating how to allocate passengers to the hubs. To do that, the
company chose three types of allocation decisions: 1) single, 2) multiple, and
3) r-allocation (each demand node can be connected to at most r hubs). The
problem is defined on a graph where V is the set of nodes. Each node can
either act as a hub or demand node. The rest of the notations are defined as
follows:
• Parameters
• wij Passenger demand from node i to node j, i, j ∈ V .
• rij Revenue from satisfying an individual passenger travelling from node
i to j
• cij Unit transportation cost from node i to j
• fk Fixed cost of installing hub at node k ∈ V
• gkl Fixed cost of activating the connection between hubs k and l
• α Discount factor
• Variables
• hk Binary variable equals to 1 is hub is located at node k ∈ V
• yiklj Binary variable, if the demand between nodes i and j is satisfied
by a path with the first hub k and the second hub l
• zkl if a connection is established between hubs k and l
• F (i)kl Fractional variable showing the number of passengers originated
at node i and routed on the inter-hub link from hub k to l
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TB028A
Decision making in multi-modal transport systems
Lecturer : Yousef Maknoon 2021–2022
Midterm (I)
• xik Binary variable if demand node i is allocated to hub node k. xkk
shows the case in which a hub is located at node k.
Tasks:
1. Define the mathematical model to solve this problem for the following
cases. Write your model in Jupytor notebook.
1 Multiple allocation. You are not allowed to use variable xik and
xkk.
2 Single allocation. You can use all variables defined above.
3 r-allocation. Set r = 3.
2. Implement your model using the sample data
Note: For ease of implementation and checking the correctness of your
model, small data set is provided ("Network5.txt"). You have the pos-
sibility to extract your model as an .lp file in Gurobi (the code is pro-
vided in the template). The .lp file provides the extended formulation
of your coded model. You can use this .lp file to verify your imple-
mentation as well as the correctness of your answers. Once you have
confidence in your implementation, you can test it with larger data set
(Network25.txt).
3. Compare your solutions for cases (1) – (3) and comments on the results.
4. Bonus Question. Perform some sensitivity analysis on the solution
of the model. The sensitivity analysis can be performed by varying
the parameters of the model. The sensitivity analysis should provide
a managerial insight into the robustness of the design. In addition to
some meaningful tables, a paragraph is also needed as a description.
Groups who provide a profound insight will get ten additional points
(the total grade of the midterm is 100).