联系我们： 手动添加方式: 微信>添加朋友>企业微信联系人>13262280223 或者 QQ: 1483266981

IB9190_A
UNIVERSITY OF WARWICK
Paper Details
Paper Code: IB9190_A
Paper Title: Advanced Analytics: Models and Applications
Exam Period: April 2023
Exam Rubric
Time Allowed: 2 hours
Exam Type: Standard Examination
Approved Calculators: Permitted
Instructions
This exam consists of 3 pages. All questions should be answered.
Each question is allocated with a specific number of marks. The total number of marks is
100.
Read carefully the instructions on the answer book and make sure that the particulars
required are entered on each answer book.
(Continued…/)
Page 1 of 4
IB9190_A
Question 1
(20 marks)
Discuss the concept of centrality in social networks and explain three different types of centrality in
detail including their definitions. Construct a simple connected network of at least six nodes and
compute all centrality values for one single node.
Question 2
(40 marks)
You are asked by a theatre to design a contingency seating plan under potential social distancing rules
imposed by the government. We focus on the minimum distance rule of 1.5m, i.e., people from
different bubbles have to be at least 1.5m apart. The theatre has several rows of staggered seats to
increase visibility as shown in Figure 1.
Figure 1: Normal seating plan
Each seat is a 0.5 × 0.5 square. The distance between two consecutive rows is 0.5 and seats of
two consecutive rows are staggered by 0.25 .
a) If a customer has occupied the middle/centre seat in the second row as shown in Figure 1,
what are the unavailable seats according to the minimum distance rule with distances
measured from seat centres Provide detailed explanations for your answer.
(5 marks)
b) Assuming that the theatre would like to sell individual tickets with a single ticket price 1,
formulate an (integer) linear optimisation problem to construct a contingency seating plan
under the minimum distance rule which maximizes the potential revenue. Explain in detail
decision variables, objective function, and constraints of the formulation with proper
notation.
(10 marks)
(Question 2 continued over the page…..)
Page 2 of 4
IB9190_A
Page 3 of 4
(Question 2 continued…)
c) The theatre actually offers family tickets with the price
for families with people, =
2,3,4 in addition to individual tickets. We assume that each family has to sit on consecutive
seats in the same row. Note that families generate bubbles and the minimum distance rule
will not apply to people from the same family. Modify the formulation in part b) to find a
contingency seating plan which maximizes the potential revenue with detailed explanations
including data preparation.
(15 marks)
d) The seat availability is reduced in the contingency seating plan due to social distancing rules.
While revenue maximization is the main objective, the theatre would also like to maintain a
similar ticket profile, i.e., proportions of different types of tickets, offered in the contingency
seating plan as compared to that of the normal seating plan. Propose how the ticket profile
of the normal seating plan can be defined and calculated given relevant data, and modify the
formulation in part c) to incorporate the secondary objective of keeping the ticket profile of
the contingency plan as close as possible to that of the normal seating plan and make sure
that it can be reformulated as an (integer) linear optimisation problem.
(10 marks)
(Continued…/)
IB9190_A
Page 4 of 4
Question 3
(40 marks)
You are asked to determine where to build entrances, ≥ 2, to a specialised eco theme park in
which visitors can only walk on paths connected to the entrances. There are potential locations for
entrances, ≥ . The aim is to maximize the total length of all paths connected to entrances given
the distance between location and location for all , = 1, … , .
a) Formulate the problem as an optimisation problem (not necessarily linear). Explain in detail
decision variables, objective function, and constraints.
(10 marks)
b) What is the optimal solution when = 2 Propose a construction heuristic to find a
solution for the general problem. Write down the algorithm with formal notation.
(8 marks)
c) Propose an improvement heuristic to solve the given problem using results from part b).
Explain all the components of the heuristic including the definition of the neighbourhood.
(7 marks)
d) Consider the following instance with = 6 locations whose coordinates are given in Table 1.
Execute the heuristics proposed in part b) and c) for = 4.
(15 marks)
1 2 3 4 5 6
(
, ) (0.8,1.0) (3.0, 1.2) (4.5,2.0) (4.0,2.5) (2.0,2.8) (1.0,2.8)
Table 1: Location information
End