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5. Numerical Study
5.1 Experiment Setting
To present the experimental results of the algorithm, we adopt seven factors to analyze
the performance under different circumstances. The first factor is the size of the
problem, which three sizes— small, medium and large—are considered. We set
10, 0 as the small size, 0, 0 as the medium size and 100,
00 as the large size for the problem. The second factor is the number of scale
levels which each facility has. We consider two scenarios: one is each facility has one
scale level and the other is each facility has three scale levels. The third factor is the
numbers of activity sessions which is under two scenarios: problems with only one
activity session and with three activity sessions.
The fourth and fifth factors are location preference and time preference which
affect the customer’s time-dependent preference over facilities. In our experiment, the
customer and facility locations are mapped onto a 2-dimentional coordinate. There are
two types of customers’ location distributions in our setting: uniformly distribution and
clustering distribution. In the former type, the locations of customers are randomly
separated in the map; in the latter type, customers tend to locate near several clusters.
NTU Management Review Vol. 33 No. 3 Dec. 2023
The parameter represents the Euclidian distance between customer and facility
��
, and we set customer ’s location preference to facility to be � . As for the time
i’s location preference to facility j to be . As for the time preference, there are two
�
�
��
scenarios. One is customers’ time preference are homogeneous, i.e., in each activity
preference, there are two scenarios. One is customers’ time preference are
session, all customers’ time preferences are the same. The other is each customer’s time
distributed from 0.5 to 1.5. Put these two factors together, the preference of customer
preference is randomly distributed. We denote a parameter r as the time preference of
homogeneous, i.e., in each activity session, all customers’ time preferences are the same.
it
customer i in activity session t. r is distributed from 0.5 to 1.5. Put these two factors
to facility in activity session , is the product of location preference and time
it
The other is each customer’s time preference is randomly distributed. We denote a ��� ijt
together, the preference of customer i to facility j in activity session t, p is the product of
preference, i.e.,
× .
location preference and time preference, i.e., .
�
parameter as the time preference of customer in activity session . is
��
�
�
�� �� ��
The last two factors are the capacity of facility and the budget of the construction
plan, both of which have two types in the experiment. The low-capacity type sets the total
The last two factors are the capacity of facility and the budget of the construction
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supply of facilities to 40 percent of the total demand, while the high-capacity type sets it to
plan, both of which have two types in the experiment. The low-capacity type sets the
80 percent. The loose budget is set to 40 percent of the total construction cost and the tight
budget is set to 80 percent. total supply of facilities to 40 percent of the total demand, while the high-capacity type
The above seven factors generate 3×2×2×2×2×2×2=192 scenarios, and we
sets it to 80 percent. The loose budget is set to 40 percent of the total construction cost
generate 30 instances for each scenario. The experiments is performed on a PC with a
3.2 GHz Intel(R) Core i7-5820K processor and 16 GB RAM. The heuristic algorithm
and the tight budget is set to 80 percent.
is implemented in Spyder 4.0 using python 3.6. And the MIP model is solved using 41
The above seven
Gurobi 8.1 and implemented through Gurobi python. factors generate 3×2×2×2×2×2×2 = 192 scenarios,
and we generate 30 instances for each scenario. The experiments is performed on a PC
5.2 Benchmark Algorithm
In order to demonstrate the performance of our algorithm, we implement a genetic 16 GB RAM. The heuristic
with a 3.2 GHz Intel(R) Core i7-5820K processor and
algorithm for comparison (see below). First, we randomly generate 100 feasible
algorithm is implemented in Spyder 4.0 using python 3.6. And the MIP model is solved
construction plans into a pool. In each iteration, using the tournament selection method
4
(Miller and Goldberg, 1995), we randomly select 5 plans from the pool and pick the best
using 41 Gurobi 8.1 and implemented through Gurobi python.
two among them. Then we implement crossover to those two plans. We randomly pick
a cross-point and divide both plans into head and tail. Then we switch one’s head with
5.2 Benchmark Algorithm
other’s head to form two new plans. The two new solutions have 10% chance to mutate.
If a solution mutates, it will randomly pick one unbuilt facility with one scale level and
In order to demonstrate the performance of our algorithm, we implement a genetic
add it into the construction plan with the budget. Finally, two new solutions will be added
algorithm for comparison (see below). First, we randomly generate 100 feasible
4
construction plans into a pool. In each iteration, using the tournament selection
4 It may be wondered whether 100 is a parameter value for the implementation of the genetic algorithm.
method (Miller and Goldberg, 1995), we randomly select 5 plans from the pool and
Therefore, we investigate this issue by examining the performance of the genetic algorithm with other
parameter values at the end of Section 5.
pick the best two among them. Then we implement crossover to those two plans. We
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randomly pick a cross-point and divide both plans into head and tail. Then we switch
one’s head with other’s head to form two new plans. The two new solutions have 10%

4 It may be wondered whether 100 is a parameter value for the implementation of the genetic
algorithm. Therefore, we investigate this issue by examining the performance of the genetic algorithm
with other parameter values at the end of Section 5.
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