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QUID 2017, pp. 2267-2273, Special Issue N°1- ISSN: 1692-343X, Medellín-Colombia
MULTI-MODE RESOURCE-CONSTRAINED PROJECT SCHEDULING AND SOFT AND HARD TIME
WINDOWS FOR ENDING ACTIVITIES
(Recibido el 23-06-2017. Aprobado el 27-08-2017)
Maryam Avar
Department of industrial engineering, Faculty of
Industrial and Mechanical Engineering, Ghazvin
Branch, Islamic Azad University, Ghazvin, Iran.
Behrouz Afshar Najafi
Department of industrial engineering, Faculty of
Industrial and Mechanical Engineering, Ghazvin
Branch, Islamic Azad University, Ghazvin, Iran
Abstract: This study developed a mathematical model to optimize multi-mode resource-constrained project scheduling
problem and soft and hard time windows for ending activities. The developed model optimized project scheduling
problem in the near real world, taking into account multi-mode time of activities, as well as hard and soft time windows
simultaneously. In order to optimize the model, meta-heuristic genetic algorithms and simulated annealing algorithm
were used. Input parameters of these algorithms were set by response level method; then, performance of the algorithms
was measured in small sized problems using exact solution software. Statistical tests were applied; efficiency of the
algorithms was evaluated in solving large-scale real-world problems. Computational results showed that the genetic
algorithm had a higher efficiency in optimizing the suggested model and was able to achieve higher quality solutions in
lower computing time.
Keywords: project scheduling, resource constraints, time windows
Citar, estilo APA: Avar, M., & Najafi, B., (2017). Multi-mode resource-constrained project scheduling and soft and hard time windows for ending
activities . Revista QUID (Special Issue), 2267-2273
1. INTRODUCTION
One of the biggest challenges facing projects worldwide
is their planning and scheduling. Definition of activities
in the form of certain projects seems to lead to more
clear planning and scheduling process and projects can
be accomplished in the defined frameworks. The project
can be defined as a committed plan with a certain initial
and final range which will achieve the considered
outcomes or products by using certain resources. Project
planning also involves organizing and managing
resources for predefined activities in the form of a
certain schedule at agreed cost to achieve the determined
goals, outcomes and products. It is a wish of all project
managers to succeed; however, it should not be forgotten
that this is not a coincidence. About half a century has
elapsed since development and application of project
management methods; during this period, a considerable
effort made to improve concepts of project management
has focused on development of project scheduling
models. The purpose of scheduling a project is to
determine the timing of various project activities during
its implementation and it is related to a decision making
process where one or more goals are optimized. Project
scheduling tends to find a proper sequence of activities
for a project to meet prioritization constraints of the
project network and various types of resource constraints
in the project simultaneously and optimize a certain
measurement criterion such as time and cost of the
project and the number of delayed activities.
Scheduling is a tool which optimizes the use of available
resources. Resources and tasks on schedule may have
different kinds. With development of the industrial
world, resources become more critical. Scheduling these
resources will increase efficiency and utilization of
capacity, reduce the time required to finish tasks and
ultimately increase profitability of an organization.
Effective scheduling of resources, such as human
resources and machinery, is vital in current competitive
world. Resources can be found in machines of a
production workshop, air lines at the airport, workers of
a construction project, or computer processing units. In
practice, scheduling of an organization uses
mathematical methods or heuristic methods to allocate
limited resources to current tasks. Proper allocation of
resources enables the organization to optimize and
achieve the goals. Everything has features like priority
level, standby time, and delivery deadlines. Objective
function can also be used in several ways, such as
minimizing total finish time or minimizing the number
of delayed tasks (Bosaghzadeh, et al 2010). In recent
years, extensive research has been done on project
scheduling.
In resource-constrained project scheduling problems
(RCPSP) and multimode resource-constrained project
scheduling problem (MRCPSP), it is assumed that
activities are carried out under ideal conditions, only a
time is considered for project completion, that is,
delivery time is considered as a point (Cleland, et al
1999). Soft and hard time windows have not been
discussed in this type of problems; this is not modeled
for project scheduling problems. This study tends to
model this problem in an integrated form. In fact, ideal
time to end an activity is considered as an interval. This
study tends to develop the concept of delivery time and
better manage the project by assigning delivery time to
each activity. Since allocation of point delivery time to
each activity can take a considerable part of flexibility
from the decision maker, this study considers interval
delivery time rather than point delivery time for each
activity to help make better decisions by higher
flexibility.
For example, Kalhor et al. (Kalhor, et al 2011) used non-
dominated archiving ant colony approach to solve time-
cost balance optimization problem. They used total time
and total cost as two optimization goals; in order to
realize the real-world conditions, uncertainty of time and
cost was examined by means of fuzzy set theorem.
Kyriadidis et al (Kopanos, et al 2014) used complex
integer linear programming models to formulate single-
mode and multimode project scheduling problems and
used a source-duty grid approach used in process
scheduling problems for display. Kopanos et al.
(Kyriakidis, et al 2012) developed a discrete and
continuous mathematical model for resource constrained
scheduling problem. Messelis et al. (Messelis, et al
2014) developed an algorithm with an automatic
selection approach for multimode resource-constrained
project scheduling problem. Sakalauskas et al.
(Sakalauskas, et al 2015) used a priority list of workable
tasks to develop a genetic algorithm.
2. PROBLEM DESCRIPTION
This study tends to develop the concept of delivery time
and better manage the project by assigning delivery time
to each activity. Since allocation of point delivery time
to each activity can take a considerable part of flexibility
from the decision maker, this study considers interval
delivery time rather than point delivery time for each
activity to help make better decisions by higher
flexibility. In this study, it is assumed that both hard and
soft intervals are present simultaneously; however, the
hard interval dominates the soft interval. In practice,
point delivery time is common for project events rather
than activities. This study tends to incorporate soft and
hard time windows in the model, taking into account
interval time of each activity. Other assumptions are as
follows:
Project scheduling problem with soft and hard
time window is considered for delivery time of
each activity;
Multimode scheduling problem is considered;
Renewable or non-renewable resources are
used;
Timing of activities is definitive;
Resources required for each activity are
definitive;
Violation of soft window is subject to fines.
Indexes
Activity index
Task mode index
Time index
Resource index
Parameters
Earliness cost per unit time
Tardiness cost per unit time
Lower bound of soft interval
Upper bound of soft interval
Lower bound of hard interval
Upper bound of hard interval
Earliest finish time of activity i
Latest finish time of activity i
Decision variables
Tardiness rate including fines for activity i
Earliness rate including fines for activity i
If activity i starts using mode m at time t 1
Otherwise 0
(1)
S.t.
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
The first constraint minimizes earliness and
tardiness rate. The second constraint examines the
relationship between end-start activities and zero-lag
time. The third constraint ensures that an activity is only
performed by a mode. The fourth constraint deals with
renewable resources, where T indicates upper bound of
the time of the project. The fifth constraint deals with the
use of non-renewable resources throughout the horizon.
The sixth constraint calculates tardiness rate including
fines by subtracting the end of activity from upper bound
of the soft interval. The seventh constraint calculates
lower bound of the soft interval minus the end of activity
and earliness rate including fines. The eighth constraint
ensures that activities cannot be finished beyond the hard
interval. The ninth constraint shows properties of
decision variables.
3. GENETIC ALGORITHM
Genetic algorithm is a powerful random search
based on natural selection mechanism. The algorithm
which is derived from nature is based on random search
to optimize learning problems and processes. In nature,
combination of right chromosomes provides better
generations. In the meantime, mutations occur in
chromosomes, which may improve the next generation.
Genetic algorithm can search different regions of
solution space simultaneously. Flowchart of the genetic
algorithm used here is shown in Figure 1.
Fig. 1. Flowchart of the suggested genetic
algorithm
3.1 Chromosome Structure
The suggested chromosome is a 3×n matrix in
which n is the number of activities and the number of
columns of the suggested chromosome. In the first row,
there is a random permutation of activities; in the second
row, there is mode number of that activity which is a
random number between 1 and maximum number of
workable modes of that activity. The third row shows
tardiness of activities. This chromosomal string is not
typically seen to solve other mathematical optimization
models in the RCPSP domain, because objective
function is make span or completion time of the project
in most of these models. Therefore, activities should
begin at the earliest possible time. In the presented
mathematical optimization model, objective function is
not make span; thus, tardiness of an activity may be a
better policy in some cases. Lower bound of this
chromosomal string is zero and its upper bound is the
length of hard time window interval.
Activity 1 Activity 2 Activity n
Mode 1 Mode 2 Mode n
...
...
Delay 1 Delay 2 Delay n...
Fig. 2. Structure of the suggested chromosome
An initial population of chromosomes is randomly
generated. The number of population of each generation
is shown by npop. According to Figure 2, chromosomal
string related to sequence of activities is generated as a
random permutation of numbers between 0 and n. The
chromosomal string related to mode number of that
activity is generated as a random number with a
uniformly discrete distribution for the number of
possible modes for each activity. The chromosomal
string related to tardiness is also generated by a
uniformly discrete distribution between zero and length
of hard time window interval.
3.2 Fitness Function
To calculate fitness of each chromosome, a well-
known approach called Serial SGS is used. To
implement this approach, mode of each activity is
initially determined by the second chromosomal string
and information is obtained on the amount of resource
utilization and duration of each activity. Then, tardiness
of each activity is determined by using the third
chromosomal string. Finally, implementation of the
project can be simulated on a timeline by considering
sequence of activities in the first chromosomal sequence.
Given constraints of RCPSP, there are two prerequisites
for locating activities in the timeline:
1. Prerequisite constraints
2. Constraints related to resource utilization
In order to manage these constraints on the suggested
chromosome, Serial SGS strategy moves on to the
sequence of activities and places them within the
timeline. Whenever prerequisite constraints are not met,
it goes to the next activity; if prerequisite constraint is
met, the considered activity is placed within the timeline
and the list of sequences is examined from the top. This
method ensures that prerequisite constraints are placed
within the timeline. For constraints related to resource
utilization, Serial SGS strategy proceeds on the time
frame to find the first day when resources required for
the activity are available; then, the activity is placed
within the timeline. In the suggested mathematical
model, constraints related to nonconformity of hard time
window are met by using penalty function. The
suggested genetic algorithm generates initial population
and uses a roulette cycle to select parents using
crossover operator.
3.3 Crossover
In this operator, the number of parents is
calculated with crossover likelihood rate; then, parents
are randomly selected using the roulette cycle. For
crossover, parents are initially selected; to run crossover
on chromosomal string related to sequence of activities,
following steps are taken. This operator is called single-
point permutation crossover. In Figure 3, it is assumed
that 13 activities are available.
Fig. 3. Structure of the suggested crossover
operator (sequence of activities)
Figure 4 shows how crossover operator works on
chromosomal string related to activity mode number in
the suggested genetic algorithm (n=9). Note that
operation of crossover on chromosomal string of
tardiness is similar to the second string, which is shown
in Figure 4.
Fig. 4. structure of the suggested crossover operator (activity mode)
3.4. Mutation
To run mutation on chromosomal string related to
sequence of activities, one of swap, reversion and
insertion operators is selected; then, this operator is
applied on the relevant chromosomal string. For
example, mutation rate considered in this genetic
algorithm is 0.1, any gene whose corresponding value is
less than 0.1 will be mutated. Figure 5 shows operation
of mutation operator in the suggested genetic algorithm.
In this example, 9 activities are defined.
Fig. 1. Structure of the suggested mutation operators
(sequence of activities)
For chromosomal string related to activity mode
number, the considered parent is selected and a random
number between zero and one is generated for each gene
in the parent chromosome and values of parent
chromosome genes are mutated with a certain mutation
rate. If the generated random number is smaller than the
considered mutation rate, the considered gene will be
randomly mutated in the parent chromosome; if the
generated random number is larger than mutation rate,
the gene will not be mutated in the parent chromosome.
For example, if mutation rate considered in this genetic
algorithm is 0.1, any gene whose corresponding value is
less than 0.1 will be mutated. Figure 6 shows operation
of mutation in the suggested genetic algorithm. In this
example, 9 activities are defined. Operation of mutation
on chromosomal string of tardiness is similar to the
second string, which is shown in Figure 6.
Fig.2. Structure of the suggested mutation operator (activity mode)
3.5. Stop Criterion of the Algorithm
This algorithm uses the number of iterations as a
criterion; that is, this algorithm stops after a certain
number of iterations and generation. In the problem, the
number of iterations is set at MaxIt.
4. SIMULATED ANNEALING ALGORITHM
Simulated annealing (SA) algorithm is a
probabilistic, sequential, and incremental search method
which starts with an initial solution and moves to
neighbouring solutions in an iterating loop. If the
neighbor's solution is better than the current one, the
algorithm puts it as the current solution (moves towards
it); otherwise, the algorithm accepts that solution at
li likelihood as the current solution. With gradual
decrease of temperature in the final steps, worse
solutions are less likely to be accepted. Therefore, the
algorithm converges to better solutions (or to the same
quality solutions). Experiments show that starting an
algorithm with a good initial solutions leads to faster
convergence. Moreover, the search for solution space
with several initial solutions in parallel leads to better
quality solutions. This technique is called parallelization
of multiple independent runs (MIR). In MIR, each initial
solution tends to search for solution space completely
independently.
4.1. Solution Representation
Solution representation and evaluation of fit of
solutions is similar to representation and evaluation of
chromosome in the genetic algorithm.
4.2. Initial Temperature
Initial temperature should be warm enough to
allow movement to adjacent position. If initial
temperature is very high, the search can move to any
neighborhood and search is randomized until the
temperature cools enough. It is a challenging problem to
find the initial temperature and it does not have a
specific method for different problems. Let maximum
distance (cost of different functions) between a
neighborhood and other neighborhoods be known; this
information can be used to calculate initial temperature
(that is, the required energy). First, a large number of
random solutions are generated and their objective
function is determined; then, standard deviation of the
obtained result is calculated and used to determine initial
temperature. The suggested algorithm, based on
preliminary tests, uses 1.5 times the standard deviation
found in initial solutions to determine the initial solution.
4.3. Final Temperature
Different methods have been proposed to
determine final temperature of SA algorithm. This study
uses a method based on which final temperature is
determined in a way that probability of accepting the
worse solutions is as large as 10-10. Upon reaching this
temperature, the algorithm will be stopped.
4.4. Temperature Reduction at Each Stage
Temperature reduction varies from one problem
to another, depending on the type of functions and its
nonlinear behavior, as well as how the functions change.
Different researchers design this temperature reduction
based on precision and speed required to achieve
minimum solution. SA algorithm converges in the case
of temperature reduction based on Equation (10).
(10)
where, is baseline temperature of outer rings of
the algorithm. As shown in Figure 7, leads to
generation of a continuous interval of temperature in
which quality of algorithm increases. Optimal value of α
is determined through analysis of experiments.
Fig.7. Temperature reduction in SA algorithm
4.5. Iteration at Any Temperature
At any temperature, iteration continues until solution
does not change in 100 successive iterations.
4.6. Stop Criterion
Stop criterion in inner and outer loops of the
suggested algorithm is as follows. In the outer loop, the
algorithm continues to evolve without any constraint,
until MaxIt iterations are done. Optimal value of MaxIt
0 100 200 300 400 500 600 700 800 900 10000.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Iteration
Tem
pera
ture
is determined through design and analysis of
experiments.
5. ANALYSIS
This section analyses efficiency of the suggested
algorithms to solve the model. First, optimal values of
input parameters are determined by using response level
method. Then, a number of random sample problems are
generated in small scale and efficiency of algorithms is
measured in finding the optimal overall solution. To
measure efficiency of algorithms in solving large-scale
problems, numerical examples are randomly generated
and run on a personal computer. The results are analysed
by using statistical tests and the more efficient algorithm
is determined.
5.1. Parameter Setting
The main parameters of this algorithm are
considered in Table 1 for setting on appropriate levels.
Due to selection of two-level factor design, two upper
and lower levels are considered for each experiment. For
forwarding response level algorithm, movement on the
upper and lower bounds as well as axial points are
considered using middle bounds and a number of central
points (here 5 central points are added). For this
algorithm, the factor design 23 is considered for three
parameters. For this purpose, the experiment is run by
MINITAB16 for the algorithm and the best value is set
for the result. Moreover, MaxIt is set at 100 in each
algorithm. Response variable of the model is cost value.
After running experiments, optimal results obtained for
algorithms used are shown in Table 2.
table 1. search interval and levels of input variables
Upper bound
Lower bound
Interval Parameter
150 100 [50-
100] npop
GA
0.7 0.4 [0.4-
0.7] pc
0.3 0.1 [0.1-
0.3] pm
50 20 [20-
50] npop
PSA 0.99 0.95 [0.95-
0.99] α
200 100 [100-
200] MaxIt
Table 2. Optimal values of GA algorithm
Optimal value Parameter
150 npop
GA 0.7 pc
0.3 pm
50 npop
PSA 0.99 α
150 MaxIt
5.2. Solving Numerical Example for the Model
This section tends to validate and solve the
suggested model. For this purpose, the suggested model
is first solved in three different sizes by Lingo 16 and the
results are compared with the genetic algorithm coded by
MATLAB 10. The problems raised in each of these three
sizes have similar dimensions and they are different only
in αi and βi values. For example, Table 3 shows input
values for the first experiment.
Table 3. Input values of the first experiment – part I
Activity 1 2 3 4 5 6 7
αi 0 200 100 400 500 250 0
βi 0 200 100 400 500 250 0
Ei 0 3 1 2 4 4 0
Ui 0 7 5 6 9 8 9
E1 1 2 0 1 2 2 0
T1 1 9 7 8 10 10 11
Maximum value available for renewable and non-
renewable resources in this example is 5 and 20 units
respectively. The number of mode is 2 for each activity.
Table 4 shows consumption factor for renewable and
non-renewable resources and runtime of each activity in
different modes.
Table 4. Input values of the first experiment – part II
Activity 1 2 3 4 5 6 7
Mode 1 2 1 2 1 2 1 2 1 2 1 2 1 2
Runtime 0 0 4 6 2 0 3 5 2 0 2 4 0 0
Consumption factor for Renewables 0 0 2 1 1 0 3 1 1 0 2 1 0 0
Consumption factor for non-renewables 0 0 3 1 0 0 4 2 0 0 3 2 0 0
Results of 15 experiments run in Lingo as well as
genetic algorithm are presented in Table 5. Since
solutions of both methods are equal in these 15
experiments, it can be claimed that the suggested model
and genetic algorithm and SA algorithm used to solve
the model are precise.
Table 5. Results of metaheuristic and precise methods in small scale
Problem size Problem No. Lingo GA
Cost Time Cost Time Cost Time
I
1 0 0.23 0 20 0 23
2 0 0.11 0 22 0 27
3 0 0.32 0 21 0 24
4 0 0.08 0 19 0 22
5 0 0.1 0 17 0 19
II
6 0 1.4 0 32 0 38
7 0 1 0 31 0 34
8 0 1.01 0 32 0 37
9 0 0.98 0 28 0 31
10 0 0.98 0 29 0 32
III
11 1755 3.71 1755 60 1755 64
12 2529 3.13 2529 61 2529 65
13 2248 3.43 2248 58 2248 61
14 2886 3.23 2886 63 2886 67
15 2750 3.28 2750 31 2750 36
5.3. Comparison of Algorithms
This section measures efficiency of algorithms in
optimizing larger-scale problems. Since the problem is
NP-hard, it is not practical to solve large-scale problems
in reasonable time. In those circumstances, the only way
to achieve solution is to use meta-heuristic methods.
Therefore, only two meta-heuristic genetic and SA
algorithms are evaluated. The results are listed in
Appendix A. Figure 8 and Figure 9 show results
obtained by running algorithms on 40 random sample
problems.
0
500
1000
1500
2000
2500
3000
3500
1 4 7 10 13 16 19 22 25 28 31 34 37 40
Problem number
GA Cost
PSA Cost
Fig. 8. Graphical comparison of algorithms in solving sample problems (solution quality)
0
1000
2000
3000
4000
1 5 9 13 17 21 25 29 33 37
Problem number
GA Time
PSA Time
Fig.3. Graphical comparison of algorithms in solving sample problems (solution time)
To compare algorithms, 95% confidence interval
is used in terms of relative percentage deviation (RPD).
RPD is calculated by following formula:
(11)
where, i is algorithm number; j is problem
number and is the best solution obtained in
the problem j. 95% confidence intervals are clear in
Figure 10 and Figure 11. According to Figure 10, GA
outperforms the other algorithm in terms of solution
quality. According to Figure 11, SA is weaker than GA
in terms of computational time.
PSA CostGA Cost
14
12
10
8
6
4
2
0
RP
D
Interval Plot of GA Cost, PSA Cost
Fisher 95% CI for the Mean
The pooled standard deviation is used to calculate the intervals.
FIG. 10. 95% CONFIDENCE INTERVALS FOR SOLUTION
QUALITY IN SAMPLE PROBLEMS
PSA TimeGA Time
12
9
6
3
0
RP
D
Interval Plot of GA Time, PSA Time
Fisher 95% CI for the Mean
The pooled standard deviation is used to calculate the intervals.
Fig. 4. 95% confidence intervals for computational time in sample problems
6. Conclusion
This study considered project scheduling model,
assuming two categories of renewable and non-
renewable resources. Non-renewable resources are
allocated once for the entire project, while renewable
resources are renewable for each period. In the suggested
model, activities are multimode. Multimode resource-
constrained project scheduling problem has been studied
by a few researchers. In this type of problems, any
activity can be done through several modes. Each mode
is a combination of duration and resource requirement.
Usually, shorter-time modes require more resources.
This assumption effectively leads to flexibility in
choosing activity modes and better decisions. One of
important goals in project scheduling is to carry out
activities at the right time with minimal resource
utilization to finish the project in the shortest time. One
way to achieve these goals is to use different activity
modes. Using different modes, the model is flexible to
select the best method to save project costs and provide
better scheduling with higher quality. As a general rule,
one can assume that more flexible assumptions improve
quality of the solutions. Since allocation of point
delivery time to each activity can take a considerable
part of flexibility from the decision maker, this study
considers interval delivery time rather than point
delivery time for each activity to help make better
decisions by higher flexibility. Main innovation of the
suggested problem is to consider soft-time and hard-time
windows, i.e. taking into account interval delivery times,
for ending activities in multimode resource-constrained
project scheduling problems. This is why the current
study is different from other studies. For this reason, a
multimode resource-constrained model with hard and
soft time windows was developed for ending activities to
minimize earliness and tardiness costs. To validate the
suggested model, 15 small-scale problems were
formulated by the model and solved precisely by Lingo.
Since the problem was NP-hard and the problem size
was enlarged, Lingo was no longer able to solve the
problem in a reasonable time and genetic meta-heuristic
algorithm was used to solve the suggested model. For
further evaluation of genetic algorithm, 30 small-scale
j5, j10 and j16 examples and 15 large-scale 32-activity
examples were run in MATLAB. Parameters of the
suggested genetic algorithm were set by using response
procedure method and different examples were solved
based on these parameters.
7. FUTURE SUGGESTIONS
Future works are recommended to address these
suggestions:
In this study, data are certain. The first
suggestion for future studies is to use modelling
approaches under uncertainties such as random
planning and robust optimization;
The problem can be addressed in allowable
discontinuation of activities;
Other additional objectives can be discussed.
Other meta-heuristic algorithms such as ant
colony and SA algorithms can be used; even
approximate solutions can be used to achieve
reliable solutions in reasonable solving time
such as branch and boundary method as an
alternative for meta-heuristic methods.
Appendix A: computational results of algorithms in 40 sample problems
RPD RPD
Pro. Activity
No.
GA
Cost
GA
Time
PSA
Cost
PSA
Time GA Cost
GA
Time
PSA
Cost
PSA
Time
1 20
272 94
293 90
0 4.44
7.72058
8 0.00
2 20
289 89
318 90
0 0.00
10.0346 1.12
3 20
283 95
266 96
6.39097
7 0.00
0 1.05
4 20
277 83
267 94
3.74531
8 0.00
0 13.25
5 20
289 101
268 94
7.83582
1 7.45
0 0.00
6 20
282 101
305 100
0 1.00
8.15602
8 0.00
7 20
275 97
262 98
4.96183
2 0.00
0 1.03
8 20
278 91
271 95
2.58302
6 0.00
0 4.40
9 20
264 90
296 95
0 0.00
12.1212
1 5.56
10 20
285 82
267 90
6.74157
3 0.00
0 9.76
11 30
547 334
525 350
4.19047
6 0.00
0 4.79
12 30
570 330
668 357
0 0.00
17.1929
8 8.18
13 30
556 330
604 353
0 0.00
8.63309
4 6.97
14 30
561 359
570 359
0 0.00
1.60427
8 0.00
15 30
559 293
648 352
0 0.00
15.9212
9 20.14
16 30
555 354
615 350
0 1.14
10.8108
1 0.00
17 30
562 368
657 350
0 5.14
16.9039
1 0.00
18 30
541 347
646 351
0 0.00
19.4085 1.15
19 30
555 303
658 353
0 0.00
18.5585
6 16.50
20 30
550 345
556 353
0 0.00
1.09090
9 2.32
21 50
1168 1218
1357 1202
0 1.33
16.1815
1 0.00
22 50
1166 1086
1182 1221
0 0.00
1.37221
3 12.43
23 50
1158 1166
1342 1230
0 0.00
15.8894
6 5.49
24 50
1216 1170
1388 1210
0 0.00
14.1447
4 3.42
25 50
1234 1040
1430 1244
0 0.00
15.8833
1 19.62
26 50
1153 1161
1338 1220
0 0.00
16.0451 5.08
27 50
1210 1072
1215 1235
0 0.00
0.41322
3 15.21
28 50
1203 1100
1408 1231
0 0.00
17.0407
3 11.91
29 50
1188 1068
1372 1313
0 0.00
15.4882
2 22.94
30 50
1245 1080
1440 1234
0 0.00
15.6626
5 14.26
31 100
2642 2305
3302 3040
0 0.00
24.9810
7 31.89
32 100
2581 2392
3105 3046
0 0.00
20.3022
1 27.34
33 100
2678 2389
3188 3240
0 0.00
19.0440
6 35.62
34 100
2667 2645
3322 3037
0 0.00
24.5594
3 14.82
35 100
2616 2359
3157 2840
0 0.00
20.6804
3 20.39
36 100
2680 2573
3024 3017
0 0.00
12.8358
2 17.26
37 100
2568 2644
3114 3034
0 0.00
21.2616
8 14.75
38 100
2658 2458
2927 2903
0 0.00
10.1203
9 18.10
39 100
2619 2698
3142 3041
0 0.00
19.9694
5 12.71
40 100
2573 2691
3210 3212
0 0.00
24.7570
9 19.36
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