Efficient dispatching rules based on data mining for the single machine scheduling problem

Jan Zizka et al. (Eds) : ICAITA, SAI, CDKP, Signal, NCO - 2015
pp. 199–208, 2015. © CS & IT-CSCP 2015 DOI : 10.5121/csit.2015.51516
EFFICIENT DISPATCHING RULES BASED
ON DATA MINING FOR THE SINGLE
MACHINE SCHEDULING PROBLEM
Mohamed Habib Zahmani1
, Baghdad Atmani2
and Abdelghani Bekrar3
1
Laboratory of Pure and Applied Mathematics,
University of Mostaganem, Mostaganem, Algeria
habib.zahmani@univ-mosta.dz
2
Laboratoire d’Informatique d’Oran,
University of Oran 1, Oran, Algeria
atmani.baghdad@univ-oran.dz
3
Laboratory of Industrial and Human Automation control,
Mechanical engineering and Computer Science,
University of Valenciennes and Hainaut-Cambresis, Valenciennes, France
abdelghani.bekrar@univ-valenciennes.fr
ABSTRACT
In manufacturing the solutions found for scheduling problems and the human expert’s
experience are very important. They can be transformed using Artificial Intelligence techniques
into knowledge and this knowledge could be used to solve new scheduling problems. In this
paper we use Decision Trees for the generation of new Dispatching Rules for a Single Machine
shop solved using a Genetic Algorithm. Two heuristics are proposed to use the new Dispatching
Rules and a comparative study with other Dispatching Rules from the literature is presented.
KEYWORDS
Data Mining, Decision Trees, Dispatching Rules, Single Machine, Scheduling, Genetic
Algorithm
1. INTRODUCTION
In today's business environment, competition has become very fierce and the customers have
become very demanding in terms of quality, cost and time. In this context of an increasingly
globalized world, and in order to guarantee the survival of the enterprise it is necessary to
enhance the manufacturing process. By doing so, the company secures a place in this highly-
competitive environment. The manufacturing process goes hand in hand with the scheduling
problem. The scheduling problem is NP-Hard due to the exponential number of solutions [1].
In this paper we focus on the Single Machine (SM) Scheduling Problem. Many methods have
been proposed to solve this problem including its many variations, namely, static and dynamic,

200 Computer Science & Information Technology (CS & IT)
with or without perturbations and a large set of objective functions (sum of tardiness, length of
schedule, etc.) [1]–[4]. Still no proposed approach can solve it for all its variations.
One of the most popular methods used to solve scheduling problem are the Dispatching Rules
(DR). These techniques are widely used [5]–[7] owing to their efficiency and their ability to
quickly define a priority for each job waiting on a machine queue. This reactivity increases the
systems responsivity and its fault tolerance in case of dynamic or perturbation scenarios.
An evolution of Dispatching Rules introduced in literature is Data Mining. DM is used in order to
create new rules using previous problems and experiments. In this way, the previously acquired
knowledge is transformed to new DR to be used for new scheduling problems. Among these
approaches we notice some in particular Koonce [8], Shahzad [9] or Aissani [10]. In all these
works DM is used and more often Decision Trees for the extraction of Dispatching Rules to be
used to schedule jobs in a new problem or reschedule in case of perturbation. In these papers
authors focus mainly on multiple-machines shops such as Flow Shop or Job Shop for the
generation of new DR.
In this paper Genetic Algorithms (GA) are employed in pretreatment process by solving the
Single Machine problem, and Decision Trees are called upon to extract hidden knowledge in the
form of Dispatching Rules. Also are present two heuristics for the setup and use of the new
Dispatching Rules since they are different from classic ones. Finally, a comparative study with
other well-known DR is performed.
2. STATE OF THE ART
In planning and scheduling, Aytug & al. [11] distinguish two ways of using Data Mining. The
first for decision support, where DM helps to identify the best DR since no one rule outperforms
all others such as in the paper of Metan & al. [12]. In this approach the state of the system is
continuously monitored and the Decision Support System changes the Dispatching Rules if need
be to optimize the objective function.
As for the second way, DM is applied to face perturbations scenarios for example a machine
breakdown or new jobs arrival. A recent study of Said & al. [13] where the DR is dynamically
changed in order to minimize the impact of the perturbation.
A third trend initially introduced by Li [14] where Decision Trees are employed to generate new
Dispatching Rules capable of mimicking a metaheuristic or even an exact method for the
resolution of a scheduling problem. This approach is proposed for a Single Machine problem
using DR. Authors use the LPT rule (Longest Processing Time) where the job having the longest
processing time is processed first. Then DT algorithm is applied for the generation of the new
DR. One drawback in this paper is the use of the LPT rule since it is a heuristic it is not capable
of finding the best solution. Therefore as an alternative, we propose the use of a Genetic
Algorithm for the problems resolution.
Other works based on the same idea use different solving methods and for other scheduling
problems. For instance in [9], a Job Shop problem is addressed using Tabu Search. The TS
algorithm is used at first to find a feasible solution, afterwards a data pretreatment of the solution
is done. Finally, Decision Trees, based on the pretreated data, generate a new DR.

Computer Science & Information Technology (CS & IT) 201
Balasundaram & al. [15] perform also a DR generation using DT in a Flow Shop environment. At
first a simple heuristic is used to solve the problem comprising 5 jobs and 2 machines. For the
scheduling, the makespan (end date of all jobs) is estimated by scheduling a job i before job j and
vice versa. The combination minimizing the makespan is used. Then, DT are applied on the
scheduling solution to find a new DR. Another idea of Khademi Zare & al. [16] using a hybrid
algorithm combining Genetic Algorithm, Data Mining, fuzzy sets, similarity algorithm and
attribute-driven deduction algorithm. DM is used to extract rules to help GA to boost its speed to
reach the optimal solution.
After a thorough analysis of these approaches, two problems arise. The first resides in the fact
that the new Dispatching Rule in a “if-then” form is only compared with the solving methods
used in the first step, a heuristic in [15], Tabu Search [9] or Shortest Processing Time for Li & al.
[14]. This comparison shows that the new DR performs nearly as efficiently as the
heuristic/metaheuristic used for the resolution of the problem, with a certain degree of error. This
difference is due to the bad decisions taken by the decision (inverse some jobs). Also, the
problem of jobs order inversion is not addressed in any of the quoted approaches, which may
have heavy consequences on the system’s performance. To illustrate the problem we propose the
following example.
Suppose that the new obtained DR is constructed using 3 jobs, J_1, J_2 and J_3. The sequence
returned using a solving method is for example: J_2, J_3 and finally J_1. The new DR, contrary
to a classic DR, can only compare jobs one by one (see Figure 1):
Figure 1. Defining sequence using the new DR
For example, while comparing the jobs the new DR will return the following results:
‫ܬ‬ଶ vs ‫ܬ‬ଷ: ‫ܬ‬ଶ is scheduled first (correct decision)
‫ܬ‬ଷ vs ‫ܬ‬ଵ: ‫ܬ‬ଷ is scheduled first (correct decision)
‫ܬ‬ଶ vs ‫ܬ‬ଵ: ‫ܬ‬ଵ is scheduled first (wrong decision)
In case of a wrong decision it becomes impossible to construct a scheduling. According to the
two first decisions, job 1 should be processed last. But with the third decision, being incorrect,
there is an ambiguity. Should job 1 be processed last taking into consideration only the two first
decisions, or must it be processed first, ignoring the two first decisions and taking only the third
one into consideration.
A second problem is that no details are provided as to how to use the new DR in particular the
approaches of Li and Shahzad [9], [14]. In those two papers the generated decision tree (DR)
have a small size (2 nodes) because of the number of jobs used (5 jobs). But in a real complex
problem the jobs number is much higher and consequently the tree size will be larger and more
complex. Also the authors never compare the new DR with other rules from literature in order to
evaluate its performance.

In this paper we propose two heuristics to take into consideration the bad decision problem and
also a comparative study with some Dispatching Rules from the literature is performed.
3. PROPOSED APPROACH
To generate Dispatching Rules based on Decision Trees it is necessary to use an exact or
approximate method to solve the problem. In this paper we use a Genetic Algorithm to solve the
Single Machine Scheduling Problem, the solution is used by the Decision Tree to create a DR.
The choice of GA is justified by its ability to quickly explore the research space, its proven
results and wide use for such a problem [1], [17]–[19]. And as done by Li & Shahzad [9], [14]
Decision Trees will be used for the DR generation.
Figure 2. Proposed approach
3.1. Single Machine
The Single Machine Scheduling Problem with Total Weighted Tardiness (SMTWT) can be
defined as follows. A set of ݊ jobs ‫ܬ‬ = ሼ‫ܬ‬ଵ, ‫ܬ‬ଶ, … , ‫ܬ‬௡ሽ to be processed on a machine. Each job ‫ܬ‬௜
consists of a single operation having a processing time ܲܶ௜ > 0, ݅ = 1, … , ݊. The importance of a
job is expressed using a positive weight ‫ݓ‬௜ > 0, ݅ = 1, … , ݊. The machine can process only one
job at a time and a job’s execution cannot be suspended. Each job is supposed to be finished
before its deadline ݀௜. If not a penalty “tardiness” is then calculated where tardiness ܶ௜ =
max ሼܵ௜ + ܲܶ௜ − ݀௜; 0ሽ. ܵ௜ denotes the ‫ܬ‬௜ start time. The scheduling objective is to minimize the
Total Weighted Tardiness:
min ܹܶܶ = ෍ ‫ݓ‬௜ܶ௜
௡
௜ୀଵ

3.2. Genetic Algorithm
Genetic Algorithms are used to explore a solution space by mimicking the biological process.
They have been successfully applied in literature for several problems including Single Machine
problem [18], [19]. The main components of GA are as follows:
• Solution encoding: a representation of solutions
• Initial population: generation of an initial population
• Fitness: measurement function for a given solution, total weighted tardiness in this case
• Selection: selection process for chromosomes to generate a new population
• Genetic operators: a genetic operator such as crossover and mutation are applied on the
selected chromosomes in order to create new ones
• Replacement: natural selection of the members of population who will survive
In this paper, the implemented GA is mainly inspired from the one proposed by Armentano [18]
with a modified initial population generation process. We suggest that the reader consult the
paper for more details.
3.3. Decision Tree
For the generation of Dispatching Rules, we use the method of Li [14] which is adapted to our
problem since the used attributes are not the same. Release time, start time, processing time and
completion time in the case of [14]; and processing time, weight and due date in this paper. To
explain the process we propose the following example:
Suppose there is 4 jobs, and the sequence returned by the GA is |3|0|2|1|
Table 1. Jobs attributes
Job N° Processing Time Weight Due Date
0 15 3 80
1 20 2 30
2 35 6 50
3 7 8 60
A comparative table is constructed (see Table 2) based on Table 1 where jobs are compared one
to another. So, job ‫ܬ‬ଵ is compared with ܰ − 1, job ‫ܬ‬ଶ with ܰ − 2 and so on. The size of the new
table is equal to ∑ (݊ − ݆)ேିଵ
௝ୀଵ . This new table will be used as an entry by the Decision Tree to
generate a new Dispatching Rule.

Table 2. Jobs comparison
Job1 N° PT1 w1 d1 Job2 N° PT2 w2 d2 Job1
1er
0 15 3 80 1 20 2 30 Yes
0 15 3 80 2 35 6 50 Yes
0 15 3 80 3 7 8 60 No
1 20 2 30 2 35 6 50 No
1 20 2 30 3 7 8 60 No
2 35 6 50 3 7 8 60 No
The C4.5 Decision Tree algorithm is the applied on the data of Table 2 to create the new DR. The
new rules is an if-then form as follows:
࢏ࢌ ‫ݓ‬ଶ ≤ 6 ࢚ࢎࢋ࢔ ‫ܬ‬ଵ ݅‫ݏ‬ ‫݀݁ݏݏ݁ܿ݋ݎ݌‬ ݂݅‫ݐݏݎ‬
࢏ࢌ ‫ݓ‬ଶ > 6 ࢚ࢎࢋ࢔ ‫ܬ‬ଶ ݅‫ݏ‬ ‫݀݁ݏݏ݁ܿ݋ݎ݌‬ ݂݅‫ݐݏݎ‬
3.4. New Dispatching Rule
In order to apply the new DR (DT), we propose two heuristics in order to take into consideration
the bad decisions.
Proposed Heuristic 1 sort by number of accumulated of “yes”
1 : Initialize vector NumberYes[N] to 0
2 : For each Job i to N
3 : For each Job j to N
4 : Decision = JobiScheduledFirst(i, j) ;
5 : If Decision = Yes
6 : NumberYes [i] = NumberYes [i] + 1 ;
7 : End if
8 : End for
9 : End for
10 : Sort NumberYes in decreasing order
Proposed Heuristic 2 quick sort
1 : While Iteration <= IterationsNumber
2 : For each Job i to N
3 : For each Job j to N
4 : Decision = JobiScheduledFirst(i, j) ;
5 : If Decision = Yes
6 : Swap(i, j);
7 : End if
8 : End for
9 : End for
10 : End while

4. EXPERIMENTS AND RESULTS
In order evaluate the performances of the GA and the new DR, we focus on the Weighted
Tardiness benchmark available in OR-Library (see http://people.brunel.ac.uk/~mastjjb/jeb/orlib/
wtinfo.html for more details). Where for each problem the best Total Weighted Tardiness is
known allowing us by the same way to compare the two heuristics and other DR from literature.
Experiments are performed on 125 problems with 40 jobs.
The population size of the GA ‫ܫ‬ is set to 100 chromosomes and the size of the selected population
for crossover/mutation is ‫2/ܫ‬ i.e. 50 chromosomes. While the number of iterations is set to 150
and if the best known solution is reached before the GA stops. The modified GA finds the best
known solution for 32 problems, that is 25.6%.
We also conducted a comparison between the GA results and the best results. To do so, a gap
using the following formula is calculated (1):
‫݁݃ܽݎ݁ݒܣ‬ ‫݁ܿ݊݁ݎ݂݂݁݅ܦ‬ = ൥ ෍
‫)݅(ܣܩ‬ − ܱܴ‫)݅(ݕݎܽݎܾ݅ܮ‬
ܱܴ‫)݅(ݎݕܽݎܾ݅ܮ‬
௉௥௢௕௟௘௠௦ ே௨௠௕௘௥
௜ୀଵ
൩ /ܲ‫ݎܾ݁݉ݑܰݏ݈ܾ݉݁݋ݎ‬ (1)
‫)݅(ܣܩ‬ is the score found using the Genetic Algorithm for a problem ݅.
ܱܴ‫)݅(ݕݎܽݎܾ݅ܮ‬ is the best known score in OR-Library for a problem ݅.
It is worth mentioning that for some problems the best known score in the OR-Library is equal to
0. Thus it becomes impossible to calculate the gap, consequently, those problems are ignored.
This reduces the number of problems to 107 (instead of 125 initially). On these 107 problems GA
has 9.76% average difference with the OR-Library.
Once the problems are solved using GA, Decision Trees are applied to generate a new
Dispatching Rule as explained in the proposed approach section. All the data of all the problems
is gathered in one file for the learning process. Then, in order to apply the new DR the two
heuristics PH1 and PH2 are used and a comparison is performed using the following formula (2)
(see Table 3). The best heuristic in then applied for the comparison with literature Dispatching
Rules.
‫݁݃ܽݎ݁ݒܣ‬ ‫݁ܿ݊݁ݎ݂݂݁݅ܦ‬ = ൥ ෍
‫)݅(ܪ‬ − ܱܴ‫)݅(ݕݎܽݎܾ݅ܮ‬
ܱܴ‫)݅(ݎݕܽݎܾ݅ܮ‬
௉௥௢௕௟௘௠௦ ே௨௠௕௘௥
௜ୀଵ
൩ /ܲ‫ݎܾ݁݉ݑܰݏ݈ܾ݉݁݋ݎ‬ (2)
‫)݅(ܪ‬ is a score found using a heuristic ‫ܪ‬ for a problem ݅.
Table 3. Comparison of PH1 and PH2
PH1 PH2
Aver. Gap (%) NP Aver. Gap (%) NP
912 1 115,32* 106*

NP is the number of times where the heuristic finds the best results.
From these results we conclude that the second heuristic PH2 is much better than the first one.
So, for the following experiments only this one is used for the comparison with the other DR.
The Dispatching Rules used for the comparison (see Table 4) study are:
• Shortest Processing Time (SPT)
• Longest Processing Time (LPT)
• Weighted Shortest Processing Time (WSPT), [2] this rule is best for the SMTWT
problem.
• Earliest Due Date (EDD)
• Critical Ratio (CR)
• Mixed Dispatching Rule (MDR) propose dans [20]
Table 4: Comparison of PH2 with other DR
PH2 SPT LPT WSPT EDD CR MDR
Gap (%) 115.32* 1203.43 4929.03 681.08 162.58 1828.13 162.58
NP 81* 0 0 16 13 0 13
Based on this results, it is clear that the new Dispatching Rule returns better results in terms of
average gap compared to the best known results of the OR-Library. Also in regards to time where
it finds the smallest Total Weighted Tardiness value.
In Figure 3 we compare the results of PH2 and MDR being the best two DR. When the objective
value is equal tp 0 it means that the optimal solution is reached by one of the two heuristics, if not
the difference in terms of Total Weighted Tardiness is shown.
Figure 3. PH2 vs MDR

Also and in order to accurately measure the new DR the set of 107 problems is split in two parts
92/15. The 92 problems will be used for the learning process to create a new DR and other 15 for
tests. The aim is to evaluate PH2 for new scheduling problems, results are shown in Table 5.
Table 5: PH2 vs classic DR for new problems
PH2 SPT LPT WSPT EDD CR MDR
Gap (%) 63.59* 126.11 360.30 68.07 123.86 274.85 123.86
NP 7* 0 0 7* 1 0 1
In case of an entirely new Single Machine Scheduling Problem, the proposed heuristic PH2 has
an average difference of 63.59% compared to the best known results. In terms of number of times
where the best score is reached it performs as well as the WSPT rule. In Figure 4 we compare the
results of PH2 and WSPT as done in Figure 3.
Figure 4. PH2 vs WSPT
From this experiments we prove the superiority of the proposed heuristic for the use of the
Decision Tree as Dispatching Rule, while taking into consideration bad decisions. The proposed
heuristic also outperforms WMDD [21], H2 et H3 [22] for the same set of data.
5. CONCLUSIONS
In this paper two heuristics for the use of Decision Trees as Dispatching Rule based on a Genetic
Algorithm are proposed. The approach was tested for Single Machine problem with Total
Weighted Tardiness objective. Experiments show the superiority of the proposed approach
compared to some well-known DR for problems used in learning or completely new ones.
In perspective, an improvement of the proposed heuristic is possible. Also, knowing that OR-
Library includes SM problems with 50 and 100 jobs, it is interesting to test the new heuristic for
such problems. Finally, it might be interesting to consider more complex problems with multiple
machines such as the Job Shop Scheduling Problem.

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