Multiple dispatching rules allocation in real time using data mining, genetic algorithms, and simulation

Abstract

In production planning and scheduling, data mining methods can be applied to transform the scheduling data into useful knowledge that can be used to improve planning/scheduling by enabling real-time decision-making. In this paper, a novel approach combining dispatching rules, a genetic algorithm, data mining, and simulation is proposed. The genetic algorithm (i) is used to solve scheduling problems, and the obtained solutions (ii) are analyzed in order to extract knowledge, which is then used (iii) to automatically assign in real-time different dispatching rules to machines based on the jobs in their respective queues. The experiments are conducted on a job shop scheduling problem with a makespan criterion. The obtained results from the computational study show that the proposed approach is a viable and effective approach for solving the job shop scheduling problem in real time.

Appendices

Appendix A

In this appendix, the detailed results of the proposed genetic algorithm for all instances are reported. Each table contains the GA’s results of a specific problem category, for instance, in Table 10 are presented the GA’s results for $15 \times 15$ problems. The tables’ columns contain the following information:

Table 11 $20 \times 15$ JSSP’s results

Table 12 $20 \times 20$ JSSP’s results

Table 13 $30 \times 15$ JSSP’s results

Table 14 $30 \times 20$ JSSP’s results

Table 15 $50 \times 15$ JSSP’s results

Table 16 $50 \times 20$ JSSP’s results

• Pb.: is the id of the problem (in order of appearance in the benchmark),

• GA’s $C_\mathrm{{max}}$: the makespan of the best-found solution (DR set) using the GA,

• Un. Sol.: is the number of unique found chromosomes (solutions) by the GA during the space search over $q^m$ possible solutions,

• Best-known $C_\mathrm{{max}}$: the best-known lower bound and upper bound (if available) for each scheduling problem in the OR-Library,

• $C_\mathrm{{max}}$ Gap: is the average difference between the GA’s solution and the best-known lower and upper bounds (see Eqs. 3 and 4),

• Bt. Sets.: is the number of the best dispatching rules sets found using the GA, i.e., the DR sets with the same best makespan, over the number of unique found solutions (Un. Sol.),

• Dispatching rules set: is a list of integer values (one of the best-found DR sets) displaying the number of rules to use on each machine. The number of integers is equal to the number of machines (15 or 20 depending on the problem) (Tables 11, 12, 13, 14, 15, 16, and 17).

Table 17 $100 \times 20$ JSSP’s results

Table 18 Solving job shop problems using $15 \times 15$ instances for learning

Table 19 Solving job shop problems using $20 \times 15$ instances for learning

Table 20 Solving job shop problems using $20 \times 20$ instances for learning

Table 21 Solving job shop problems using $30 \times 15$ instances for learning

Table 22 Solving job shop problems using $30 \times 20$ instances for learning

Table 23 Solving job shop problems using $50 \times 15$ instances for learning

Table 24 Solving job shop problems using $50 \times 20$ instances for learning

Table 25 Solving job shop problems using $100 \times 20$ instances for learning

Appendix B

In this appendix, the decision tree results (learning 100) of the decision tree are presented. For instance, in Table 18 the decision tree is generated using the scheduling data of $15 \times 15$ problems and the other 70 instances are solved using the DT. The tables contain the following information:

• Pb. Category: the size (category) of the problem instances solved using the DT,

• Av. DT’s $C_{\max }$: the average $C_{\max }$ obtained by the DT when solving the instances of the current problems category,

• Av. GA’s $C_{\max }$: the average $C_{\max }$ obtained by the GA when solving the instances of the current problems category,

• $C_{\max }$ Gap: the average gap between the DT and the GA (see equation 6).

From Tables 18, 19, 20, 21, 22, 23, 24, and 25, it can be noted that the lowest makespan gap between the decision tree and the genetic algorithm is of 7.36% and is obtained using the $30 \times 15$ job shop instances for learning and solving the $100 \times 20$ problems, while the highest gap is equal to 22.66% involving the same learning dataset when solving the $20 \times 15$ JSSP.

An interesting observation is that the more the jobs in a problem, the lesser the gap between the decision tree and the genetic algorithm. When solving the problems $15 \times 15$, $20 \times 15$, $20 \times 20$, $30 \times 15$, $30 \times 20$, $50 \times 15$, $50 \times 20$, and $100 \times 20$ using the different learning datasets, the average gap is of 19.50, 17.90, 15.37, 14.79, 12.97, 12.39, 10.85, and 8.20%, respectively. This is due to the number of jobs waiting on each machines’ queue. For example, with a small number of jobs on a machine’s queue, i.e., 2, 3, or 4 jobs, the selection of the best dispatching rules is not efficient because the voting procedure does not manage to identify the best rules (no popular DR). However, with more jobs on the queues, the vote becomes more useful resulting in better results (lower makespan).