MINIMASI MAKESPAN PADA PERSOALAN PENJADWALAN ORDERED FLOWSHOP MENGGUNAKAN PSO

The production scheduling problem is in the kind of flowshop with n jobs and m machines, to get the order of the schedule for allocating operations of the jobs to the available machines so as to get the minimum total time for completion of all job or commonly called makespan. This study uses an optimization technique approach with the PSO algorithm to get minimum makespan on the ordered flowhop scheduling problem. The performance of the scheduling algorithm presented is evaluated by testing on a benchmark data set of 240 variations in the combination number of jobs and machines. The minimum measure is obtained as a result of scheduling with PSO, whose process stops at a certain iteration when in the last 10 iterations there is no change in the value of a better makespan. The performance of the PSO algorithm is efficient at regular flow scheduling with the use of the most iterations of 19 iterations and the longest execution time of 28.42 seconds or less than half a minute, namely scheduling instances with the largest number of machines and jobs. In this research, only the analysis of the resulting minimal forward and the time of execution was carried out. Further research can be extended by not only measuring the minimum makespan, such as measuring total flowtime, total tardiness, and others

Solving FJSSP With a Genetic Algorithm

The Flexible Job Shop Scheduling Problem is an NP-Hard combinatorial problem. This paper aims to find a solution to this problem using genetic algorithms, and discuss the effectiveness of this. Initially, I did exploratory work on whether neural networks would be effective or not, and found a lot of trade offs between using neural networks and chromosome sequencing. In the end, I decided to use chromosome sequencing over neural networks, due to the scope of my problem being on a small scale rather than on a large scale. Therefore, the genetic algorithm was implemented using chromosome sequencing. My chromosomes were represented as binary strings with reserved bits for the machine and job numbers. This allowed me to experiment with different mutations such as random bit flip mutation and machine job swap mutations. The biggest benefit of genetic algorithms over heuristic algorithms is the potential for improvement. While greedy gives good results initially, genetic beats out greedy quickly after a small number of epochs. Furthermore, I suspect that genetic algorithms should be much faster than other learning algorithms, but as this is an under-documented metric, I decided to contribute my own results to help document this metric. For future work, it would be interesting to see how a neural network model would have reacted, and how its time to find a solution would compare to chromosome sequencing. Another interesting topic is a scheduler that can adapt to any variation of the Job Shop Scheduling Problem, as this would be very useful in the real world. One final interesting topic would be to implement some kind of dynamic job loading for this genetic algorithm, as in real world situations, new jobs and tasks get scheduled all the time. But, this is a very complicated problem, thus it is best left to the future

A New Slope Index for Solving NxM Flow Shop Sequencing Problems with Minimum Makespan

A flow shop sequencing problem is one of the classical problems in the production scheduling. In a flow shop, a particular case of manufacturing process follows a fixed linear structure. The purpose of this paper is to find the minimum total processing time (makespan) of sequencing ‘n’ jobs on ‘m’ machines for a flow shop problem in a static workshop. The proposed approach is based on the slope of each job on its journey from the first to the last machine. This approach is compared with five well-known heuristics (Palmer, Gupta, CDS, Dannenbring, Hundal) and one more recent technique that is based on the harmonic triangle. The results obtained from this study for different sizes of ‘n’x’m’ flow shop sequencing problems ranging from 4x4 to 50x20 indicate that the proposed approach is efficient with an encouraging percentage of improvements compared with all other six heuristic techniques

Iterative beam search algorithms for the permutation flowshop

We study an iterative beam search algorithm for the permutation flowshop (makespan and flowtime minimization). This algorithm combines branching strategies inspired by recent branch-and-bounds and a guidance strategy inspired by the LR heuristic. It obtains competitive results, reports many new-best-so-far solutions on the VFR benchmark (makespan minimization) and the Taillard benchmark (flowtime minimization) without using any NEH-based branching or iterative-greedy strategy. The source code is available at: https://gitlab.com/librallu/cats-pfsp

Solving blocking flowshop scheduling problem with makespan criterion using q-learning-based iterated greedy algorithms

This study proposes Q-learning-based iterated greedy (IGQ) algorithms to solve the blocking flowshop scheduling problem with the makespan criterion. Q learning is a model-free machine intelligence technique, which is adapted into the traditional iterated greedy (IG) algorithm to determine its parameters, mainly, the destruction size and temperature scale factor, adaptively during the search process. Besides IGQ algorithms, two different mathematical modeling techniques. One of these techniques is the constraint programming (CP) model, which is known to work well with scheduling problems. The other technique is the mixed integer linear programming (MILP) model, which provides the mathematical definition of the problem. The introduction of these mathematical models supports the validation of IGQ algorithms and provides a comparison between different exact solution methodologies. To measure and compare the performance of IGQ algorithms and mathematical models, extensive computational experiments have been performed on both small and large VRF benchmarks available in the literature. Computational results and statistical analyses indicate that IGQ algorithms generate substantially better results when compared to non-learning IG algorithms

Hybrid multiobjective genetic algorithm for integrated dynamic scheduling and routing of jobs and automated guided vehicles in flexible manufacturing systems

The dynamic continues trend of adoption and improvement inventive automated technologies is one of the main competing strategies of many manufacturing industries. Effective integrated operations management of Automated Guided Vehicle (AGV) system in Flexible Manufacturing System (FMS) environment results in the overall system performance. Routing AGVs was proved to be NP-Complete and scheduling of jobs was also proved to be NP hard problems. The running time of any deterministic algorithms solving these types of problems increases very rapidly with the size of the problem, which can be many years with any computational resources available presently. Solving AGVs conflict free routing, dispatching and simultaneous scheduling of the jobs and AGVs in FMS in an integrated manner is identified as the only means of safeguarding the feasibility of the solution to each sub-problem. Genetic algorithm has recorded of huge success in solving NP-Complete optimization problems with similar nature to this problem. The objectives of this research are to develop an algorithm for integrated scheduling and conflict-free routing of jobs and AGVs in FMS environment using a hybrid genetic algorithm, ensure the algorithm validity and improvement on the performance of the developed algorithm. The algorithm generates an integrated scheduling and detail paths route while optimizing makespan, AGV travel time, mean flow time and penalty cost due to jobs tardiness and delay as a result of conflict avoidance. The integrated algorithms use two genetic representations for the individual solution entire sub-chromosomes. The first three sub-chromosomes use random keys to represent jobs sequencing, operations allocation on machines and AGV dispatching, while the remaining sub-chromosomes are representing particular routing paths to be used by each dispatched AGV. The multiobjective fitness function use adaptive weight approach to assign weights to each objective for every generation based on objective improvement performance. Fuzzy expert system is used to control genetic operators using the overall population performance history. The algorithm used weight mapping crossover (WMX) and Insertion Mutation (IM) as genetic operators for sub-chromosomes represented with priority-based representation. Parameterized uniform crossover (PUX) and migration are used as genetic operators for sub-chromosomes represented using random-key based encoding. Computational experiments were conducted on the developed algorithm coded in Matlab to test the effectiveness of the algorithm. First scenario uses static consideration, the second scenario uses dynamic consideration with machine failure recovery. Sensitivity analysis and convergence analysis was also conducted. The results show the effectiveness of the proposed algorithm in generating the integrated scheduling, AGVs dispatching and conflict-free routing. The comparison of the result of the developed integrated algorithm using two benchmark FMS scheduling algorithms datasets is conducted. The comparison shows the improvement of 1.1% and 16% in makespan of the first and the second benchmark production dataset respectively. The major novelty of the algorithm is an integrated approach to the individual sub-problems which ensures the legality, and feasibility of all solutions generated for various sub-problems which in the literature are considered separately

Benchmarking Permutation Flow Shop Problem: Adaptive and Enumerative Approaches Implementations via Novel Threading Techniques

A large number of real-world planning problems are combinatorial optimization problems which are easy to state and have a finite but usually very large number of feasible solutions. The minimum spanning tree problem and the shortest path problem are some which are solvable through polynomial algorithms. Even though there are other problems such as crew scheduling, vehicle routing, production planning, and hotel room operations which have no properties such as to solve the problem with polynomial algorithms. All these problems are NP-hard. The permutation flow shop problem is also NP-hard problem and they require high computation. These problems are solvable as in the form of the optimal and near-optimal solution. Some approach to get optimal are exhaustive search and branch and bound whereas near optimal are achieved annealing, Genetic algorithm, and other various methods. We here have used different approach exhaustive search, branch and bound and genetic algorithm. We optimize these algorithms to get performance in time as well as get the result closer to optimal. The exhaustive search and branch and bound gives all possible optimal solutions. We here have shown the comparative result of optimal calculation for 10 jobs with varying machine number up to 20. The genetic algorithm scales up and gives results to the instances with a larger number of jobs and machines

A permutation flowshop model with time-lags and waiting time preferences of the patients

The permutation flowshop is a widely applied scheduling model. In many real-world applications of this model, a minimum and maximum time-lag must be considered between consecutive operations. We can apply this model to healthcare systems in which the minimum time-lag could be the transfer times, while the maximum time-lag could refer to the number of hours patients must wait. We have modeled a MILP and a constraint programming model and solved them using CPLEX to find exact solutions. Solution times for both methods are presented. We proposed two metaheuristic algorithms based on genetic algorithm and solved and compared them with each other. A sensitivity of analysis of how a change in minimum and maximum time-lags can impact waiting time and Cmax of the patients is performed. Results suggest that constraint programming is a more efficient method to find exact solutions and changes in the values of minimum and maximum time-lags can impact waiting times of the patients and Cmax significantly

New hard benchmark for flowshop scheduling problems minimising makespan

[EN] In this work a new benchmark of hard instances for the permutation flowshop scheduling problem with the objective of minimising the makespan is proposed. The new benchmark consists of 240 large instances and 240 small instances with up to 800 jobs and 60 machines. One of the objectives of the work is to generate a benchmark which satisfies the desired characteristics of any benchmark: comprehensive, amenable for statistical analysis and discriminant when several algorithms are compared. An exhaustive experimental procedure is carried out in order to select the hard instances, generating thousands of instances and selecting the hardest ones from the point of view of a gap computed as the difference between very good upper and lower bounds for each instance. Extensive generation and computational experiments, which have taken almost six years of combined CPU time, demonstrate that the proposed benchmark is harder and with more discriminant power than the most common benchmark from the literature. Moreover, a website is developed for researchers in order to share sets of instances, best known solutions and lower bounds, etc. for any combinatorial optimisation problem.Eva Vallada and Ruben Ruiz are partially supported by the Spanish Ministry of Science and Innovation, under the project "RESULT - Realistic Extended Scheduling Using Light Techniques" with reference DPI2012-36243-C02-01 co-financed by the European Union and FEDER funds and by the Universitat Politecnica de Valencia, for the project MRPIV with reference PAID/2012/202. The authors would like to acknowledge the help received from Juan Cabota in the early development of the web of instances.Vallada Regalado, E.; Ruiz García, R.; Framinan, JM. (2015). New hard benchmark for flowshop scheduling problems minimising makespan. European Journal of Operational Research. 240(3):666-677. doi:10.1016/j.ejor.2014.07.033S666677240