Research On Scheduling Parallel Batch Processing Machines With Non-identical Melting Jobs

Precision casting is a new method for mold manufacturing, and is applied in some mold enterprises with demands for small batch manufacturing and more complex mold cavities. Aluminum alloy melting is one of the key processes of precision casting. Reasonable scheduling of melting jobs in batches has important significance for saving energies, reducing emissions, reducing costs and improving the efficiency of mold manufacturing.The melting jobs scheduling is a batch scheduling with non-identical jobs and unequal release times, and there is a monotone increasing function relationship between the processing time and the weight of melting batches. Algorithms of parallel batch scheduling on single machine and identical parallel machines cannot be directly applied to melting batch scheduling because the processing time of parallel batches is the maximum processing time of all the jobs in the batch. Base on scheduling problems of parallel batch processing machines with non-identical melting jobs, the researches focused on batch rules, scheduling optimization rules and efficient solution algorithms on single machine, identical parallel machines, uniform parallel machines and unrelated parallel machines. The main works were as follows:(1) For melting aluminum alloy in precision casting of molds, the features of melting batch were studied, and batch scheduling unified model of parallel batch processing machines with non-identical melting jobs to minimize the maximum completion time.(2) Scheduling algorithm of single batch processing machine with non-identical melting jobs. Scheduling single batch processing machine is a base of scheduling parallel batch processing machines. According to the characteristics of melting jobs, the unified model was simplified as a model of single batch processing machine. With the equal release times, based on the batch weight fit (BWF) rule, the genetic algorithm was proposed. With the unequal release times, the genetic algorithm was proposed by the batch release time first (BRF) and job left shift (JLS) heuristic rulers. Simulation experiments showed that algorithms were more efficient than the simulated annealing algorithms. (3) Scheduling algorithm of identical batch processing machines with non-identical melting jobs. The method of two phases was adopted that jobs were grouped to batches, and then batches were assigned to batch processing machines. Firstly, BWF、BRF rulers could be used to form batches because of the same type machine capacity constraints. Secondly, the longest processing time (LPT) and the earliest release time (ERT) heuristic rulers could be adopted to assign to batch processing machines. Then, the minimum completion time difference for identical parallel batch-processing machines (MCDPM) and the job adjustment of the latest batch for identical parallel batch-processing machines with unequal release times (JALBPMR) optimization rules were proposed to further optimize the batch scheduling results by LPT and ERT rulers. The optimization rules could effectively avoid premature convergence of genetic algorithms.(4) Scheduling algorithm of uniform batch processing machines with non-identical melting jobs. Based the features of identical capacities and non-identical speeds, for improvement of scheduling algorithms of identical batch processing machines, genetic algorithms of uniform batch processing machines were proposed that MCDPM was replaced by the minimum completion time difference for uniform parallel batch-processing machines (MCDQM) rule and JALBPMR was replaced by the job adjustment of the latest batch for uniform parallel batch-processing machines with unequal release times (JALBQMR) rule. With equal and unequal release times, simulation experiments demonstrated that algorithms had good solution qualities and efficiencies.(5) Scheduling algorithm of unrelated batch processing machines with non-identical melting jobs. Because capacities of the machines are not equal, the solved methods of identical and uniform batch processing machines didn’t fit. With the equal release times, the machine earliest completion time and batch first fit (MECT-BFF) heuristic was proposed to group jobs into batches and assign batches to machines at the same time. With the unequal release times, referenced the BWF and BRF batches ruler, the maximum capacity constraints were used to judge whether a batch need to be repaired, and the minimum capacity constraints were used to group jobs to new batches that jobs came from batches repaired. Then the earliest release time and machine earliest completion time (ERT-MECT) heuristic was proposed to group jobs into batches and assign batches to machines. Hybrid particale swarm optimization algorithms were proposed, and experiment results showed that the algorithms had good solution qualities.(6) The scheduling module of melting jobs developed and applied. The scheduling module of melting jobs based on the research results of the paper were embedded in the production planning and control system. The system was applied successfully in the enterprises.In conclusion, scheduling problems of parallel batch processing machines with non-identical melting jobs were systematically, deeply studied. Scheduling unified model was established. Some rulers were proposed, such as BWF, BRF batch rules, JLS, MCDPM, MCDQM, JALBPMR, JALBQMR optimization rules and MECT-BFF, ERT-MECT scheduling rules. Based on various machine environments, some efficient solution algorithms were proposed. The researches had enriched the theory researches and application fields of batch scheduling.