A Mathematical Model for Lot-streaming Hybrid Flow Shop Scheduling Problem by Considering Learning Effect and Buffer Capacity

Abstract

Lot streaming, is an effective technique to increase efficiency in a production system by splitting a job into several smaller parts to overlap operations between successive machines in a multi-stage production system. In this paper, a hybrid flow shop scheduling problem with lot streaming, learning effect and buffer's limitation is considered. A bi-objective mathematical model is presented for minimizing the total tardiness and the makespan. To validate the proposed model, the bi-objective model converted to single objective model by weighting method and an example is solved using GAMS software.Since the problem is NP-hard,NSGA-II and NRGA are used to solve the large scale of the problems and the first available machine (FAM) rule is used to assign the jobs to the machines from the first stage onwards in solution representation. Also, Taguchi method is used to tune the algorithms parameters. For evaluating the performance of the algorithms, the results obtained from GAMS compared with outputs of the GA algorithms. Also, 30 instance problems are randomly generated and six indicators are used to compare the algorithms together. After performing the experiments and comparingNSGA-II and NRGAalgorithms with each other based on each index, the appropriate algorithm is selected.