Developing a multi-objective flexible job shop scheduling optimization model using Lexicographic procedure considering transportation time

Abstract

A multi-objective flexible job shop scheduling problem (FJSSP) that considers transportation time using mathematical programming is proposed to optimise three conflicting objectives: minimising makespan, total cost, and total lateness. The proposed model was developed and verified in three stages. In the first stage, only one objective was considered. The minimisation of the makespan and total cost was considered separately in the first stage. In the second stage, only two objectives were considered. In this stage, the minimisation of the makespan and total cost was considered instantaneously. In the third stage, a model was developed to optimise the three objectives. The proposed model was formulated using mixed-integer nonlinear programming (MINLP) and solved using the DICOPT solver based on general algebraic modelling system (GAMS) optimisation software. This model includes the transportation times between machines in the FJSSP, and the problem is called the “flexible job shop scheduling problem with transportation time” (TT-FJSSP). The proposed model gave better results in comparison with the other recent developed models. The effect of changing the maximum allowable deviation when optimising the three objectives was studied to achieve more-practical results.