This paper presents mathematical modeling of joint lot sizing and scheduling problem in a job shop environment under a set of realistic working conditions. One main realistic assumption of the current study is dealing with flexible machines able to change their working speeds, known as process compressibility. The production schedules should be subject to limited available time in every planning period. Also, the model assumes that periodical sequences should be determined in a way that they obey from a fixed global sequence. Another complicating aspect of the problem is about consideration of precedence relationships for the needed processes of an item type over the corresponding machines. As the problem is proved to be strongly NP-hard, it is solved by a particle swarm optimization (PSO) algorithm. The proposed algorithm is self-controller about its working parameters, time to stop the search process, search diversification/intensification, and totally about its behavior. Performance of the algorithm is verified in terms of optimality gap using Lingo 11.0 on a set of randomly generated test data. 
A self-adaptive PSO for joint lot sizing and job shop scheduling with compressible process times