A complete immunoglobulin-based artificial immune system algorithm for two-stage assembly flowshop scheduling problem with part splitting and distinct due windows

This paper considers a two-stage assembly flowshop scheduling problem with distinct due windows to minimise the sum of weighted earliness and tardiness. There are several identical parallel machines which produce parts in the first stage. When the required parts are available, a single assembly machine can group these parts into products in the second stage. It is assumed that a part can be split into sub-parts which can be processed independently on the parallel machines in the first stage. Setup is also considered. A mathematical model is established to describe and define the proposed problem. A new decoding method is developed by extending an existing decoding method. Two novel operators, named part splitting (PS) and optimal idle time insertion (ITI), are incorporated into the decoding procedure for improving the quality of the solution. A rule named Priority of Earliness and Tardiness (PET) and a Complete Immunoglobulin-based Artificial Immune System (C-IAIS) algorithm are proposed for solving the problem. To evaluate PET and C-IAIS algorithm, several existing algorithms are used in the experiments. Computational results show that C-IAIS algorithm performs better than other algorithms for solving the proposed problem.