A scatter search approach with dispatching rules for a joint decision of cell formation and parts scheduling in batches

A joint decision of cell formation and parts scheduling is addressed for a cellular manufacturing system where each type of machine and part may have multiple numbers and parts must require processing and transferring in batches. The joint decision problem is not only to assign batches and associated machine groups to cells, but also to sequence the processing of batches on each machine in order to minimise the total tardiness penalty cost. A nonlinear mixed integer programming mathematical model is proposed to formulate the problem. The proposed model, within nonlinear terms and integer variables, is difficult to solve efficiently for real size problems. To solve the model for practical purposes, a scatter search approach with dispatching rules is proposed, which considers two different combination methods and two improvement methods to further expand the conceptual framework and implementation of the scatter search so as to better fit the addressed problem. This scatter search approach interactively uses a combined dispatching rule to solve a scheduling sub-problem corresponding to each integer solution visited in the search process. A computational study is performed on a set of test problems with various dimensions, and computational results demonstrate the effectiveness of the proposed approach.