Lot streaming in a multiple product permutation flow shop with intermingling

Abstract

In this paper we study the multi-product lot streaming problem in a permutation flow shop. The problem involves splitting given order quantities of different products into sublots and determining their optimal sequence. Each sublot has to be processed successively on all machines. The sublots of the particular products are allowed to intermingle, that is sublots of different jobs may be interleaved. A mixed integer programming formulation is presented which enables us to find optimal sublot sizes as well as the optimal sequence simultaneously. With this formulation, small- and medium-sized instances can be solved in a reasonable time. The model is further extended to deal with different settings and objectives. As no lot streaming instances are available in the literature, LSGen, a problem generator, is presented, facilitating valid and reproducible instances. First results concerning the average benefit of lot streaming with multiple products are presented, and are based on a computational study with 160 small- and medium-sized instances.