Mixed integer programming for scheduling flexible flow lines with limited intermediate buffers

This paper presents new mixed integer programming formulations for scheduling of a flexible flow line with blocking. The flexible flow line consists of several processing stages in series, separated by finite intermediate buffers, where each stage has one or more identical parallel machines. The line produces several different product types and each product must be processed by, at most, one machine in each stage. A product which has completed processing on a machine may remain there and block the machine until a downstream machine becomes available for processing. The objective is to determine a production schedule for all products so as to complete the products in a minimum time. The basic mixed integer programming formulations have been enhanced to model blocking scheduling with alternative processing routes where for each product a set of routes is available for processing. A reentrant flow line where a product visits a set of stages more than once is also considered. Numerical examples are presented to illustrate applications of the various models proposed.