The Lagrangean Relaxation for the Flow Shop Scheduling Problem with Precedence Constraints, Release Dates and Delivery Times

Abstract

This work aims to present a methodology to support a company in the automotive business on scheduling the jobs on its final processes. These processes are: (i) checking the final product and (ii) loading the dispatch trucks. These activities are usually found in the outbound area of any manufacturing company. The problem faced is defined as the flow shop problem with precedence constraints, release dates, and delivery times. The major objective is to minimize the latest date a client receives its products. We present a time-indexed integer mathematical model to compute feasible solutions for the presented problem. Moreover, we take advantage of the Lagrangean Relaxation procedure to compute valid lower and upper bounds. The experiments were held based on the company’s premises. As a conclusion, the results showed that the methodology proposed was able to compute feasible solutions for all the instances tested. Also, the Lagrangean Relaxation approach was able to calculate better bounds in a shorter computational time than the Mathematical problem for the more complicated instances.