Three-machine flowshop scheduling with outsourcing lead-time

This paper addresses a scheduling issue in a three-machine flowshop with incorporating the outsourcing lead-time. In this problem, the first and second operations of jobs can either be handled in-house or outsourced to subcontractors, whereas the third operation must be processed in-house. Outsourcing a job not only incurs costs depending on each operation but also introduces a lead-time for the outsourced operation, meaning that the subsequent operation can only commence after this lead-time has elapsed. The goal of this paper is to minimize the weighted sum of both outsourcing and scheduling costs, which may be defined as either makespan or total completion time. The study explores the properties of the optimal solution and introduces two approaches: the Biased Random-Key Genetic Algorithm and the Branch-and-Bound algorithm. Computational experiments demonstrate that the proposed algorithms yield efficient and effective solutions.