Heuristic approaches for scheduling of a two-machine flowshop with outsourcing lead-time

This article studies a scheduling problem of a two-machine flowshop , considering outsourcing lead-time, where outsourcing a job incurs outsourcing cost as well as outsourcing lead-time. Each job has an option of being outsourced, i.e. the first operation of the outsourced job is handled by an external subcontractor while the second operation must be processed in-house after its delivery. The objective is to find a schedule for minimizing the weighted sum of the outsourcing costs and the total completion time. For the problem, the subset of jobs to be outsourced and the processing order of jobs are interwoven, implying that decisions have to be made simultaneously. This study examines the properties of the optimal solution and proposes various heuristics based on iterative local search and the biased random-key genetic algorithm. Extensive computational experiments are carried out in various settings.