Scheduling with divisible jobs and subcontracting option

Abstract

In electronics industry, aircraft manufacturing, distributed computer systems and supply chains, it is common that many jobs are divisible and can be considered as a batch of potentially infinitely small and independent items. Subcontracting divisible jobs means that a job can be partially processed by an in-house machine and the remaining of it can be processed by a subcontractor’s machine. Considering three subcontracting pricing strategies: non-increasing, non-decreasing and constant over time, this paper studies a scheduling problem with divisible jobs and subcontracting option in which both the manufacturer and the subcontractor are in single-machine environment. The objective is to minimize the sum of total weighted tardiness and total subcontracting costs. A mixed integer programming (MIP) model is formulated. Then a Lagrangian-based Benders Dual Decomposition (denoted by LB-BDD) method is developed based on the MIP formulation. Extensive computational experiments are conducted on five groups of randomly generated problem instances, and the results show that the proposed LB-BDD method outperforms the basic Benders Decomposition (denoted by BD) method and solving the MIP model directly in Gurobi solver.