A branch and bound algorithm for an identical parallel machine scheduling problem with a job splitting property

We focus on the problem of scheduling n independent jobs on m identical parallel machines with the objective of minimizing total tardiness of the jobs considering a job splitting property. In this problem, it is assumed that a job can be split into sub-jobs and these sub-jobs can be processed independently on parallel machines. We develop several dominance properties and lower bounds for the problem, and suggest a branch and bound algorithm using them. Computational experiments are performed on randomly generated test problems and results show that the suggested algorithm solves problems of moderate sizes in a reasonable amount of computation time. Scope and purpose In this paper, we consider an operations scheduling problem in a real manufacturing system that produces printed circuit boards (PCBs). In the PCB manufacturing system, production orders are specified by the product types, production quantities and due dates. In a bottleneck workstation of the manufacturing system, in which there are multiple parallel machines, a job required for a production order can be split into basic processing units, each of which can be processed on a machine. We present an algorithm that can give an optimal schedule for a scheduling problem in the workstation for the objective of minimizing total tardiness of production orders. Since meeting due dates of customers' orders become more and more important for the survival of a manufacturing company in highly competitive market environments of these days, the algorithm may provide the company with a competitive edge in the industry.