A scheduling problem for PCB assembly: A case with multiple lines

A production scheduling problem for printed circuit board (PCB) assembly with multiple lines is addressed. The investigated problem is to schedule a set of PCB assembly jobs with different ready times and due dates on multiple assembly lines, with the objective to minimize the sum of total weighted tardiness of jobs and weighted makespan. The feature that each job can be completed by different lines with different process times makes the problem a special type of unrelated parallel-machine scheduling problem (PMSP) with special constraints and a unique objective. A mixed-integer linear programming model for the problem is established and verified through solving some small-sized problem instances to optimality. In order to solve the real-world problems, a steady-state genetic algorithm with an improved replacement strategy is proposed. Experimental tests and a case study are conducted to examine the usefulness and effectiveness of the approach.