Minimizing total weighted tardiness for non-identical parallel batch processing machine

Batch processing machines are commonly used in manufacturing. Scheduling batch processing machine problem is NP-hard even for makespan objective. The research problem under study is commonly observed in electronics manufacturing. In electronics manufacturing, after assembly the Printed Circuit Boards (PCBs) are subjected to environmental stress tests (e.g. thermal cycling, vibration, etc.) to detect any early component failures. The focus of this research is on scheduling these testing machines. The PCBs are referred to as jobs and the environmental testing machines are referred to as batch processing machines in this research.;The job processing (or testing) times, due dates and sizes are given. Several machines, each with different capacity, can process a batch of jobs simultaneously. The objective is to minimize the total weighted tardiness. A mathematical model is proposed for the problem under study. The problem under study can be easily shown to be NP-hard. Consequently, solving the problem to optimality, especially when the size of the problem grows, using a commercial solver requires prohibitively long run times. A column generation approach was proposed to determine a good lower bound. Moreover, meta-heuristic approaches, such as Particle Swarm Optimization and Differential Evolution, are proposed to improve the solution quality and run time.;The column generation approach was implemented using callable libraries in CPLEX (a mixed integer commercial solver). The meta-heuristic approaches were developed in MATLAB. An experimental study was conducted to evaluate the different solution approaches on a set of benchmark problem instances. Based on the experimental study, it can be concluded that the commercial solver, CPLEX, is highly effective to solve small problem instances. Column generation was better, in terms of computational time, when compared to CPLEX. Particle Swarm Optimization outperformed Differential Evolution, CPLEX, and column generation on larger problem instances, in terms of solution quality and computational time. The proposed approaches to solve the problem under study will benefit practitioners to solve a real life problem commonly observed in electronics manufacturing.