We discuss a bicriteria scheduling problem for parallel identical batch processing machines in semiconductor wafer fabrication facilities (wafer fabs). Only jobs that belong to the same family can be batched together. The performance measures of interest are the total weighted completion time and the electricity power cost. Unequal release dates of the jobs are taken into account. The jobs can have nonidentical sizes. We provide a Mixed Integer Linear Programming (MILP) formulation for the general setting. Moreover, we analyze the special case where all jobs have the same size, the maximum batch size is an integer multiple of this job size, and all jobs are available at time zero. We prove certain properties of Pareto-optimal schedules for this special case. These properties lead to a MILP formulation that is more tractable than the one for the general setting. We perform computational experiments with the ε-constraint method for both formulations.