We study scheduling of activities of multiple projects with the consideration of capacity allocation, activity preemption, and relative tardiness costs. Our study is motivated by the maintenance, repair and overhaul (MRO) operations in the aviation industry, which consist of a finite number of major tasks performed on multiple components of the equipment. The MRO tasks are carried out based on certain precedence relations. Typically, the MRO shop handles multiple aircraft sets, referred to as work orders, at a given time. The work orders belong to different customers who have different criticalities for the MRO company, release dates, and delivery date requirements. The objective of the MRO company is to achieve minimum total weighted tardiness by optimizing the sequencing and capacity allocation of all tasks at all stations across all work orders. We develop a mathematical model for the problem and test its computational performance via numerical examples.