Reactive project scheduling is an important branch of project scheduling under uncertainty. This paper proposes a resource-constrained multi-project reactive scheduling problem (RCMPRSP) with new project arrival to minimize the adjustment cost of the baseline schedule while achieving the deterministic multi-project scheduling goal. Although the RCMPRSP aims to minimize the adjustment cost, it adds a constraint to ensure that the reactive schedule is one of the schedules with shortest possible make-span after new project arrival.