Rescheduling is a necessary procedure for a flexible job shop when newly arrived priority jobs must be inserted into an existing schedule. Instability measures the amount of change made to the existing schedule and is an important metrics to evaluate the quality of rescheduling solutions. This paper focuses on a flexible job-shop rescheduling problem (FJRP) for new job insertion. First, it formulates FJRP for new job insertion arising from pump remanufacturing. This paper deals with bi-objective FJRPs to minimize: 1) instability and 2) one of the following indices: a) makespan; b) total flow time; c) machine workload; and d) total machine workload. Next, it discretizes a novel and simple metaheuristic, named Jaya, resulting in DJaya and improves it to solve FJRP. Two simple heuristics are employed to initialize high-quality solutions. Finally, it proposes five objective-oriented local search operators and four ensembles of them to improve the performance of DJaya. Finally, it performs experiments on seven real-life cases with different scales from pump remanufacturing and compares DJaya with some state-of-the-art algorithms. The results show that DJaya is effective and efficient for solving the concerned FJRPs.