In order to accommodate potential fluctuations of uncertain parameters, a systematic three-stage method for the design of flexible multiperiod heat exchanger networks (HENs) is proposed, which satisfies not only the requirement of the multiperiod operation but also the flexibility of the subperiod operation. In the first stage, an initial multiperiod HEN is constructed based on the synthesis of the single period HEN. In the second stage, the structure and heat transfer area arrangement of the initial multiperiod HEN are modified and optimized by considering both the multiperiod operational characteristics and the subperiod operational flexibilities. In the third stage, the flexibilities of the modified multiperiod HEN in each subperiod are examined and improved by solving a subperiod debottleneclang model. A case study of a HEN in a vacuum gas oil hydrotreating unit is carried out to illustrate the application of the proposed method. Results indicate that the heat transfer areas and total annual cost of the multiperiod HEN will be underestimated if the parametric fluctuations in subperiods are neglected. A cost-effective multiperiod HEN with sufficient flexibility in subperiods can be obtained by using the proposed method when the parametric fluctuations are taken into consideration. (C) 2018 Elsevier Ltd. All rights reserved.