Users of online shopping platforms typically purchase multiple items at a time in the form of a shopping basket. Personalized within-basket recommendation is the task of recommending items to complete an incomplete basket during a shopping session. In contrast to the related task of session-based recommendation, where the goal is to complete an ongoing anonymous session, we have access to the shopping history of the user in within-basket recommendation. Previous studies have shown the superiority of neighborhood-based models for session-based recommendation and the importance of personal history in the grocery shopping domain. But their applicability in within-basket recommendation remains unexplored. We propose PerNIR, a neighborhood-based model that explicitly models the personal history of users for within-basket recommendation in grocery shopping. The main novelty of PerNIR is in modeling the short-term interests of users, which are represented by the current basket, as well as their long-term interest which is reflected in their purchasing history. In addition to the personal history, user neighbors are used to capture the collaborative purchase behavior. We evaluate PerNIR on two public and proprietary datasets. The experimental results show that it outperforms 10 state-of-the-art competitors with a significant margin, i.e., with gains of more than 12% in terms of hit rate over the second best performing approach. Additionally, we showcase an optimized implementation of our method, which computes recommendations fast enough for real-world production scenarios.