With the growth of marketplaces and smart supply chains, there has been unprecedented research on data-driven operations. Algorithms for resource allocation and personalisation allow us to match supply with demand more efficiently in industries such as retail, transportation, and healthcare. Yet, these algorithms generally optimise for a single user-platform interaction, e.g., a purchase decision in a given product category. A major issue for platform operations is to develop a holistic viewpoint on user experience, supported by new data sources tracking longitudinal behaviour such as mobile trace data and clickstream data. Thus, I propose to design algorithms that optimise engagement for repeated user interactions in multi-touch operational platforms. As a case study, I will explore a highly relevant, yet uncharted application of "pathway operations": visitor experience in art institutions such as museums and galleries across physical and digital layouts. My research work will range from theoretical advancements in algorithm design to applied work in collaboration with museums. First, I will develop a new predictive utility maximisation framework for pathway choice models, which can be estimated from trajectory-based pathway data. Second, I will study the design and rigorous analysis of algorithms incorporating pathway choice models at their core, including novel formulations of assortment, online matching and multi-armed bandit problems. Third, building on an ongoing collaboration with a large museum, I will turn to simulations and implementations of these algorithms together with researchers in empirical fields. We will generate open-source code to help institutions like museums craft new experiences for their visitors, ranging from recommended physical routes to personalised virtual exhibitions. This research work will contribute to broader initiatives for an interactive, non-invasive and museum-centric digital ecosystem for our artistic heritage.