This paper proposes a multi-day needs-based model for activity and travel demand analysis. The model captures the multi-day dynamics in activity generation, which enables the modeling of activities with increased flexibility in time and space (e.g., e-commerce and remote working). As an enhancement to activity-based models, the proposed model captures the underlying decision-making process of activity generation by accounting for psychological needs as the drivers of activities. The level of need satisfaction is modeled as a psychological inventory, whose utility is optimized via decisions on activity participation, location, and duration. The utility includes both the benefit in the inventory gained and the cost in time, monetary expense as well as maintenance of safety stock. The model includes two sub-models, a Deterministic Model that optimizes the utility of the inventory, and an Empirical Model that accounts for heterogeneity and stochasticity. Numerical experiments are conducted to demonstrate model scalability. A maximum likelihood estimator is proposed, the properties of the log-likelihood function are examined and the recovery of true parameters is tested. This research contributes to the literature on transportation demand models in the following three aspects. First, it is arguably better grounded in psychological theory than traditional models and allows the generation of activity patterns to be policy-sensitive (while avoiding the need for ad hoc utility definitions). Second, it contributes to the development of needs-based models with a non-myopic approach to model multi-day activity patterns. Third, it proposes a tractable model formulation via problem reformulation and computational enhancements, which allows for maximum likelihood parameter estimation.
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