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This paper presents a set-partitioning formulation and a novel decomposition heuristic (D-H) solution algorithm to solve large-scale instances of the urban crowdsourced shared-trip delivery (CSD) problem. The CSD problem involves dedicated vehicles (DVs) and shared personal vehicles (SPVs) fulfilling delivery orders, wherein the SPVs have their own trip origins and destinations. The D-H begins by assigning as many package delivery orders (PDOs) to SPVs as possible, where the D-H enumerates the set of routes each SPV can feasibly traverse and then solves a PDO-SPV-route assignment problem. For PDO-DV assignment and DV routing, the D-H solves a multi-vehicle routing problem with time-window, tour duration, and capacity constraints using an insertion heuristic. Finally, the D-H seeks potential solution improvements by switching PDOs between SPV and DV routes through a simulated annealing (SA)-inspired procedure. The D-H outperforms a commercial solver in terms of computational efficiency while obtaining near-optimal solutions for small problem instances. The SA-inspired switching procedure outperforms a large neighborhood search algorithm regarding run time, and the two are comparable regarding solution quality. Finally, the paper uses the D-H to analyze the impact of several relevant factors on city-scale CSD system performance, namely the number of participating SPVs and the maximum willingness to detour of SPVs. Consistent with the existing literature, we find that CSD can substantially reduce delivery costs. However, we find that CSD can increase vehicle miles traveled. Our findings provide meaningful insights for logistics practitioners, while the algorithms illustrate promise for large real-world systems.