Tactical parking enforcement planning: Optimizing resource allocation under driver response

Municipal parking enforcement shapes driver compliance, equity, and revenue, yet most analytical models emphasize local equilibria or operational routing rather than the tactical allocation of resources across heterogeneous regions. We develop an integrated behavioral–optimization framework linking enforcement intensity, driver choice, and revenue. Using the Lambert–W function, we derive a closed-form critical staffing threshold n⋆ that delineates the transition from weak to effective deterrence. This behavioral mechanism is embedded in a dynamic program that allocates limited patrol units across regions while enforcing a uniform minimum detection-probability constraint as an equity requirement. Computational experiments on synthetic city archetypes and a six-region case study show that (i) moderate fines and balanced staffing maximize long-run revenue, (ii) overstaffing and excessively high fines yield diminishing returns, (iii) technology that raises detection efficiency can maintain deterrence with fewer officers, and (iv) equity constraints reallocate resources toward underserved areas at modest fiscal cost. The framework provides a tractable, data-informed basis for setting staffing, fines, and technology investments that unifies behavioral deterrence with tactical enforcement planning.