Redesigning Service Level Agreements: Equity and Efficiency in City Government Operations

Abstract

We consider government service allocation -- how the government allocates resources (e.g., maintenance of public infrastructure) over time. It is important to make these decisions efficiently and equitably -- though these desiderata may conflict. In particular, we consider the design of Service Level Agreements (SLA) in city government operations: promises that incidents such as potholes and fallen trees will be responded to within a certain time. We model the problem of designing a set of SLAs as an optimization problem with equity and efficiency objectives under a queuing network framework; the city has two decision levers: how to allocate response budgets to different neighborhoods, and how to schedule responses to individual incidents. We: (1) Theoretically analyze a stylized model and find that the "price of equity" is small in realistic settings; (2) Develop a simulation-optimization framework to optimize policies in practice; (3) Apply our framework empirically using data from NYC, finding that: (a) status quo inspections are highly inefficient and inequitable compared to optimal ones, and (b) in practice, the equity-efficiency trade-off is not substantial: generally, inefficient policies are inequitable, and vice versa.

Figures (12)

• Figure 1: The Department of Parks and Recreation of NYC responds to service requests on "Hazard" and "Illegal Tree Damage" events related to street trees, among others. We find that even conditional on the same category of incidents, the distribution of the response time (in this case defined by the time from the first service request to the completion of an inspection) varies by Borough. Moreover, substantial amounts of service requests are not responded to within the publicly available SLAs, with some others not inspected at all. The empirical distribution of the response times also does not correspond to the priority defined in the SLAs: though hazard incidents have a looser SLA compared to illegal tree damage incidents (14 days versus 8 days), they are generally inspected sooner, reflecting their higher average risk rating.
• Figure 2: Cost borne by each census tract under three different inspection policies: (a) historical inspections, (b) the most efficient Borough budget policy, and (c) the most equitable Borough budget policy, evaluated on data from 2019. Instead of evaluating $\hat{p}_{k,b}$ (fraction of inspected incidents) and $\hat{z}_{k,b}$ (median of inspection delays) for each Borough $b$, we evaluate them for each census tract in NYC, which are finer-grained sub-divisions of Boroughs. We then calculate the cost for each census tract analogous to \ref{['eq:cost']}. Note that the three plots are colored using the same scale. Census tracts with no incidents in 2019 are in gray. Qualitatively, the most efficient and equitable policies are far more similar to each other than they are to the status quo.
• Figure 3: Pareto frontier of equity-efficiency trade-off, under different classes of policies and historical inspections. Lower values on each axis indicate better performance: more efficient policies are more to the left, and more equitable policies are more to the bottom.
• Figure 4: Number of service(inspection) requests and inspections by week from 2019 to 2022.
• Figure 5: Distribution of risk ratings for Hazard incidents across boroughs, with means of risk ratings within each borough marked out.

Theorems & Definitions (10)

• Proposition 2.1
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• Proposition 2.3
• Proposition 2.4
• Proposition 2.5
• Proposition B.1
• Proposition B.1
• Proposition B.1
• Proposition B.1
• Proposition B.1