I started with a basic 'ratio of distance traveled backward vs forward' framing and the interviewer pushed back pretty fast.
Define backtracking as unnecessary reverse movement along a driver's route relative to the optimal path to a pickup or destination, then operationalize it as a per-driver-hour rate using GPS traces and assignment logs. Describe a robust pipeline: clean and map-match GPS, segment trips, detect backtracking via distance/time thresholds and path comparison, and validate with simulation and manual review.
Pro tip: Frame the metric in terms of business impact—backtracking wastes driver time and fuel, reduces marketplace efficiency, and can signal poor routing or assignment logic—so your metric ties directly to Uber's goals. Also, acknowledge trade-offs: a too-sensitive threshold may flag legitimate detours (e.g., traffic, road closures), so validation against ground truth is essential.
Specify backtracking as a driver moving away from the optimal path to the next assignment (pickup or drop-off) by a significant distance or time, excluding necessary detours due to traffic or road network constraints. Use assignment logs to know the intended destination and GPS to track actual movement.
Compute total backtracking distance (or time) per driver per hour: sum the lengths of detected backtracking segments across all trips in a driver's shift, then divide by total active driver-hours. Normalize to account for varying shift lengths and trip volumes.
Map-match GPS points to the road network, then compare the actual path to the optimal route (e.g., from a routing engine). Flag segments where the driver's movement increases the remaining distance to the destination by more than a threshold (e.g., 500m or 2 minutes) and persists for a minimum duration.
Validate using manual review of sampled segments, simulation of known backtracking patterns, and correlation with external data (e.g., traffic incidents, road closures). Also check for false positives from GPS noise or map-matching errors.
Deploy the metric in dashboards, monitor distribution and trends, and iterate on thresholds and definitions based on feedback from operations and drivers. Use A/B tests to see if interventions reduce backtracking and improve efficiency.
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Start by defining the decision variables clearly, distinguishing between assignment and repositioning. Then formulate the objective as minimizing expected backtracking, expressed as a function of these variables. Finally, explicitly state each constraint (ETA service levels, driver utilization, zone fairness, repositioning cost cap) in mathematical terms.
Pro tip: Mention that the model should be solved as a mixed-integer linear program (MILP) or a min-cost flow problem, and discuss potential trade-offs and scalability. This shows awareness of practical implementation challenges.
Introduce binary variables for assigning drivers to ride requests and repositioning tasks, and continuous variables for expected backtracking or costs.
Express the objective as minimizing expected backtracking, which could be a weighted sum of distances or probabilities of future requests.
List constraints: ETA service levels (e.g., maximum wait time), minimum driver utilization (e.g., percentage of time on trips), zone fairness (e.g., equitable distribution of drivers), and repositioning cost cap.
Briefly mention how to solve the model (e.g., MILP, min-cost flow) and address scalability and real-time considerations.
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I picked rolling horizon because it's the most operationally realistic and I've seen it work in similar contexts.
Start by clarifying the problem characteristics (e.g., problem size, time constraints, objective, and whether decisions are online or offline) to justify the modeling choice. Then compare time-expanded network min-cost flow and mixed-integer programming in terms of scalability, solution quality, and real-time feasibility, and propose a hybrid or decomposition approach. Finally, discuss solution methods like rolling horizon, column generation, and Lagrangian relaxation, and how to balance approximation quality with computational speed.
Pro tip: Emphasize that in real-time systems, the goal is often to find a good solution quickly rather than the optimal one, so discuss how you would measure and control the trade-off between solution quality and latency.
Ask questions to understand the problem size, time constraints, objective, and whether it's a static or dynamic setting. This determines whether a time-expanded network or MIP is more appropriate.
Discuss the strengths and weaknesses of time-expanded network min-cost flow (efficient for large-scale, linear costs) versus mixed-integer programming (flexible for complex constraints but computationally expensive).
Explain how rolling horizon, column generation, or Lagrangian relaxation can be used to solve the problem in real time, and under what conditions each is suitable.
Discuss how to evaluate and control the trade-off between solution quality and computation time, including bounds, heuristics, and fallback strategies.
Summarize your chosen approach, justifying it based on the problem characteristics and real-time requirements, and mention potential extensions or improvements.
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Offline I said replay simulation on historical logs with the new assignment policy, measuring the backtracking metric against a baseline.
Start by defining the backtracking reduction model and the specific improvements you're evaluating. Then outline a two-pronged evaluation: offline using historical data and simulations to measure accuracy and efficiency, and online via a controlled A/B test to measure impact on key business metrics. Emphasize the importance of aligning offline and online metrics and using guardrails to detect unintended consequences.
Pro tip: When designing the online experiment, ensure you have sufficient power and consider sequential testing to avoid peeking. Also, pre-register your metrics and analysis plan to prevent p-hacking and build trust with stakeholders.
Clearly state what the improvement is (e.g., reduced backtracking, faster convergence) and define both offline metrics (e.g., accuracy, precision, recall, computational cost) and online metrics (e.g., booking conversion, ETA accuracy, user engagement).
Use historical data to simulate the new model versus the old one. Measure performance on held-out data, conduct sensitivity analysis, and ensure the improvement generalizes across different segments and time periods.
Set up an A/B test with proper randomization, control, and treatment groups. Determine sample size and duration based on power analysis, and define guardrail metrics to monitor for negative side effects.
Compare offline and online results, check for statistical significance, and investigate any discrepancies. Use segmentation to understand heterogeneous treatment effects and ensure the improvement is robust.
Based on the combined evidence, decide whether to roll out, iterate, or abandon the improvement. Document learnings and consider follow-up experiments to further optimize.
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The toy example request threw me off a little.
Start by framing demand uncertainty as a core challenge in optimization, then compare robust and stochastic optimization approaches, highlighting their trade-offs in a data science context. Use a concrete example with three zones and five-minute intervals to illustrate how each method handles uncertainty, and conclude with practical considerations for implementation at Uber.
Pro tip: Emphasize that the choice between robust and stochastic optimization depends on the business objective and data availability; at Uber, real-time decision-making often favors robust optimization for its computational efficiency and worst-case guarantees.
Clearly state the optimization goal (e.g., minimize wait time or maximize driver utilization) and identify sources of demand uncertainty (e.g., random ride requests). Mention that uncertainty can be modeled as scenarios or probability distributions.
Explain that robust optimization hedges against worst-case scenarios within an uncertainty set, while stochastic optimization optimizes expected performance over a probability distribution. Discuss trade-offs: robustness vs. optimality, computational complexity, and data requirements.
Use three zones (e.g., downtown, airport, suburbs) and five-minute intervals (e.g., 12 intervals per hour). For robust optimization, define an uncertainty set (e.g., demand varies ±20% from nominal) and solve for the worst-case. For stochastic optimization, assume a distribution (e.g., Poisson) and optimize expected demand.
Mention how to evaluate solutions using metrics like expected cost, worst-case cost, and value of stochastic solution. Highlight practical considerations: data availability, computational time, and integration with real-time systems.
Summarize when to use each approach: robust for high uncertainty and risk-aversion, stochastic when reliable probabilistic data exists. Suggest hybrid approaches or scenario-based optimization as a middle ground.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.