Formulate OR model to reduce driver backtracking

Define driver backtracking in a marketplace and describe how to reduce it.

Start by specifying a quantitative per-driver-hour backtracking metric $B$ built from GPS and assignment logs, then outline an algorithm for identifying backtracking segments and checking them against labels.

Next, build an optimization model that matches drivers to trip requests and repositioning jobs so expected backtracking is minimized subject to business requirements such as ETA service-level agreements, minimum utilization, zone fairness, and a repositioning-cost cap.

Lay out the decision variables, objective, and constraints clearly; pick a modeling framework—for example, a time-expanded network minimum-cost flow with penalties or a mixed-integer program—and describe a real-time solution technique such as rolling horizon, column generation, or Lagrangian relaxation along with its approximation quality.

Finally, describe how to validate gains through offline evaluation and an online experiment, and explain how robust or stochastic optimization can address demand uncertainty, using a small three-zone example with five-minute intervals to show the constraints.

Overview:

This question tests the ability to define a quantitative driver-backtracking metric from GPS and assignment logs, detect and validate backtracking segments, and formulate constrained dispatch and repositioning optimization models, drawing on statistics, operations research, and stochastic optimization.