# Chance-Constrained Routing Cuts Multi-Trade Overtime 18%

Chase Pierce · August 19, 2026

> Chance-Constrained Routing Cuts Multi-Trade Overtime 18%. The Math of Overtime Risk Chance constraints shift the optimization objective from minimizing ...

## The Math of Overtime Risk

Chance constraints shift the optimization objective from minimizing average travel time to bounding the probability of schedule failure. In field service logistics, this means every route must satisfy a constraint where the probability of completing within the 8-hour shift is at least 90%. This threshold is not arbitrary; it is derived from historical travel-time distributions ingested directly from telematics systems like Verizon Connect, which capture real-world variance in traffic, site access delays, and inter-job transit. By enforcing this probabilistic bound, the routing model explicitly accounts for the tail risk that deterministic approaches ignore.

The mechanism relies on a two-stage stochastic program. The first stage assigns jobs to crews based on static parameters, while the second stage evaluates overtime risk dynamically. For each candidate route, the solver runs a Monte Carlo simulation generating 1,000 scenarios per route, sampling from the telematics-derived distributions to estimate the likelihood of exceeding the shift limit. This allows the algorithm to penalize routes that look efficient on paper but carry high variance in their execution. The implementation uses Python with Gurobi 10.0 to solve a mixed-integer program containing 120 binary variables per crew. Despite the complexity, the solver achieves an optimality gap of less than 2% in under 3 minutes, enabling near-real-time dispatch adjustments without compromising solution quality.

The critical distinction lies in how the objective function handles uncertainty. Deterministic routing minimizes expected travel time, effectively treating all variance as noise to be averaged out. Chance-constrained routing minimizes expected travel time subject to a tail-risk constraint on overtime. This forces the optimizer to accept slightly higher expected travel times if doing so significantly reduces the probability of a route spilling into overtime. Furthermore, the constraint is enforced per crew per day, not per job. This aggregation allows the model to make trade-offs between jobs with high variance and those with low variance, balancing the portfolio of tasks assigned to a single crew rather than optimizing each stop in isolation.

In a controlled pilot, the chance-constrained model applied a 90% threshold, which reduced the number of routes exceeding 8 hours from 22% to 4%. This reduction demonstrates the efficacy of the approach in curbing overtime without requiring uniform buffer additions, which typically misallocate slack and degrade response times. The following table compares the structural properties of the two routing paradigms to highlight why the chance-constrained approach yields superior risk management.

| Feature | Deterministic Routing | Chance-Constrained Routing |
| --- | --- | --- |
| Objective Function | Minimize expected travel time | Minimize expected travel time + tail-risk constraint |
| Variance Handling | Averages variance; ignores tails | Models distribution via Monte Carlo (1,000 scenarios) |
| Constraint Scope | Per job or global average | Per crew per day (portfolio-level trade-off) |
| Solver Performance | N/A (simple heuristic) | Gurobi 10.0:

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