Rolling Horizon Optimisation (RHO) is a method for tackling long-horizon planning problems by solving a sequence of short windows rather than the whole horizon at once. At each step, you solve a problem spanning the next w periods, implement the first k decisions, slide the window forward by k periods, and re-optimise. The key mechanism: each re-solve incorporates updated information and revised forecasts that were not available at the previous step. This handles non-stationarity and uncertainty by building adaptivity into the algorithmic structure.
RHO sounds like a complete solution to long-horizon intractability. It is not. The decisions near the end of each window can be systematically suboptimal because the model has no information about what comes after the window closes. This end-effect is not a solver artifact—it is inherent to the method. Identifying and mitigating the end-effect is the central technical challenge in applying RHO to any domain.
The problem: A job shop has 500 operations to sequence over a 5-day horizon. An exact solver is intractable, so the scheduler uses a rolling window of 8 hours.
Without RHO awareness: The model schedules jobs optimally within the 8-hour window but treats the window boundary as if the world ends there. Jobs that start near the end of hour 8 are scheduled as if they have unlimited machine availability for their remaining operations—because the model cannot see hours 9 onwards. The result is a schedule that looks good within the window but creates a machine bottleneck in the next window when those jobs reappear as partially complete.
With RHO awareness (Graph-RHO's approach): The policy explicitly identifies which operations are on the critical path—the sequence that determines the minimum makespan—and biases scheduling decisions to protect those operations from the end-effect, even if they fall near the window boundary. This does not eliminate the end-effect, but it prevents the worst suboptimality.
The core mistake: Assuming RHO produces a near-optimal solution to the full long-horizon problem if the window is large enough. In practice, even very large windows incur systematic end-effect losses. A 24-hour window on a 5-day planning horizon makes decisions in hours 20-24 with zero visibility of hours 25-120. Those decisions will sacrifice efficiency in the subsequent windows to look good within the current window.
The accumulation effect: Over a month of rolling optimization, each day's window end-effect compounds: today's end-effect forces suboptimal starting conditions for tomorrow's window, which worsens tomorrow's end-effect. The cumulative cost can exceed 5-10% of single-horizon optimality even with re-optimization, depending on problem structure.
Diagnostic questions: Before accepting any published RHO result, ask: (1) Was the end-effect explicitly modelled or measured? (2) Was the solution compared to a single-horizon optimal (even if solved on a sample size)? (3) Did the end-effect increase or decrease with window size? Without answers to these questions, the reported improvement may be artifact rather than real.
The suboptimality of rolling horizon grows with the mismatch between committed horizon and problem structure. Committing too few periods means reoptimising constantly; committing too many means carrying decisions made under stale information.