Resource Leveling
Resource Optimization · Schedule Smoothing
Construction · Resource & Workforce · TacticalPeak-to-trough labor swings of 40–60% between weeks cost contractors €800–€2,500 per worker in hiring/layoff overhead, with productivity losses of 15–20% from constant crew turnover. Every month, a project superintendent must smooth the resource histogram — shifting non-critical activities within their float to minimize peak demand. This is the resource leveling problem — computationally hard when combined with precedence and deadline constraints.
Where This Decision Fits
Construction operations chain — the highlighted step is what this page optimizes
The Problem
Why resource leveling matters in construction
Given a scheduled project with 12 activities, precedence relationships, and float windows, the superintendent must shift activities within their slack to minimize peak resource usage (workers per day). Activities cannot violate precedence constraints or extend the project deadline.
Unleveled schedules create sharp peaks and valleys in the resource histogram. Peaks force expensive overtime hiring or subcontracting, while valleys leave crews idle. The resource leveling problem seeks a schedule that keeps daily resource demand as uniform as possible — reducing peak-to-average ratios and smoothing the workforce over the project duration.
This problem is NP-hard in the general case: even with a fixed project deadline, finding the optimal shift for each activity within its float is computationally intractable for large networks. The classic objective, proposed by Burgess & Killebrew (1962), minimizes the sum of squared daily resource usage — a convex proxy that penalizes peaks quadratically.
subject to
ESi ≤ si ≤ LSi // activity i starts within its float window
si + di ≤ sj // precedence: i finishes before j starts
r(t) = Σi active at t wi // daily resource usage
Where si is the start time of activity i, di is its duration, wi is its daily worker requirement, ESi / LSi are the earliest/latest start from CPM, and r(t) is total resource demand on day t.
See RCPSP theory and scheduling algorithmsTry It Yourself
Level the resource histogram for a construction project
Resource Leveling Optimizer
12 Activities · Target Peak 18| Activity | Duration | Workers | ES | LS | Float | Predecessors |
|---|
Ready. Click “Solve & Compare All Algorithms” to run.
| Algorithm | Peak | Σr² | Time |
|---|
The Algorithms
Approaches to resource leveling
Burgess-Killebrew
O(n · T · F) per iterationThe classic resource leveling heuristic (1962). For each activity with float, evaluate all possible start times within its float window and choose the one that minimizes the sum of squared daily resource usage. Iterate until no further improvement is found. The squared objective penalizes peaks quadratically, naturally smoothing the histogram toward uniformity.
Greedy Shift
O(n · T)A fast single-pass heuristic that identifies the highest-peak day, then shifts the activity contributing most to that peak as late as possible within its float. Repeat until no further peak reduction is possible. Simple and fast, but may get stuck in local optima since it only considers one activity at a time.
Simulated Annealing
Iterative · O(iterations · n · T)A probabilistic search that randomly shifts activities within their float windows. Improvements are always accepted; worse solutions are accepted with decreasing probability as the “temperature” cools. This allows escape from local optima and often finds solutions superior to greedy approaches, especially on larger networks with many interdependent float windows.
Related Scheduling Variants
Resource leveling is a family member of the RCPSP genealogy
Resource leveling shares the precedence and renewable-resource constraints of the base RCPSP, but changes the objective: instead of minimising project makespan, leveling minimises the peak or variance of the resource-usage profile subject to a fixed deadline. This makes it a secondary optimisation — you first solve RCPSP for makespan, then level within the resulting slack. The relevant family members on this site:
- RCPSP — base, makespan objective. The canonical formulation that resource leveling post-processes. → Open Project Scheduling
- Time-Cost Tradeoff / MRCPSP. Crashing activities to meet a deadline; a complementary way to reshape the resource profile. → Open Time-Cost Tradeoff
- Crew Task Assignment (GAP). Assigns specific crews to activities; resource leveling answers the crew-count sizing question upstream. → Open Crew Assignment
- Linear / LOB Scheduling. Repetitive projects where resource-continuity objectives dominate scheduling; closely related objective philosophy. → Open Linear Scheduling
Key References
Cited above · DOIs & permanent URLs
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