A teaching project based on a real one. The noise model and the data structure come from the production records of the linear part of a large construction project (about 328 thousand daily records): the shape and width of the spread, the share and size of delays and speed-ups, three similar sites over five years, monthly records, seasonal windows of works. The records themselves are generated from this model, while the works, outputs and seasonal profiles are illustrative.
Examples
Three typical noise regimes in work-progress data. Which estimator is more accurate depends on the regime, so the examples include cases where IF&PA wins and cases where it performs on a par with the other estimators.
Where IF&PA is more accurate
Where other estimators are more accurate
Conditions
Which method to prefer
Summary over the teaching project: medians over eight data sets of each regime, two resource streams. Any data set can be reproduced on the tabs above — choose the regime and the set number.
| Noise regime | Norm error | Norm bias | Best over sets | IF&PA plan | MM plan | What to choose |
|---|---|---|---|---|---|---|
| Controlled time study time study, machine pace: narrow bounded noise, rare distant delays |
IF&PA 0.62 % MM 1.09 % · median 1.9 % · LS 95 % | MM +0.1 % · IF&PA +0.2 % | IF&PA — 8 of 8 | reference duration, no overruns, reserve 0.4 % | reference duration, isolated overruns, reserve 0.5 % | IF&PA, width κ(m) |
| Production records daily reports in retrospect: wide normal noise, anomaly share differs by work |
MM 12.1 % IF&PA 12.5 % · median 12.7 % · LS 40 % | MM +5.7 % IF&PA +0.5 % · median +5.7 % | MM — 3, IF&PA — 3, median — 2 | reference duration, 8 overruns, reserve 6.2 %, under-allocated 5.1 % | reference duration, 6 overruns, reserve 7.0 %, under-allocated 2.9 % | a tie in error, but MM overstates norms (hidden reserve); IF&PA with κ = 1 is almost unbiased — an explicit buffer removes overruns |
| Adverse conditions mass delays, mixed technologies under one code |
IF&PA 16.2 % shortest half 16.6 % · median 25 % · MM 28 % · LS 63 % | MM +26 % IF&PA +4.2 % · median +23 % | IF&PA — 5, shortest half — 3 | reference duration, 9 overruns, reserve 9.2 %, under-allocated 5.7 % | duration +29 %, no overruns, reserve 27 % — hidden buffer | IF&PA, majority rule (or shortest half) |
Least squares errs by 40–95 % in every regime: its plan is 29–32 % longer than the reference and holds 33–55 % of extra resources. Error is the mean relative norm error over “work × month” cells; bias is the same error with its sign: plus means the norm is overstated and the plan holds extra reserve; overruns are “resource × month” pairs where the need at execution exceeds the limit; reserve and under-allocation are in per cent of the actual need.
How the experiment works
- History. Three similar sites over five years: for each work and month — the volume Vk and the actual duration Tk, shifts. Model Tk = b · Vk · εk · ηk: b is the true seasonal labour norm, ε the core noise, η an anomaly (delay, speed-up, another technology).
- Norms. In every “work × month” cell with five or more observations the norm is estimated from the ratios Tk/Vk: least squares, median, MM-estimator, shortest half and IF&PA. The truth is known by construction, so the error of every estimator is visible.
- Schedule. A month is a “knapsack” with a capacity for every resource type, a segment of a work is an “item” whose weight depends on that month's norm; precedence follows a moving front, works run only in their season. The minimum duration is found by bisection over the horizon; its minimality is proven by the HiGHS solver.
- Execution. The plan from every estimator is “executed” with the true norms: resource limit overruns (the plan fell short), reserve (allocated beyond need) and under-allocation.
Model limitations: works are continuous in volume (segments are a nominal split), crew relocation costs are not counted, norms enter the plan as point estimates. Details — in the paper after publication.