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Twelve-activity building project with a crew of 4 and 2 technicians: resource histograms, Burgess–Killebrew leveling within float and the resource-constrained schedule

Tool	Resource Loading and Leveling
Source	National Aeronautics and Space Administration (2010). NASA Schedule Management Handbook. NASA/SP-2010-3403, NASA Headquarters, Washington, DC (§5.6 resource loading, leveling and rates); Burgess, A. R., and Killebrew, J. B. (1962). "Variation in Activity Level on a Cyclical Arrow Diagram." Journal of Industrial Engineering, Vol. 13, No. 2, pp. 76–83 (sum-of-squares criterion); Kolisch, R. (1996). "Serial and Parallel Resource-Constrained Project Scheduling Methods Revisited: Theory and Computation." European Journal of Operational Research, Vol. 90, No. 2, pp. 320–333 (schedule-generation schemes).
Level	Professional

Problem

A building project of twelve activities (site preparation, foundations, framing, electrical and plumbing rough-in, roofing, exterior finish, insulation, drywall, interior finish, landscaping, final inspection) in whole working days with finish-to-start logic has a crew of 4 at 400 per unit-day and 2 technicians at 500 per unit-day, each activity demanding a stated number of units of each per day. Find the critical path, the early-start resource histograms and the over-allocated days, level the schedule within its float by the Burgess–Killebrew sum-of-squares criterion and compare it with the exact optimum, build the shortest resource-feasible schedule by the serial scheme with the minimum-float rule and compare it with the parallel scheme, the exact enumeration and the 30-day deadline, and give the time-phased cost baseline.

Inputs to Enter

Activities: A 3 d Crew 2; B 4 d after A, Crew 3 Tech 1; C 5 d after B, Crew 3 Tech 2; D 3 d after C, Crew 2 Tech 2; E 3 d after C, Crew 2 Tech 1; F 2 d after C, Crew 2; G 4 d after F, Crew 2 Tech 1; H 2 d after D and E, Crew 1; I 4 d after H, Crew 2; J 5 d after I, Crew 2 Tech 1; K 3 d after G, Crew 1 Tech 1; L 1 d after J and K, Tech 1
Resources: Crew 4 per day at 400 per unit-day; Tech 2 per day at 500 per unit-day
5-day week from 2026-03-02, deadline 30 working days, priority rule minimum total float, serial scheme, exact check on

Open the Resource Loading and Leveling tool (loaded with this example)

Answers

Critical path 27 working days (A-B-C-D-H-I-J-L and A-B-C-E-H-I-J-L); Crew demand 80 unit-days (74.1 % of 4 × 27), Tech 36 (66.7 %)
Early schedule: Crew peak 6 on days 13–15 (excess 6 unit-days), Tech peak 4 (3, 3, 4 on days 13–15, excess 4); weighted sum of squares F = 35.125
Leveling: three moves (G 14→15, F 12→15, K 21→23) give F = 33.625, equal to the exact optimum over the 56 feasible start combinations; Crew peak 4 with no over-allocation, Tech still 3 on days 13–15 because both rough-ins are critical
Resource-constrained: serial scheme 30 days (E after D, F in the gap), parallel scheme 30 days, exact enumeration 30 days (32 nodes): the 3-day extension is the least possible; the deadline of 30 is met exactly, finish 2026-04-10
Cost: 80 × 400 + 36 × 500 = 50,000 in every schedule; cumulative curves of the early, late, leveled and constrained schedules drawn as the time-phased budget baseline

Notes

The tool's default inputs are this project; press Submit. The case is illustrative (the NASA handbook prints no numeric example) and every number is reproduced by the independent numpy implementation References/Resource-Leveling/checks/resource_check.py (test_resource_leveling.php, 527 checks, which also cover a six-activity brute-force leveling bound, SS/FF lags, time-phased availability and twelve seeded random instances against an exact start-time search).