Amogh N P
✦ In loving memory of Amogh N P — Architect · Designer · Visionary ✦
A construction site with a tall tower crane, mobile cranes and stacked building materials under a clear sky — the finite crews, plant and money a schedule must resource.
Unit IIIProject Management

Resource Planning — Cost & Resources

The cost slope, the optimum duration, and levelling vs smoothing.

≈ 45 min + studio task

Time costs money two ways at once. Direct cost rises when you compress an activity; indirect cost rises the longer the project runs — so total cost is U-shaped, with an optimum least-cost duration. Learn the cost slope, crashing the network to that optimum, and updating with actuals; then resource allocation, resource smoothing (within float, deadline fixed) and resource levelling (to a limit, deadline may move).

Learning objectives

By the end of this lesson, you will be able to — mapped to the course outcomes for Project Management:

1
CO3 · Understand

Distinguish direct, indirect and total project cost and the optimum-duration curve.

2
CO3 · Apply

Compute the cost slope and crash the network for least cost.

3
CO3 · Apply

Update a schedule with actual progress data.

4
CO6 · Analyse

Tell resource smoothing from resource levelling and apply each.

Direct, indirect, optimum

The cost model & crashing

Add the falling direct cost to the rising indirect cost and the total is U-shaped; crash the cheapest-slope critical activity toward the bottom of that U — and stop at the optimum.[1, 3]

The total-cost curve cost project duration → direct cost (falls) indirect cost (rises) total = direct + indirect optimum (least-cost) duration Crash toward the optimum — but past it, total cost rises again. Crashing does not always save money.
DiagramTotal project cost is U-shaped — direct cost falls and indirect cost rises with duration, with a minimum at the optimum duration

Two costs, one curve

DIRECT cost is tied to activities — labour, material, plant; it FALLS as you allow more time (normal working) and RISES when you compress (overtime, extra crews, premiums). INDIRECT cost is overheads, supervision, site establishment and finance — roughly PROPORTIONAL to duration, so it RISES the longer the job runs. Add them and TOTAL project cost is U-SHAPED against duration. The bottom of that U is the OPTIMUM (least-cost) DURATION.[1]

The cost slope activity cost activity duration → normal (time, cost) crash (min time, high cost) Δ time Δ cost slope = Δcost / Δtime (₹ per day saved) Crash the critical activity with the LOWEST slope first — and never below its crash time.
DiagramThe cost slope — the extra cost per day saved by crashing an activity from its normal to its crash point
Finite crews and cranes

Resources — smoothing & levelling

Resources are finite and their demand peaks; smoothing shaves the peaks within float without moving the deadline, while levelling caps demand at a limit and may extend the duration.[1, 2]

Smoothing vs levelling SMOOTHING — within float, deadline fixed peaks shaved · same end date LEVELLING — to a limit, deadline may move limit capped · duration extends → Smoothing protects the DATE (works within float). Levelling protects the RESOURCE (works to a limit and may push the date). They are not the same technique. Time-constrained → smoothing. Resource-constrained → levelling.
DiagramResource smoothing evens out demand within float keeping the deadline; levelling schedules to a resource limit and may extend the duration

Finite crews and cranes

Network analysis assumes resources are available when the logic wants them — but crews, cranes, formwork and money are FINITE. RESOURCE ALLOCATION assigns the limited resources to activities, and the demand often PEAKS uncomfortably (everything wants the same crane in week 6). The aggregated demand over time is the RESOURCE HISTOGRAM; the goal of the next two techniques is to tame its peaks.[1]

Smoothing vs levelling

At a glance

AspectSmoothingLevelling
What is fixedSmoothing: the project end dateLevelling: the resource limit
Constraint typeSmoothing: time-constrainedLevelling: resource-constrained
UsesSmoothing: only activities' floatLevelling: may delay any activity
Effect on durationSmoothing: noneLevelling: may extend it
GoalSmoothing: even out peaksLevelling: stay under the cap
Vocabulary

Key terms

Direct / indirect cost

Activity costs (rise when crashed) / time-proportional overheads (rise with duration).

Total-cost curve

Direct + indirect; U-shaped against duration, minimum at the optimum duration.

Cost slope

(Crash − normal cost) / (normal − crash time): rupees per day of compression.

Crashing

Deliberately shortening activities, cheapest-slope-first, to reduce project time.

Resource smoothing

Reschedule within float to even out demand; the end date is unchanged.

Resource levelling

Schedule to a resource limit; the project duration may extend.

Apply it

Studio task

A three-activity chain A → B → C has normal times 8, 6, 5 days and normal costs ₹6,000, ₹4,000, ₹3,000; crash times 6, 4, 3 days and crash costs ₹7,000, ₹4,600, ₹4,200. Indirect cost is ₹400/day. Compute each cost slope, decide which activity to crash first, and find the optimum (least-cost) duration and its total cost. Explain in one line why you stop where you do.

Check your understanding

Self-assessment

1. As a project's duration is shortened by crashing, INDIRECT cost generally —

2. The cost slope of an activity equals —

3. Resource LEVELLING differs from smoothing because it —

In a nutshell

Recap

Direct cost rises when you crash; indirect cost rises with duration — total cost is U-shaped with an optimum.
Cost slope = (crash − normal cost) / (normal − crash time); crash the lowest-slope critical activity first.
Crash only while the crashing cost/day is below the indirect saving/day; stop at the least-cost optimum.
Update the schedule with actuals — the critical path moves as work slips or is crashed.
Smoothing reschedules within float (deadline fixed); levelling schedules to a resource limit (deadline may move).
The evidence

References & further reading

  1. [1]B.C. Punmia & K.K. Khandelwal, Project Planning and Control with PERT and CPM — cost model, cost slope, crashing, levelling.
  2. [2]PMI, PMBOK Guide & Practice Standard for Scheduling — resource smoothing vs levelling.
  3. [3]J.D. Wiest & F.K. Levy, A Management Guide to PERT/CPM — time–cost trade-off and optimum duration.
  4. [4]K.K. Chitkara, Construction Project Management — updating and resource management in Indian practice.

Further reading

  • B.C. Punmia & K.K. Khandelwal — Project Planning and Control with PERT and CPM.
  • K.K. Chitkara — Construction Project Management.
  • J.D. Wiest & F.K. Levy — A Management Guide to PERT/CPM.

Sources gathered and fact-checked June 2026. Published values vary by source, sample and method — treat as indicative and confirm against the cited standard before structural use.