Studio Matrx Monthly · Volume 1 · Issue 2 · July 2026
Amogh N P
✦ In loving memory of Amogh N P — Architect · Designer · Visionary ✦
A close abstract of a rising and a falling cost curve crossing on graph paper with a marked lowest point, beside a calculator, warm desk light, no legible text
Unit IVProject Management in Interior Design

Time & Cost Optimization

Faster is not automatically cheaper — there is a least-cost duration

55 minByAmogh N P· Architect & interior designer

To shorten a project you crash it — add resources to critical activities — and that raises direct cost, while indirect (overhead) cost falls the sooner you finish. The two pull opposite ways, so total cost traces a U-curve with a least-cost optimum duration. The cost slope tells you the price of a day saved, so you crash the cheapest critical activities first — and only to the optimum, because ‘faster is always cheaper’ is a myth.

Learning objectives

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

1
CO4 · Understand

Distinguish direct, indirect and contingency costs and how each changes with duration.

2
CO4 · Apply

Use the cost slope to crash the right critical activities in the right order.

3
CO4 · Evaluate

Find the least-cost optimum duration on the total-cost curve.

Two costs that pull opposite ways

Direct and indirect cost, and the slope

Direct costs (labour, materials) rise as you rush; indirect costs (overheads) rise with duration — so total cost has a minimum in between. The cost slope = (crash cost − normal cost) / (normal time − crash time) is the extra cost per day saved — buy your days from the cheapest source first.[1]

Direct, indirect & total cost Two costs pull opposite ways as duration changes project duration → cost ₹ DIRECT cost falls as you slow down INDIRECT cost overheads rise with time TOTAL cost minimum Total cost = direct + indirect, and it bottoms out somewhere in the middle
DiagramA cost versus duration chart: direct cost falling as duration rises, indirect cost rising, and the total-cost U-curve
Cost slope of crashing How much extra to buy each day saved time → cost ₹ NORMAL (Tn, Cn) — slow, cheap CRASH (Tc, Cc) — fast, dear days saved ₹ more COST SLOPE Cc − Cn Tn − Tc = ₹ extra per day saved A flat slope is cheap to crash; a steep slope is costly
DiagramThe cost slope of crashing an activity: normal and crash points on a graph, and the cost-slope formula

Two costs that pull opposite ways

A project has two kinds of cost that behave in OPPOSITE ways as its duration changes. DIRECT costs — labour, materials, equipment for the actual work — RISE if you rush (overtime, extra crews, express delivery all cost more), so direct cost goes UP as duration goes DOWN. INDIRECT costs — site overheads, supervision, rent, and the client's cost of not having the space — accrue per day, so they go UP as duration goes UP. Add to these a CONTINGENCY for the risks and delays you cannot foresee. Because direct and indirect costs pull opposite ways, the TOTAL cost is not lowest at the fastest schedule nor at the slowest — it has a minimum somewhere in between, and finding it is the whole game.[1, 4]

Shorten the right activities, no further

Crashing to the optimum

You crash only critical activities (others buy nothing but cost), lowest cost slope first, re-checking each step — because shortening one path can make another critical. And you stop at the optimum: the least-cost duration on the total-cost curve. ‘Faster is always cheaper’ is a myth — past the optimum, every day bought costs more than it saves.[1, 4]

Crashing the network Buy time by adding resources — but only where it pays time → NORMAL 10 days fewer workers, lower cost CRASHED 6 days more crew, extra shifts, higher cost 4 days saved Rule of thumb: crash the CRITICAL activities with the lowest cost slope first — never the ones with float. Shorten the critical path where each day is cheapest to buy
DiagramCrashing an activity: shown normal, longer and cheaper, then crashed, shorter and more costly, with a note to crash critical activities first
The optimum duration The least-cost point on the total-cost curve project duration → total cost ₹ OPTIMUM least-cost time crash too much: costs shoot up too slow: overheads pile up Crashing past the optimum costs more, not less — stop at the bottom
DiagramThe total-cost U-curve with its lowest point marked as the optimum least-cost project duration

Shorten the right activities

You cannot shorten a project by crashing just any activity — only the CRITICAL ones control the finish, so crashing a non-critical activity buys nothing but cost. So the method is: find the critical path, then crash the critical activity with the LOWEST cost slope (the cheapest day), one step at a time, re-checking the network each step — because shortening one path can make ANOTHER path critical, and then you must crash both. You keep going only as long as it is worth it. Crashing is precise, disciplined work: the right activities, in the right order, by the right amount — guided by the cost slope and the critical path together.[1]

Fact vs folklore

At a glance

AspectThe factThe folklore
Direct cost (labour, materials)RISES as you rush — overtime, extra crewsFalls the faster you go
Indirect cost (overheads)RISES with duration — accrues per dayIs fixed regardless of time
The cost slope(Crash − normal cost) / (normal − crash time) — price per day savedThe total project cost
You crashCRITICAL activities, lowest cost slope firstAny activity, in any order
Total cost vs durationA U-curve with a least-cost OPTIMUM in betweenAlways lowest at the fastest schedule
'Faster is always cheaper'A myth — crash only TO the optimum, no furtherTrue — always crash more
Vocabulary

Key terms

Direct cost

The cost of the actual work — labour, materials, equipment — which rises as you shorten (crash) the schedule with overtime, extra crews and express delivery.

Indirect cost

Overheads that accrue per day — site running, supervision, rent, the client's cost of delay — so they rise the longer the project takes.

Contingency

A cost allowance for the risks and delays that cannot be foreseen — part of an honest budget, separate from direct and indirect cost.

Cost slope

(Crash cost − normal cost) / (normal time − crash time) — the extra direct cost per day saved by crashing an activity; crash the lowest-slope critical activities first.

Crashing

Shortening the project by adding resources to critical activities to cut their duration — precise work: the right activities, in the right order, by the right amount.

Optimum duration

The least-cost project duration — the minimum of the U-shaped total-cost curve; crash to it, and no further, because past it every day bought costs more than it saves.

Apply it

Study task

Take a small project with four or five activities and give each a normal time and cost and a crash time and cost. Compute the cost slope of each — (crash cost − normal cost) / (normal time − crash time) — and rank them cheapest to dearest. Find the critical path. Now shorten the project by one day at a time by crashing the cheapest critical activity available, re-checking after each step whether a new path has become critical. Track how direct cost climbs and (assuming a daily overhead) how indirect cost falls, and find the total-cost minimum — the optimum duration. Then answer honestly: if the client demanded a finish faster than the optimum, by how much would each further day cost them? The goal is to prove, in numbers, that faster is not automatically cheaper.

Check your understanding

Self-assessment

1. How do direct and indirect costs change with project duration?

2. What is the cost slope, and what is it for?

3. Which activities do you crash to shorten a project?

4. Is 'faster is always cheaper' true?

In a nutshell

Recap

A project has DIRECT costs (rise as you rush) and INDIRECT costs (rise with duration), plus a CONTINGENCY — they pull opposite ways.
The COST SLOPE = (crash − normal cost) / (normal − crash time) is the price per day saved; buy your days from the cheapest source first.
You crash only CRITICAL activities, lowest cost slope first, re-checking each step — because shortening one path can make another critical.
TOTAL cost traces a U-curve with a least-cost OPTIMUM duration — the minimum, where overhead savings still exceed crashing costs.
'Faster is always cheaper' is a MYTH — crash TO the optimum and no further; going faster still is a real choice, but one that costs extra, not saves.
The evidence

References & further reading

  1. [1]B. C. Punmia & K. K. Khandelwal, Project Planning and Control with PERT and CPM — direct and indirect cost, cost slope, crashing, and the least-cost optimum duration. https://www.laxmipublications.com/
  2. [4]M. Y. Khan & P. K. Jain, Management Accounting — project cost, cost behaviour and cost-time optimisation. https://www.mheducation.co.in/

Further reading

  • B. C. Punmia & K. K. Khandelwal, Project Planning and Control with PERT and CPM.
  • M. Y. Khan & P. K. Jain, Management Accounting.

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.

A

The author

Amogh N P

Architect, interior designer, and creative polymath. Studio Matrx began in his notebooks — his vision of design made honest, useful, and open to everyone. Its Academy is written and taught in his memory, and free, forever.

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