Time–Cost Trade-off Analysis

Smart planning, better results

Every project can be finished faster by spending more. The interesting question is where that stops being true — the duration at which the money saved on overheads no longer covers the money spent on acceleration.

The analysis on the poster is the classic one, worked through properly. Eight activities from excavation to MEP works, each with a normal duration and cost and a crashed duration and cost, giving a cost slope in rupees per week saved. Direct cost rises as duration falls; indirect cost falls; the total cost curve is the sum, and it has a minimum. In the worked example that minimum sits at twenty-four weeks, four weeks below the normal schedule, at a total of ₹52.80 lakh — an 8.7 per cent saving.

The reason the method matters is that intuition gets it wrong in both directions. Managers either refuse to crash at all, and pay indirect costs for longer than they need to, or they crash everything, and pay a fortune to compress activities that were never on the critical path and so saved no time at all.

That second error is the common one. Crashing an activity with float changes nothing about the project duration and costs real money. The whole discipline of the method is: find the critical path, crash the cheapest critical activity by one unit, recompute the path because it may have changed, and repeat until the total cost starts rising.

Where the numbers in a crashing study come from

The weak point of most time–cost studies is the crash cost estimate. Normal durations and costs are usually available from schedules of rates or from the contractor's own data. Crash costs — what it actually costs to do the same activity in three weeks instead of four — are far softer, because they depend on overtime rates, additional plant, crew size limits and productivity loss from crowding.

An honest study states the basis of each crash estimate and acknowledges the productivity penalty. Doubling the crew rarely halves the duration; congestion, supervision limits and learning all bite. A study that assumes linear scaling will overstate what crashing can achieve, and a practitioner reading it will notice immediately.

The same care applies to indirect cost. It is often taken as a flat weekly figure, which is a reasonable simplification for site overheads but not for finance charges or for penalty and bonus clauses that step at specific dates. Where the contract has a liquidated damages provision, that belongs in the model, and it usually shifts the optimum considerably.

Beyond the textbook curve

Classical crashing assumes deterministic durations, which no site has. Where the schedule risk matters, the stronger analysis is stochastic: assign a distribution to each activity duration, run a Monte Carlo simulation, and report the probability of finishing by a given date rather than a single number. A twenty-four-week plan with a forty per cent chance of being met is a different proposition from one with an eighty-five per cent chance.

Resource constraints change the answer too. A schedule that is optimal on paper may be impossible if it needs two tower cranes on a site that has one. Resource-constrained scheduling and levelling are part of the same study, and skipping them is how a thesis produces a plan that a site engineer would laugh at.

Where a genuine research contribution is wanted rather than an application, the usual route is multi-objective: time, cost and one more objective such as quality, safety or carbon, solved with a genetic algorithm to produce a trade-off front instead of a single optimum. We build those too, and the optimisation page on this site covers how they are assessed.