Time cost trade-off concept with example

Time-cost trade-off (TCTO) is the technique of shortening a project's duration by crashing (speeding up) selected activities while watching the total cost. Direct cost (labour, materials, machines) rises as an activity is crashed, while indirect cost (overheads, supervision, penalties) falls as the project becomes shorter. The sum of the two is lowest at an optimum duration.

 Cost
  ^
  |T                              T     T = total cost
  | T                          T        D = direct cost
  |   T                     T           I = indirect cost
  |      T              T
  |         T    *   T       * = minimum total cost
  |D
  | D                               I
  |   D                       I
  |      D               I
  |          D     I
  |            I D
  |       I         D
  |  I                   D      D
  +-------------------------------------> Duration
   crash        optimum            normal

Use in determining project duration

• Cost slope of an activity = (crash cost - normal cost) / (normal time - crash time).
• Only critical activities are crashed, cheapest slope first, until the slope exceeds the indirect cost saved per unit time or the crash limit is reached.
• The duration with the minimum total cost is the optimum duration; the shortest feasible duration is the crash duration.

Example

Two activities in series: A (normal 6 days, Rs 3,000; crash 4 days, Rs 4,000) and B (normal 5 days, Rs 2,000; crash 4 days, Rs 2,300). Indirect cost Rs 400/day.

Slope of A = (4000 - 3000)/(6 - 4) = Rs 500/day; slope of B = (2300 - 2000)/(5 - 4) = Rs 300/day.

Crashing B costs Rs 300 and saves Rs 400, so it is worthwhile. Crashing A (Rs 500) costs more than the Rs 400 saved. The optimum duration is 10 days with a total cost of Rs 9,300 (against Rs 9,400 at the normal duration).