TCTO numerical: least cost schedule, Rs 2000/week

Given data and method

Indirect cost = 2,000 Rs/week. Time-cost trade-off (TCTO) crashes the activities on the critical path, one time-unit at a time, always choosing the cheapest cost slope, as long as the saving in indirect cost is more than the extra direct cost.

Assumption: the costs of activity 2-3 (C) are blurred in the scan; they are taken as normal Rs 8,000 and crash Rs 10,000 (slope Rs 1,000/week). The result (optimum 8 weeks) holds for any crash slope of C below Rs 2,000 per week. Network: 1-2 (A) then 2-3 (C) in series, with 1-3 (B) in parallel.

$$\text{Cost slope}=\frac{\text{Crash cost}-\text{Normal cost}}{\text{Normal duration}-\text{Crash duration}}$$

Paths at normal duration

• A-C = 9 weeks
• B = 8 weeks

Critical activities (on the longest path or paths): A, C; normal duration = 9 weeks; normal direct cost = 17,000 Rs.

Crashing, step by step

(Rows with several activities show activities crashed together because two paths are critical.)

Result

• Optimum (minimum-cost) schedule: duration 8 weeks, direct cost 18,000 + indirect 16,000 = 34,000 Rs.
• Activities crashed at the optimum: C by 1. Durations: A=4, B=8, C=4.
• Minimum possible duration: 7 weeks, with total cost 36,000 Rs (direct 22,000 + indirect 14,000).

Answer: least cost schedule = 8 weeks (A = 4, B = 8, C = 4 weeks), total cost Rs 34,000 against Rs 35,000 for the normal 9-week schedule. A further week would need A or C together with B (Rs 4,000 > Rs 2,000 saved).