Lowest-Cost Team Allocation for a 90-Connection Broadband Rollout
A BSNL JTO must commission 90 new broadband connections in a block within 30 days. Three teams are available. Team A can complete 5 connections per day at ₹1,200 per connection; Team B can complete 3 per day at ₹1,000; Team C can complete 2 per day at ₹800. Team A is unavailable for the first 6 days because of fiber-splicing training, and Team B can work only 20 days because of approved leave. Team C is available for all 30 days. At least 18 connections require splicing work that only Team A can do, and these must be included in Team A’s output. The JTO wants the lowest-cost plan that meets the deadline and the splicing constraint, while not exceeding any team’s available days. A junior engineer proposes using Team A for all 18 splicing connections, Team C for 60 connections, and Team B for the remaining 12.
1. Check the feasibility and cost of the junior engineer’s plan. Determine whether it is the minimum-cost feasible plan, showing your reasoning.
Read the worked answer
Junior plan: A = 18, C = 60, B = 12. Total = 90.
Feasibility:
- Team A: 18 / 5 = 3.6 days, so 4 working days. A is unavailable for the first 6 days but has 24 available days afterwards, so 4 days is feasible.
- Team B: 12 / 3 = 4 days, within its 20-day limit.
- Team C: 60 / 2 = 30 days, exactly the full 30-day window. The plan meets the deadline and the splicing constraint.
Cost: A: 18 x ₹1,200 = ₹21,600 B: 12 x ₹1,000 = ₹12,000 C: 60 x ₹800 = ₹48,000 Total = ₹81,600.
Why it is minimum-cost: Team A must do at least 18 connections, and it is the most expensive per connection, so use exactly 18. Team C is cheapest, so use its full capacity of 60. The remaining 12 connections go to Team B, which is cheaper than A and has enough days. Any substitution of C by B or A raises cost; any substitution of B by A raises cost by ₹200 per connection. Therefore ₹81,600 is the minimum-cost feasible plan, but it has no slack on Team C’s 30-day schedule.
2. If Team B becomes unavailable from day 15, propose a contingency plan that still meets the 90-connection deadline and state the cost impact.
Read the worked answer
Team B can work only during days 1–14, which is still enough for its 12 connections (4 days). The simplest contingency is to schedule all 12 Team B connections in the first 4 days, before day 15, while Team C runs continuously and Team A starts after day 6. The original ₹81,600 plan still works.
If that early scheduling is not possible, replace Team B’s 12 connections with Team A. Team A would then do 18 + 12 = 30 connections, requiring 6 working days after day 6, which fits the 24 available days. Team C still does 60 connections over 30 days. New cost: A: 30 x ₹1,200 = ₹36,000 C: 60 x ₹800 = ₹48,000 Total = ₹84,000. The cost impact is +₹2,400. Do not shift the work to Team C because Team C is already at its 60-connection, 30-day capacity limit; doing so would miss the deadline.