Five Inspection Points Before the Payment Cut-off
Five inspection points on a canal-lining project must be covered on five consecutive working days, Monday to Friday, one per day: B (bridge), C (canal lining), D (drain), E (embankment) and F (filter house). The executive engineer gives you these constraints: C cannot be inspected on Monday or Friday; B must be inspected immediately before D; E is fixed for Wednesday because the concrete pour is scheduled that day; F must come after C; and D must come before E. The vehicle log shows a single route, so no two inspections can share a day. The contractor will be penalised ₹5,000 for each day any inspection slips beyond Friday. On Tuesday morning you are told that the E inspection may be postponed to Friday if the pour is delayed, but the contractor wants the original sequence retained if possible. You must finalise the programme today and record the reasoning in the site diary.
1. Determine the only possible schedule, showing each deduction.
Read the worked answer
Work from the fixed point: E = Wednesday (day 3).
D must be before E, so D is day 1 or day 2. B must be immediately before D, so D cannot be day 1. Therefore D = day 2 and B = day 1.
The remaining slots are day 4 and day 5 for C and F. C cannot be Friday (day 5) and must come before F, so C = day 4 and F = day 5.
The only schedule is: Monday B, Tuesday D, Wednesday E, Thursday C, Friday F.
Check every constraint: C is not Monday or Friday; B is immediately before D; E is Wednesday; F is after C; D is before E. None is violated. Any other placement either puts D on Monday, which leaves no day for B before it, or puts C on Friday, which is prohibited.
2. If the E inspection cannot be held on Wednesday, what is the earliest alternative day, and what schedule results?
Read the worked answer
E must be after D, so E cannot move to Monday or Tuesday. The earliest alternative is Thursday (day 4).
Test E = day 4. D must be before E, and B is immediately before D. If D were day 3, B would be day 2, leaving days 1 and 5 for C and F; C cannot be day 1 or day 5, so that fails. Therefore D = day 2 and B = day 1. C and F then occupy days 3 and 5; C must come before F, so C = day 3 and F = day 5.
The schedule is Monday B, Tuesday D, Wednesday C, Thursday E, Friday F, which satisfies all constraints. So Thursday is feasible and is earlier than the contractor's proposed Friday. Friday would also work as B, D, C, F, E, but it is not the earliest option.
3. The contractor proposes moving B to Thursday and keeping D on Friday. Does that solve the problem? Explain.
Read the worked answer
No. B must be immediately before D. If B is on Thursday, D must be on Friday. But D must come before E, and E is fixed for Wednesday in the original programme; D on Friday is after E, which violates the order. Even if E were allowed to move, D on Friday leaves no working day after D for E within the week.
So moving B to Thursday cannot satisfy the constraints, and it does not avoid the ₹5,000 per day penalty. The only way to keep B on Thursday would be to move E beyond Friday, which breaches the completion week and requires a formal extension rather than a schedule tweak. The correct response is to reject the proposal in writing and retain the feasible Thursday schedule for E if Wednesday is lost.