Scheduling Five Loan Files at a Single-Window Branch
Five loan files-P, Q, R, S and T-must be reviewed by one credit officer on five consecutive working days, Monday to Friday, one file per day. The branch has fixed these dependencies: P must be reviewed before R because R's legal opinion depends on P's property papers; Q cannot be scheduled on Monday or Friday because the valuer is unavailable; S must be reviewed immediately the day after T because the same co-applicant signs both documents; and R cannot be reviewed on Friday because the sanction committee meets only in the morning. A trainee proposes the order P–R–Q–S–T and asks whether it can be approved. The credit officer also wants to know every feasible order before committing to a customer appointment on Wednesday. The branch cannot add a sixth day or review two files on the same day.
1. List every feasible review order and explain how the dependencies reduce the possibilities.
Read the worked answer
Because S must be immediately after T, the pair (T, S) can occupy only (Mon, Tue), (Tue, Wed), (Wed, Thu) or (Thu, Fri). Q must be before T and cannot be Monday or Friday.
- (T, S) = (Mon, Tue): Q would need to be before Monday, impossible.
- (T, S) = (Tue, Wed): Q would need to be Monday, but Monday is barred.
- (T, S) = (Wed, Thu): Q must be Tuesday. P and R then take Monday and Friday, with P before R, so R would be Friday-barred.
- (T, S) = (Thu, Fri): Q can be Tuesday or Wednesday. If Q is Tuesday, the remaining days are Monday and Wednesday for P and R, giving P, Q, R, T, S. If Q is Wednesday, the remaining days are Monday and Tuesday, giving P, R, Q, T, S.
So there are exactly two feasible orders: P–Q–R–T–S and P–R–Q–T–S. The key reduction is that S's immediate-after-T condition fixes a two-day block, and Q's Monday/Friday ban eliminates most placements.
2. The trainee's proposed order is P–R–Q–S–T. Identify the first rule it breaks, and state whether moving one file can repair it.
Read the worked answer
The proposed order breaks the rule that S must be reviewed immediately the day after T. In P–R–Q–S–T, S is on Thursday and T is on Friday, so S is immediately before T, not after it. The earlier conditions are otherwise satisfied: P is before R, Q is on Wednesday (not Monday or Friday), and R is on Tuesday (not Friday).
The defect can be repaired by moving T to Thursday and S to Friday, producing P–R–Q–T–S. That order is feasible: P before R, Q on Wednesday, T on Thursday, S immediately after T on Friday, and R not on Friday. The trainee should not simply swap S and T without rechecking Q's position, because a different swap could push Q onto Friday or break the P-before-R rule. The manager should approve the corrected order only after checking all four constraints again.
3. If the co-applicant can come only on Thursday, so T must be Thursday, what follows for the Wednesday appointment?
Read the worked answer
If T is Thursday, S must be Friday. Q must be before Thursday and cannot be Monday or Friday, so Q is either Tuesday or Wednesday. P and R occupy the remaining two days, with P before R.
There are two possibilities:
- Q on Tuesday: P on Monday, R on Wednesday, T on Thursday, S on Friday → P–Q–R–T–S. Wednesday's file is R.
- Q on Wednesday: P on Monday, R on Tuesday, T on Thursday, S on Friday → P–R–Q–T–S. Wednesday's file is Q.
So the Wednesday appointment cannot be fixed to one file from the given facts. The officer must decide whether the valuer or the legal file is more urgent. If the customer appointment is for Q, the branch should choose the second order; if it is for R, the branch should choose the first. The manager should confirm the choice with the valuer before promising a slot.