The Interrogation Scheduling Conflict
You are a supervisory special agent managing a team of 4 agents (A, B, C, D). Two high-priority interrogations are scheduled for tomorrow: Suspect X at 9:00 AM and Suspect Y at 11:00 AM. Each interrogation requires exactly 2 agents and lasts 2 hours. Agent A is certified for high-pressure interrogations and must be on both teams. Agent B is available only from 8:00 AM to 12:00 PM. Agent C is available all day but has a court appearance at 10:00 AM that lasts 1 hour. Agent D is available all day but must leave by 1:00 PM. Additionally, agency policy requires that no agent can participate in more than one interrogation per day, except for the lead agent (A) who can do both if necessary. You need to assign agents to both interrogations without violating availability or policy.
1. Determine if it is possible to staff both interrogations under the given constraints. If yes, provide a valid assignment. If no, explain which constraint makes it impossible and propose the smallest policy change that would allow staffing.
Read the worked answer
Interrogation X: 9-11 AM, needs 2 agents including A. Interrogation Y: 11 AM-1 PM, needs 2 agents including A. Agent A can do both (exception). For X, second agent must be available 9-11. B is available until 12, so B can do X. C is in court 10-11, so C cannot do X (overlap 10-11). D is available. So X could be A+B or A+D. For Y, second agent must be available 11-1. B is only until 12, so B cannot do Y (needs until 1). C is available after 11 (court ends at 11), so C can do Y. D is available until 1, so D can do Y. Policy: no agent except A can do more than one interrogation. So if B does X, B cannot do Y (already cannot). If D does X, D cannot do Y. So we need distinct second agents for X and Y. Possible: X: A+B, Y: A+C (C available 11-1). Check C: court 10-11, so at 11 is free. Works. Or X: A+D, Y: A+C. Both work. So yes, possible. Example: X: A and B; Y: A and C.
2. Suppose Agent B becomes unavailable entirely. Re-evaluate feasibility. If still possible, give an assignment. If not, what is the minimal change (e.g., allowing an agent other than A to do both, or adjusting times) that would make it possible?
Read the worked answer
Without B: Available agents: A (both), C (free after 11), D (until 1). For X (9-11): needs A + one other. C is in court 10-11, so cannot do X. D is available 9-11. So X must be A+D. For Y (11-1): needs A + one other. D is already used in X and cannot do both (policy). C is available 11-1. So Y can be A+C. Thus assignment: X: A+D; Y: A+C. This works because D is free 9-11 and C is free 11-1. No policy change needed. So still possible.