Shift Coverage with Cross-Trained Staff
A distribution center runs two shifts: Day (7:00–15:00) and Evening (15:00–23:00). Six employees are cross-trained on the forklift certification that the evening receiving dock requires. Their availability notes are: Dana (day only, certified), Eli (either shift, certified, prefers evening), Frank (evening only, certified, requested fewer than 20 hrs/week), Gina (either shift, certified, has a standing medical appointment Tuesdays at 16:00), Hugo (day only, certified, on vacation all week), Ivy (evening only, not certified, training finishes next month). The evening dock needs two certified operators every night. Frank is limited to 18 hours this week. Gina can work any evening except Tuesday.
1. Which employees can actually be scheduled on the evening dock this week, and what is the binding constraint on each?
Read the worked answer
Filter to certified + evening-available:
- Eli: certified, available either shift → schedulable evening.
- Frank: certified, evening only, but capped at 18 hrs → schedulable but hours-limited (18 hrs ≈ 2 full shifts + a partial).
- Gina: certified, either shift, but unavailable Tuesday 16:00 → schedulable Mon/Wed/Thu/Fri evenings only.
- Ivy: evening but not certified → excluded regardless of availability.
- Dana, Hugo: certified but day-only (Hugo also on vacation) → excluded.
So the schedulable pool is Eli, Frank, Gina. The binding constraints differ: certification (Ivy), shift (Dana/Hugo), and individual limits (Frank's hours, Gina's Tuesday).
2. Tuesday needs two certified evening operators. Can the requirement be met, and what is your plan?
Read the worked answer
Tuesday removes Gina (appointment at 16:00, which overlaps the whole evening shift). Remaining evening-certified: Eli and Frank. Frank is capped at 18 hrs/week, so spending a full 8-hr Tuesday shift on him is feasible only if his total stays ≤18.
Plan: schedule Eli and Frank on Tuesday. To protect Frank's cap, keep his other assignments to ≤10 hrs (e.g., one 8-hr shift plus a 2-hr partial, or two shorter shifts). If Frank's Tuesday shift would push him over 18, the requirement cannot be met from the current pool - you'd need to either authorize overtime, call in a certified day-shift employee (Dana) on a one-time basis, or reschedule the dock. The key judgment: don't assume the requirement is met just because two names exist; check the hour cap against the actual shift length.