1. Consecutive Work Limit Conflicting with Group-Based Staffing Requirements
In some situations, staffing requirements and working limits may conflict with each other.
When a shift requires a specific number of staff from a particular group, but the available staff in that group cannot legally work the required number of consecutive days due to defined limits, the scheduling problem may become infeasible.
This occurs when group-based staffing requirements force a staff member to work more consecutive days than the allowed limit, leaving the algorithm with no valid assignment that satisfies all constraints.
Example Scenario
Assume the following configuration:
A Morning Shift requires a total of 6 staff members.
Among them, 1 staff member must belong to the Office group.
Staff are scheduled to work 6 consecutive days per week (Sunday is off).
The maximum consecutive working day limit is set to 5.
If there is only one staff member in the Office group, that person must work all required days to satisfy the group requirement.
However, doing so would require the staff member to work 6 consecutive days, which violates the maximum consecutive work limit of 5 days.
Because the system cannot assign another staff member from the required group, and the consecutive work limit cannot be exceeded, the schedule becomes infeasible.
A similar situation can occur even when the group initially contains multiple staff members.
For example, if the Office group has two members but one of them is on leave for part of the planning period, the remaining staff member may still be required to work more consecutive days than allowed, again resulting in an infeasible schedule.
This type of scenario occurs when group-based staffing requirements and consecutive work limits cannot be satisfied simultaneously.
Possible Resolution
To resolve this situation, the group-based staffing requirement may need to be adjusted, the maximum consecutive working day limit may need to be reconsidered, or additional staff may need to be added to the relevant group to ensure that the workload can be distributed without violating the defined limits.
2. Consecutive Work Limit Conflict Caused by Leave
A schedule may become infeasible even when staffing requirements are normally manageable if one or more staff members become unavailable during the planning period.
This happens when the available staff pool becomes too small to both cover the required shifts and distribute rest days within the maximum consecutive working day limit.
Example Scenario
Assume the following configuration:
There are 10 staff members in the department.
There are two shifts per day: Morning and Evening.
Each shift requires 4 staff members.
This means 8 staff members must work each day.
Therefore, only 2 staff members can rest on any given day.
The maximum consecutive working day limit is set to 5.
Under this setup, the schedule is already very tight, because the system has only 2 daily rest slots to rotate across 10 staff members.
Now assume that 1 staff member is on leave for 1 week.
During that week:
the available staff pool drops from 10 to 9
the daily staffing requirement remains 8
this means only 1 staff member can rest per day
Mathematically, over a 6-day working block, the schedule requires:
8 × 6 = 48 staff assignments
But with 9 staff members and a maximum consecutive work limit of 5, the maximum assignable capacity is:
9 × 5 = 45 staff assignments
Since the required assignments (48) exceed the maximum possible assignments (45), at least one staff member would have to work more than 5 consecutive days.
Because the consecutive work limit is a hard constraint, the scheduling problem becomes infeasible.
Possible Resolution
To resolve this situation, the staffing requirements may need to be reduced or additional staff may need to be added to the available staff pool.