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.

Assume the following configuration:

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.

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.

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.

Assume the following configuration:

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:

Mathematically, over a 6-day working block, the schedule requires:

But with 9 staff members and a maximum consecutive work limit of 5, the maximum assignable capacity is:

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.

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.

A schedule may become infeasible when the number of available staff on a specific day is not enough to satisfy the total staffing requirements.

This can happen even when there are no group-based staffing requirements. If too many staff members are on leave on the same day, the remaining available staff pool may be smaller than the required number of assignments.

In Oplist, total staffing requirements may be relaxed by 1 staff member when necessary. However, group-based staffing requirements cannot be relaxed. This means that a shortage of 1 staff member in the total requirement may still allow the system to generate a schedule, but any unmet group-based requirement remains a hard constraint and may cause the schedule to become infeasible.

In some cases, the system may still generate a schedule by applying the allowed relaxation to the total staffing requirement. However, if the shortage exceeds the allowed relaxation limit, the schedule becomes infeasible.

Assume the following configuration:

This means the total staffing requirement for that day is:

5 + 4 = 9 staff assignments

Now assume that 3 staff members are on leave on that day.

During that day:

9 - 8 = 1 staff member

Because total staffing requirements may be relaxed by 1 staff member, the system may still generate a schedule.

For example, instead of assigning 9 staff members in total, the system may assign 8 staff members and return a feasible schedule with relaxation.

However, if 4 staff members are on leave on the same day:

9 - 7 = 2 staff members

Since the shortage is greater than the allowed relaxation amount, the system cannot satisfy the staffing requirement even with relaxation.

Because the available staff pool is too small to cover the required shifts, the schedule becomes infeasible.

This type of scenario is especially common during public holidays, religious holidays, or special periods when many staff members request or are assigned leave on the same day.

To resolve this situation, the staffing requirements for that specific day or date range may need to be adjusted.

For example, if the day is a public holiday, religious holiday, or special operational period, the user can define that day as a special day and set different staffing requirements for the affected shifts.

Reducing the Morning and Evening Shift requirements for the special day allows the schedule to reflect the reduced available staff pool and prevents the schedule from becoming infeasible.

A schedule may become infeasible when post-shift assignment rules and shift sequence limits restrict the same staff members in overlapping ways.

This can happen when a staff member who works a Night Shift cannot work a Day Shift the next day, while the system also limits how many times the same staff member can work the same shift within a short period.

Even if the total number of staff seems sufficient, these combined rules may reduce the number of eligible staff for a required shift below the required staffing level.

Assume the following configuration:

This means the total staffing requirement per day is:

3 Day + 2 Night = 5 staff assignments

Since there are 6 staff members, only 1 staff member can be off each day.

Now consider a 3-day planning period.

Over 3 days, the schedule requires:

Day Shift assignments:

3 × 3 = 9

Night Shift assignments:

2 × 3 = 6

Total assignments:

9 + 6 = 15

The department has:

6 staff × 3 days = 18 staff-days

So, in terms of total capacity, the department appears to have enough staff.

There are 18 available staff-days and only 15 required assignments.

This means the infeasibility is not caused by a simple lack of total staff capacity.

The problem appears because of the combined effect of the Night-to-Day restriction and the shift sequence limits.

On Day 1, 2 staff members must work the Night Shift.

Because of the post-shift rule, these 2 staff members cannot work the Day Shift on Day 2.

Therefore, the 3 Day Shift assignments on Day 2 must come from the remaining 4 staff members.

Among those remaining 4 staff members:

Since Day 2 requires 3 Day Shift staff, at least 2 of the Day 2 Day Shift workers must be staff who also worked the Day Shift on Day 1.

This means at least 2 staff members will have the following pattern:

Day 1: Day Shift
Day 2: Day Shift

Because of the Day Shift sequence rule, these staff members cannot work the Day Shift again on Day 3.

At the same time, Day 2 also requires 2 Night Shift workers.

Because of the post-shift rule, those 2 Night Shift workers cannot work the Day Shift on Day 3.

So, on Day 3:

These are different staff members because a staff member cannot work both Day Shift and Night Shift on the same day.

Therefore, at least 4 out of 6 staff members are not eligible for the Day Shift on Day 3.

This leaves at most:

6 - 4 = 2 eligible staff members

However, the Day Shift requirement on Day 3 is still:

3 staff members

Since only 2 staff members can legally work the Day Shift, but 3 are required, the schedule becomes infeasible.

This happens even though the total number of staff appears sufficient and even though there is 1 off slot available each day.

The infeasibility is caused by the interaction between:

To resolve this situation, one or more of the conflicting rules may need to be adjusted.

For example, the Day Shift or Night Shift sequence rule may need to be relaxed, the Night-to-Day restriction may need to be reconsidered, or the staffing requirements may need to be reduced for the affected days.

Another possible solution is to add more staff to the department so that the Day Shift and Night Shift assignments can be distributed without causing too many staff members to become ineligible for the following day.