Modeling a gap between workload and number of employees to be scheduled by creating and using new workload levels

At least one non-transitory computer readable storage media comprising a plurality of instructions to be executed by at least one processor, the plurality of instructions comprising:

• instructions to at least one processor to formulate, for inclusion in a constraint to be used in scheduling employees to perform an activity a among a plurality of predetermined activities to be performed in an organization within a time slot s among a plurality of predetermined time slots in a day, a representation of a sum of a first sequence of variables;
• wherein the sum of the first sequence of variables represents a gap between:
• a number of employees needed to perform the activity a in the time slot s;
• and
• the number of employees to be scheduled in the time slot s and skilled at performing the activity a;
• instructions to the at least one processor to prepare, for inclusion in a function to be optimized during scheduling, a representation of a scalar product of the first sequence of variables and a second sequence of values;
• wherein each value in the second sequence, which is multiplied with a corresponding variable in the first sequence, depends on a corresponding distance between:
• the number of employees needed to perform the activity a in the time slot s;
• and
• a workload level indicated by the corresponding variable with which said each value is multiplied;
• and
• instructions to the at least one processor to store in the memory, the representation of sum and the representation of the scalar product.

An apparatus to smoothen workload coverage in employee scheduling, the apparatus comprising:

• means for formulating, for inclusion in a constraint to be used in scheduling employees to perform an activity a among a plurality of predetermined activities to be performed in an organization within a time slot s among a plurality of predetermined time slots in a day, a representation of a sum of a first sequence of variables;
• wherein the sum of the first sequence of variables represents a gap between:
• a number of employees needed to perform the activity a in the time slot s;
• and
• the number of employees to be scheduled in the time slot s and skilled at performing the activity a;
• means for preparing, for inclusion in a function to be optimized during scheduling, a representation of a scalar product of the first sequence of variables and a second sequence of values;
• wherein each value in the second sequence, which is multiplied with a corresponding variable in the first sequence, depends on a corresponding distance between:
• the number of employees needed to perform the activity a in the time slot s;
• and
• a workload level indicated by the corresponding variable with which said each value is multiplied;
• and
• means for storing in memory, the representation of the sum and the representation of the scalar product.