This examples builds on top of the nurse scheduling example to model regular and overtime compensation, subject to a budget requirement. Besides the scheduling constraints for the nurses, there is a $10,000 budget for a 4-day planning horizon. All nurses are paid a base hourly rate of $50/hr and there is an hourly shift differential of $10/hr for shifts starting at 19hr. Any hour worked after 40 hours is paid at 1.5x the average base hourly rate (i.e., ($50+$60)/2=$55).
Regular and overtime compensation
The base hourly rate, shift differentials and overtime multipliers are
represented with the hourlyContract field in employee. In an
hourly contract, the baseHourlyRate and the
hourlyRateShiftDifferentials model the compensation for regular (non-overtime)
work. These values are also used to estimate an average base hourly rate for
overtime compensation when overtimePeriods are provided. Typically an overtime
period matches a week, and multiple overtime periods can be provided as long as
these don't overlap. The hourly contract for the first nurse (Adam), is
represented as:
{
"employees": [{
"id": "Adam",
"roleIds": ["Registered Nurse"],
...
scheduling constraints
...
"hourlyContract": {
"baseHourlyRate": 50,
"hourlyRateShiftDifferentials": {
"2023-05-01 19hr": 10,
"2023-05-02 19hr": 10,
"2023-05-03 19hr": 10,
"2023-05-04 19hr": 10
},
"overtimePeriods": [
{
"overtimeMultiplier": 1.5,
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5
},
"maximumRegularHours": 40
}
]
}
}
}
Example with all four employees and their hourly contract
{
"employees": [
{
"id": "Adam",
"roleIds": [
"Registered Nurse"
],
"schedulingConstraints": [
{
"priority": "PRIORITY_HIGH",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"minimumRestMinutes": 720
},
{
"priority": "PRIORITY_MEDIUM",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"maximumMinutes": 2160
}
],
"hourlyContract": {
"baseHourlyRate": 50,
"hourlyRateShiftDifferentials": {
"2023-05-01 19h": 10,
"2023-05-02 19h": 10,
"2023-05-03 19h": 10,
"2023-05-04 19h": 10
},
"overtimePeriods": [
{
"overtimeMultiplier": 1.5,
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5
},
"maximumRegularHours": 40
}
]
}
},
{
"id": "Grace",
"roleIds": [
"Registered Nurse"
],
"schedulingConstraints": [
{
"priority": "PRIORITY_HIGH",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"minimumRestMinutes": 720
},
{
"priority": "PRIORITY_MEDIUM",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"maximumMinutes": 2160
}
],
"hourlyContract": {
"baseHourlyRate": 50,
"hourlyRateShiftDifferentials": {
"2023-05-01 19h": 10,
"2023-05-02 19h": 10,
"2023-05-03 19h": 10,
"2023-05-04 19h": 10
},
"overtimePeriods": [
{
"overtimeMultiplier": 1.5,
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5
},
"maximumRegularHours": 40
}
]
}
},
{
"id": "James",
"roleIds": [
"Registered Nurse"
],
"schedulingConstraints": [
{
"priority": "PRIORITY_HIGH",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"minimumRestMinutes": 720
},
{
"priority": "PRIORITY_MEDIUM",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"maximumMinutes": 2160
}
],
"hourlyContract": {
"baseHourlyRate": 50,
"hourlyRateShiftDifferentials": {
"2023-05-01 19h": 10,
"2023-05-02 19h": 10,
"2023-05-03 19h": 10,
"2023-05-04 19h": 10
},
"overtimePeriods": [
{
"overtimeMultiplier": 1.5,
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5
},
"maximumRegularHours": 40
}
]
}
},
{
"id": "Alonso",
"roleIds": [
"Registered Nurse"
],
"schedulingConstraints": [
{
"priority": "PRIORITY_HIGH",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"minimumRestMinutes": 720
},
{
"priority": "PRIORITY_MEDIUM",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"maximumMinutes": 2160
}
],
"hourlyContract": {
"baseHourlyRate": 50,
"hourlyRateShiftDifferentials": {
"2023-05-01 19h": 10,
"2023-05-02 19h": 10,
"2023-05-03 19h": 10,
"2023-05-04 19h": 10
},
"overtimePeriods": [
{
"overtimeMultiplier": 1.5,
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5
},
"maximumRegularHours": 40
}
]
}
}
]
}
Budget requirement
The total budget of $10,000 is represented with a budget requirement. The start and end times are optional, and if given, only shifts and overtime periods within this time window are considered towards this budget constraint. The corresponding representation for the first nurse (Adam) can be updated to:
{
"totalBudget": 10000,
"priority": "PRIORITY_HIGH"
}
Example of a complete request
{
"employees": [
{
"id": "Adam",
"roleIds": [
"Registered Nurse"
],
"schedulingConstraints": [
{
"priority": "PRIORITY_HIGH",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"minimumRestMinutes": 720
},
{
"priority": "PRIORITY_MEDIUM",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"maximumMinutes": 2160
}
],
"hourlyContract": {
"baseHourlyRate": 50,
"hourlyRateShiftDifferentials": {
"2023-05-01 19h": 10,
"2023-05-02 19h": 10,
"2023-05-03 19h": 10,
"2023-05-04 19h": 10
},
"overtimePeriods": [
{
"overtimeMultiplier": 1.5,
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5
},
"maximumRegularHours": 40
}
]
}
},
{
"id": "Grace",
"roleIds": [
"Registered Nurse"
],
"schedulingConstraints": [
{
"priority": "PRIORITY_HIGH",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"minimumRestMinutes": 720
},
{
"priority": "PRIORITY_MEDIUM",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"maximumMinutes": 2160
}
],
"hourlyContract": {
"baseHourlyRate": 50,
"hourlyRateShiftDifferentials": {
"2023-05-01 19h": 10,
"2023-05-02 19h": 10,
"2023-05-03 19h": 10,
"2023-05-04 19h": 10
},
"overtimePeriods": [
{
"overtimeMultiplier": 1.5,
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5
},
"maximumRegularHours": 40
}
]
}
},
{
"id": "James",
"roleIds": [
"Registered Nurse"
],
"schedulingConstraints": [
{
"priority": "PRIORITY_HIGH",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"minimumRestMinutes": 720
},
{
"priority": "PRIORITY_MEDIUM",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"maximumMinutes": 2160
}
],
"hourlyContract": {
"baseHourlyRate": 50,
"hourlyRateShiftDifferentials": {
"2023-05-01 19h": 10,
"2023-05-02 19h": 10,
"2023-05-03 19h": 10,
"2023-05-04 19h": 10
},
"overtimePeriods": [
{
"overtimeMultiplier": 1.5,
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5
},
"maximumRegularHours": 40
}
]
}
},
{
"id": "Alonso",
"roleIds": [
"Registered Nurse"
],
"schedulingConstraints": [
{
"priority": "PRIORITY_HIGH",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"minimumRestMinutes": 720
},
{
"priority": "PRIORITY_MEDIUM",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"maximumMinutes": 2160
}
],
"hourlyContract": {
"baseHourlyRate": 50,
"hourlyRateShiftDifferentials": {
"2023-05-01 19h": 10,
"2023-05-02 19h": 10,
"2023-05-03 19h": 10,
"2023-05-04 19h": 10
},
"overtimePeriods": [
{
"overtimeMultiplier": 1.5,
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5
},
"maximumRegularHours": 40
}
]
}
}
],
"shifts": [
{
"id": "2023-05-01 7h",
"locationId": "department",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 19
}
},
{
"id": "2023-05-01 13h",
"locationId": "department",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 13
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 2,
"hours": 1
}
},
{
"id": "2023-05-01 19h",
"locationId": "department",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 19
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 2,
"hours": 7
}
},
{
"id": "2023-05-02 7h",
"locationId": "department",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 2,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 2,
"hours": 19
}
},
{
"id": "2023-05-02 13h",
"locationId": "department",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 2,
"hours": 13
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 3,
"hours": 1
}
},
{
"id": "2023-05-02 19h",
"locationId": "department",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 2,
"hours": 19
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 3,
"hours": 7
}
},
{
"id": "2023-05-03 7h",
"locationId": "department",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 3,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 3,
"hours": 19
}
},
{
"id": "2023-05-03 13h",
"locationId": "department",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 3,
"hours": 13
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 4,
"hours": 1
}
},
{
"id": "2023-05-03 19h",
"locationId": "department",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 3,
"hours": 19
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 4,
"hours": 7
}
},
{
"id": "2023-05-04 7h",
"locationId": "department",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 4,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 4,
"hours": 19
}
},
{
"id": "2023-05-04 13h",
"locationId": "department",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 4,
"hours": 13
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 1
}
},
{
"id": "2023-05-04 19h",
"locationId": "department",
"startDateTime": {
"year": 2023,
"month": 5,
"day": 4,
"hours": 19
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
}
}
],
"coverageRequirements": [
{
"startDateTime": {
"year": 2023,
"month": 5,
"day": 1,
"hours": 7
},
"endDateTime": {
"year": 2023,
"month": 5,
"day": 5,
"hours": 7
},
"locationId": "department",
"roleRequirements": [
{
"roleId": "Registered Nurse",
"targetEmployeeCount": 2,
"priority": "PRIORITY_MANDATORY"
}
]
}
],
"roleIds": [
"Registered Nurse"
],
"locationIds": [
"department"
],
"budgetRequirements": [
{
"totalBudget": 10000,
"priority": "PRIORITY_HIGH"
}
]
}
Response example
The response of the solver contains the assignment of nurses to shifts and the status of the optimization procedure. For example, the shifts assigned to the first employee are returned as:
{
"solutionStatus": "OPTIMAL",
"shiftAssignments": [
{
"employeeId": "Adam",
"shiftId": "2023-05-01 7hr",
"roleId": "Registered Nurse"
},
{
"employeeId": "Adam",
"shiftId": "2023-05-02 7hr",
"roleId": "Registered Nurse"
},
{
"employeeId": "Adam",
"shiftId": "2023-05-03 7hr",
"roleId": "Registered Nurse"
},
{
"employeeId": "Adam",
"shiftId": "2023-05-04 7hr",
"roleId": "Registered Nurse"
},
... ]
}
Example of a complete response
{
"solutionStatus": "OPTIMAL",
"shiftAssignments": [
{
"employeeId": "Adam",
"shiftId": "2023-05-01 7h",
"roleId": "Registered Nurse"
},
{
"employeeId": "Adam",
"shiftId": "2023-05-02 7h",
"roleId": "Registered Nurse"
},
{
"employeeId": "Adam",
"shiftId": "2023-05-03 7h",
"roleId": "Registered Nurse"
},
{
"employeeId": "Adam",
"shiftId": "2023-05-04 7h",
"roleId": "Registered Nurse"
},
{
"employeeId": "Grace",
"shiftId": "2023-05-01 19h",
"roleId": "Registered Nurse"
},
{
"employeeId": "Grace",
"shiftId": "2023-05-02 19h",
"roleId": "Registered Nurse"
},
{
"employeeId": "Grace",
"shiftId": "2023-05-03 19h",
"roleId": "Registered Nurse"
},
{
"employeeId": "Grace",
"shiftId": "2023-05-04 19h",
"roleId": "Registered Nurse"
},
{
"employeeId": "James",
"shiftId": "2023-05-01 19h",
"roleId": "Registered Nurse"
},
{
"employeeId": "James",
"shiftId": "2023-05-02 19h",
"roleId": "Registered Nurse"
},
{
"employeeId": "James",
"shiftId": "2023-05-03 19h",
"roleId": "Registered Nurse"
},
{
"employeeId": "James",
"shiftId": "2023-05-04 19h",
"roleId": "Registered Nurse"
},
{
"employeeId": "We",
"shiftId": "2023-05-01 7h",
"roleId": "Registered Nurse"
},
{
"employeeId": "We",
"shiftId": "2023-05-02 7h",
"roleId": "Registered Nurse"
},
{
"employeeId": "We",
"shiftId": "2023-05-03 7h",
"roleId": "Registered Nurse"
},
{
"employeeId": "We",
"shiftId": "2023-05-04 7h",
"roleId": "Registered Nurse"
}
]
}