Shift scheduling

The shift scheduling app is available in one modeling language as a Mixed Integer Problem (MIP). You can also choose to make customizations to the model by instantiating the app first.

Nextmv Go SDK
- Default solver: HiGHS
- Marketplace subscription app IDs
  - Go: nextmv-shift.scheduling

Bash

nextmv community clone -a shift-scheduling-gosdk

Once you have the code locally, you can customize the model, run it locally and deploy it to Nextmv Platform.

Input

The format for timestamps should be RFC3339, e.g.: "2023-01-01T00:00:00Z".

The input schema is a JSON payload defining the available workers and the required demand to satisfy for a shift scheduling problem. Nextmv's tools are designed to operate directly on business data (in JSON) to produce decisions that are actionable by software systems. This makes decisions more interpretable and easier to test. It also makes integration with data warehouses and business intelligence platforms significantly easier. An input contains the following components:

Field name	Required	Data type	SI Unit	Description	Example
`workers`	Yes	`array` of `worker`	NA	Workers to assign.	See `worker`
`required_workers`	Yes	`array` of `required worker`	NA	A predicted need of workers at certain times.	See `required worker`

Here you can find a sample .json with the input schema:

JSON

{
  "workers": [
    {
      "availability": [
        {
          "start": "2023-09-03T04:00:00+02:00",
          "end": "2023-09-03T11:00:00+02:00"
        },
        {
          "start": "2023-09-04T14:00:00+02:00",
          "end": "2023-09-04T22:00:00+02:00"
        }
      ],
      "id": "1"
    },
    {
      "availability": [
        {
          "start": "2023-08-28T15:00:00+02:00",
          "end": "2023-08-29T00:00:00+02:00"
        },
        {
          "start": "2023-08-29T16:00:00+02:00",
          "end": "2023-08-29T17:00:00+02:00"
        }
      ],
      "id": "2"
    },
    {
      "availability": [
        {
          "start": "2023-08-29T02:00:00+02:00",
          "end": "2023-08-29T11:00:00+02:00"
        },
        {
          "start": "2023-08-30T16:00:00+02:00",
          "end": "2023-08-31T03:00:00+02:00"
        },
        {
          "start": "2023-08-31T15:00:00+02:00",
          "end": "2023-08-31T22:00:00+02:00"
        },
        {
          "start": "2023-09-01T07:00:00+02:00",
          "end": "2023-09-01T12:00:00+02:00"
        },
        {
          "start": "2023-09-01T23:00:00+02:00",
          "end": "2023-09-02T05:00:00+02:00"
        },
        {
          "start": "2023-09-02T03:00:00+02:00",
          "end": "2023-09-02T08:00:00+02:00"
        },
        {
          "start": "2023-09-03T07:00:00+02:00",
          "end": "2023-09-03T11:00:00+02:00"
        }
      ],
      "id": "3"
    },
    {
      "availability": [
        {
          "start": "2023-08-28T11:00:00+02:00",
          "end": "2023-08-28T19:00:00+02:00"
        },
        {
          "start": "2023-08-28T20:00:00+02:00",
          "end": "2023-08-29T03:00:00+02:00"
        },
        {
          "start": "2023-08-29T04:00:00+02:00",
          "end": "2023-08-29T06:00:00+02:00"
        },
        {
          "start": "2023-08-29T22:00:00+02:00",
          "end": "2023-08-29T22:00:00+02:00"
        },
        {
          "start": "2023-08-30T12:00:00+02:00",
          "end": "2023-08-30T14:00:00+02:00"
        },
        {
          "start": "2023-09-04T06:00:00+02:00",
          "end": "2023-09-04T07:00:00+02:00"
        }
      ],
      "id": "4"
    }
  ],
  "required_workers": [
    {
      "start": "2023-08-29T09:00:00+02:00",
      "end": "2023-08-29T09:30:00+02:00",
      "count": 2
    },
    {
      "start": "2023-08-29T09:30:00+02:00",
      "end": "2023-08-29T10:00:00+02:00",
      "count": 3
    },
    {
      "start": "2023-08-29T10:00:00+02:00",
      "end": "2023-08-29T10:30:00+02:00",
      "count": 1
    },
    {
      "start": "2023-08-29T10:30:00+02:00",
      "end": "2023-08-29T11:00:00+02:00",
      "count": 2
    },
    {
      "start": "2023-08-29T11:00:00+02:00",
      "end": "2023-08-29T11:30:00+02:00",
      "count": 4
    },
    {
      "start": "2023-08-29T11:30:00+02:00",
      "end": "2023-08-29T12:00:00+02:00",
      "count": 3
    }
  ]
}

Worker

A worker is used in the input schema.

Field name	Required	Data type	Description	Example
`availability`	Yes	`array` of `availability`	The availability times of the worker	See `availability`
`id`	Yes	`string`	ID for the worker.	`{"id": "1"}`

Availability

Availability is used in the worker schema.

Field name	Required	Data type	SI Unit	Description	Example
`start`	Yes	`timestamp`	NA	The start of an availability time window for a worker.	`{"start": "2023-01-01T00:00:00Z"}`
`end`	Yes	`timestamp`	NA	The end of an availability time window for a worker.	`{"end": "2023-01-01T00:00:00Z"}`

Required Worker

A worker is used in the input schema.

Field name	Required	Data type	Description	Example
`start`	Yes	`timestamp`	The start of a required worker time window.	`{"start": "2023-01-01T00:00:00Z"}`
`end`	Yes	`timestamp`	The end of a required worker time window.	`{"end": "2023-01-01T00:00:00Z"}`
`count`	Yes	`int`	The number of required workers for that time window.	`{"count": 1}`

Output

The output schema defines the solution to the shift scheduling problem in JSON format. The output schema contains the following components.

Field name	Always present	Data type	SI Unit	Description	Example
`solutions`	Yes	`array` of `solution`	NA	Solutions to the shift scheduling problem.	`{"solutions": []}`
`statistics`	Yes	`statistics`	NA	Summary statistics of the solution.	`{"statistics": {"total_cost": 123}}`
`version`	Yes	`string`	NA	Version of the Nextmv SDK used to generate the solution.	`{"version": {"sdk": "v1.2.3"}}`
`options`	No	`object`	NA	Arbitrary model and solver options that were used.	`{"options": {"foo": "bar"}}`

JSON

{
  "options": {
    "limits": {
      "day": {
        "max_duration": 36000000000000
      },
      "shift": {
        "max_duration": 28800000000000,
        "min_duration": 7200000000000,
        "recovery_time": 28800000000000
      },
      "week": {
        "max_duration": 144000000000000
      }
    },
    "penalty": {
      "over_supply": 1000,
      "under_supply": 500
    },
    "solve": {
      "control": {
        "bool": [],
        "float": [],
        "int": [],
        "string": []
      },
      "duration": 3000000000,
      "mip": {
        "gap": {
          "absolute": 0.000001,
          "relative": 0.0001
        }
      },
      "verbosity": "off"
    }
  },
  "solutions": [
    {
      "assigned_shifts": [
        {
          "end": "2023-08-29T11:00:00+02:00",
          "start": "2023-08-29T03:00:00+02:00",
          "worker_id": "3"
        }
      ],
      "number_assigned_workers": 1
    }
  ],
  "statistics": {
    "result": {
      "custom": {
        "constraints": 2713,
        "provider": "HiGHS",
        "status": "optimal",
        "variables": 913
      },
      "duration": 0.123,
      "value": 5500
    },
    "run": {
      "duration": 0.123
    },
    "schema": "v1"
  },
  "version": {
    "go-highs": "VERSION",
    "go-mip": "VERSION",
    "sdk": "VERSION"
  }
}

Solution

Field name	Always present	Data type	SI Unit	Description	Example
`assigned_shifts`	Yes	`array` of `assigned_shift`	NA	Solution to the shift scheduling problem.	`{"assigned_shifts": []}`
`number_assigned_workers`	Yes	`int`	NA	The number of assigned distinct workers.	`{"number_assigned_workers": 1}`

Assigned shift

Field name	Always present	Data type	SI Unit	Description	Example
`start`	Yes	`timestamp`	NA	Start time of the worker's shift	`{"start": "2023-01-01T00:00:00Z"}`
`end`	Yes	`timestamp`	NA	End time of the worker's shift	`{"end": "2023-01-01T00:00:00Z"}`
`worker_id`	Yes	`string`	NA	The ID of the worker assigned to this shift.	`{"id": "1"}`

Statistics

Field name	Always present	Data type	SI Unit	Description	Example
`result`	No	`result`	NA	Final result of the solutions.	See `result`
`run`	Yes	`run`	NA	Information about the run.	See `run`
`schema`	Yes	`string`	NA	Schema of the statistics.	`{"schema": "v1"}`

Here you can find additional definitions used in the statistics schema:

result

Field name	Always present	Data type	SI Unit	Description	Example
`duration`	Yes	`float`	`seconds`	Time duration to get to the final result.	`{"duration": 0.123}`
`value`	Yes	`float`	NA	Value of the final result.	`{"value": 0.123}`
`custom`	Yes	`any`	NA	Custom solver metrics.	See `custom`

run
Field name Always present Data type SI Unit Description Example
duration Yes float seconds Time duration of the run. {"duration": 0.123}

Field name	Always present	Data type	SI Unit	Description	Example
`duration`	Yes	`float`	`seconds`	Time duration of the run.	`{"duration": 0.123}`

custom

Field name	Always present	Data type	SI Unit	Description	Example
`constraints`	Yes	`int`	NA	Number of constraints.	`{"constraints": 123}`
`provider`	Yes	`string`	NA	Solver provider.	`{"provider": "highs"}`
`status`	Yes	`string`	NA	Solver status.	`{"status": "optimal"}`
`variables`	Yes	`int`	NA	Number of variables.	`{"variables": 123}`

Run options

These are the default options that are available with shift scheduling.

Bash

Nextmv Hybrid Optimization Platform
Usage:
  -limits.day.maxduration duration
    	maximum working time per day (env LIMITS_DAY_MAX_DURATION) (default 10h0m0s)
  -limits.shift.maxduration duration
    	maximum working time per shift (env LIMITS_SHIFT_MAX_DURATION) (default 8h0m0s)
  -limits.shift.minduration duration
    	minimum working time per shift (env LIMITS_SHIFT_MIN_DURATION) (default 2h0m0s)
  -limits.shift.recoverytime duration
    	minimum time between shifts (env LIMITS_SHIFT_RECOVERY_TIME) (default 8h0m0s)
  -limits.week.maxduration duration
    	maximum working time per week (env LIMITS_WEEK_MAX_DURATION) (default 40h0m0s)
  -penalty.oversupply float
    	penalty for over-supplying a demand (env PENALTY_OVER_SUPPLY) (default 1000)
  -penalty.undersupply float
    	penalty for under-supplying a demand (env PENALTY_UNDER_SUPPLY) (default 500)
  -runner.input.path string
    	The input file path (env RUNNER_INPUT_PATH)
  -runner.output.path string
    	The output file path (env RUNNER_OUTPUT_PATH)
  -runner.output.solutions string
    	{all, last} (env RUNNER_OUTPUT_SOLUTIONS) (default "last")
  -runner.profile.cpu string
    	The CPU profile file path (env RUNNER_PROFILE_CPU)
  -runner.profile.memory string
    	The memory profile file path (env RUNNER_PROFILE_MEMORY)
  -solve.control.bool string
    	List of solver-specific control options (configurations) with bool values. Example: "name1=value1,name2=value2", where value1 and value2 are bool values. (env SOLVE_CONTROL_BOOL)
  -solve.control.float string
    	List of solver-specific control options (configurations) with float values. Example: "name1=value1,name2=value2", where value1 and value2 are float values. (env SOLVE_CONTROL_FLOAT)
  -solve.control.int string
    	List of solver-specific control options (configurations) with int values. Example: "name1=value1,name2=value2", where value1 and value2 are int values. (env SOLVE_CONTROL_INT)
  -solve.control.string string
    	List of solver-specific control options (configurations) with string values. Example: "name1=value1,name2=value2", where value1 and value2 are string values. (env SOLVE_CONTROL_STRING)
  -solve.duration duration
    	Maximum duration of the solver. (env SOLVE_DURATION) (default 30s)
  -solve.mip.gap.absolute float
    	Absolute gap stopping value. If the problem is an integer problem the solver will stop if the gap between the relaxed problem and the best found integer problem is less than this value. (env SOLVE_MIP_GAP_ABSOLUTE) (default 1e-06)
  -solve.mip.gap.relative float
    	Relative gap stopping value. If the problem is an integer problem the solver will stop if the relative gap between the relaxed problem and the best found integer problem is less than this value. (env SOLVE_MIP_GAP_RELATIVE) (default 0.0001)
  -solve.verbosity value
    	{off, low, medium, high} Verbosity of the solver in the console. (env SOLVE_VERBOSITY)

Valid time units for -solver.duration are as follows, according to time.ParseDuration from Go's standard library:

ns (nanoseconds)
us/µs (microseconds)
ms (milliseconds)
s (seconds)
m (minutes)
h (hours)

A how-to guide for specifying the input and output schemas in shift scheduling.