Cost flow

The cost flow app is available in one modeling language as a network flow problem. You can also choose to make customizations to the model by instantiating the app first.

OR-Tools
- Marketplace subscription app IDs
  - Python: nextmv-cost.flow.ortools

Bash

nextmv community clone -a cost-flow-ortools

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

Input

The input schema is a JSON payload defining nodes of the network with their supply (negative supply equals a demand) as well as the edges between nodes. 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
`projects`	Yes	`array` of `project`	NA	The list of available projects.	See `project`
`workers`	Yes	`array` of `worker`	NA	A list of all available workers to fulfill the projects.	See `worker`

Project

Field name	Required	Data type	SI Unit	Description	Example
`id`	Yes	`string`	NA	The ID of the project.	`{"id": "project_1"}`
`required_skills`	Yes	`array` of `string`	NA	A list of skills required for this project.	`{"required_skills": ["programming"]}`
`value`	Yes	`float`	NA	The value of the project.	`{"value": 100}`
`required_time`	Yes	`float`	NA	The required time to fulfill this project.	`{"required_time": 2}`

Worker

Field name	Required	Data type	SI Unit	Description	Example
`id`	Yes	`string`	NA	The ID of the worker.	`{"id": "worker_1"}`
`skills`	Yes	float	NA	A list of skills the worker can offer.	`{"skills": ["programming"]}`
`available_time`	Yes	map	NA	The number of time units this worker is available.	`{"available_time": 3`

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

JSON

{
  "projects": [
    {
      "id": "project-1",
      "required_skills": ["programming"],
      "value": 3000,
      "required_time": 2
    },
    {
      "id": "project-2",
      "required_skills": ["programming", "design"],
      "value": 4500,
      "required_time": 4
    },
    {
      "id": "project-3",
      "required_skills": ["design"],
      "value": 3500,
      "required_time": 3
    },
    {
      "id": "project-4",
      "required_skills": ["design"],
      "value": 2450,
      "required_time": 2
    },
    {
      "id": "project-5",
      "required_skills": ["programming"],
      "value": 4000,
      "required_time": 5
    }
  ],
  "workers": [
    {
      "id": "worker-1",
      "skills": ["programming"],
      "available_time": 3
    },
    {
      "id": "worker-2",
      "skills": ["programming", "design"],
      "available_time": 9
    },
    {
      "id": "worker-3",
      "skills": ["design"],
      "available_time": 4
    }
  ]
}

Output

The output schema defines the solution to the order fulfillment problem in JSON format. The output schema contains the following components.

Field name	Always present	Data type	SI Unit	Description	Example
`solution`	Yes	`array` of `solution`	NA	Solutions to the order fulfillment problem.	See `solution`
`statistics`	Yes	`statistics`	NA	Summary statistics of the solution.	`{"statistics": {"total_cost": 123}}`

Bash

{
  "solution": {
    "assignments": [
      {
        "project": "project-1",
        "time_units": 2,
        "value": 3000,
        "worker": "worker-1"
      },
      {
        "project": "project-5",
        "time_units": 1,
        "value": 4000,
        "worker": "worker-1"
      },
      {
        "project": "project-2",
        "time_units": 4,
        "value": 4500,
        "worker": "worker-2"
      },
      {
        "project": "project-4",
        "time_units": 1,
        "value": 2450,
        "worker": "worker-2"
      },
      {
        "project": "project-5",
        "time_units": 4,
        "value": 4000,
        "worker": "worker-2"
      },
      {
        "project": "project-3",
        "time_units": 3,
        "value": 3500,
        "worker": "worker-3"
      },
      {
        "project": "project-4",
        "time_units": 1,
        "value": 2450,
        "worker": "worker-3"
      }
    ],
    "flows": [
      {
        "capacity": 3,
        "flow": 3,
        "from": 0,
        "to": 4,
        "value": 0
      },
      {
        "capacity": 9,
        "flow": 9,
        "from": 0,
        "to": 5,
        "value": 0
      },
      {
        "capacity": 4,
        "flow": 4,
        "from": 0,
        "to": 6,
        "value": 0
      },
      {
        "capacity": 3,
        "flow": 2,
        "from": 4,
        "to": 7,
        "value": 3000
      },
      {
        "capacity": 3,
        "flow": 1,
        "from": 4,
        "to": 11,
        "value": 800
      },
      {
        "capacity": 9,
        "flow": 0,
        "from": 5,
        "to": 7,
        "value": 0
      },
      {
        "capacity": 9,
        "flow": 4,
        "from": 5,
        "to": 8,
        "value": 4500
      },
      {
        "capacity": 9,
        "flow": 0,
        "from": 5,
        "to": 9,
        "value": 0
      },
      {
        "capacity": 9,
        "flow": 1,
        "from": 5,
        "to": 10,
        "value": 1225
      },
      {
        "capacity": 9,
        "flow": 4,
        "from": 5,
        "to": 11,
        "value": 3200
      },
      {
        "capacity": 4,
        "flow": 3,
        "from": 6,
        "to": 9,
        "value": 3500
      },
      {
        "capacity": 4,
        "flow": 1,
        "from": 6,
        "to": 10,
        "value": 1225
      },
      {
        "capacity": 2,
        "flow": 2,
        "from": 7,
        "to": 1,
        "value": 0
      },
      {
        "capacity": 4,
        "flow": 4,
        "from": 8,
        "to": 1,
        "value": 0
      },
      {
        "capacity": 3,
        "flow": 3,
        "from": 9,
        "to": 1,
        "value": 0
      },
      {
        "capacity": 2,
        "flow": 2,
        "from": 10,
        "to": 1,
        "value": 0
      },
      {
        "capacity": 5,
        "flow": 5,
        "from": 11,
        "to": 1,
        "value": 0
      },
      {
        "capacity": 3,
        "flow": 0,
        "from": 4,
        "to": 3,
        "value": 0
      },
      {
        "capacity": 9,
        "flow": 0,
        "from": 5,
        "to": 3,
        "value": 0
      },
      {
        "capacity": 4,
        "flow": 0,
        "from": 6,
        "to": 3,
        "value": 0
      },
      {
        "capacity": 0,
        "flow": 0,
        "from": 2,
        "to": 7,
        "value": 0
      },
      {
        "capacity": 0,
        "flow": 0,
        "from": 2,
        "to": 8,
        "value": 0
      },
      {
        "capacity": 0,
        "flow": 0,
        "from": 2,
        "to": 9,
        "value": 0
      },
      {
        "capacity": 0,
        "flow": 0,
        "from": 2,
        "to": 10,
        "value": 0
      },
      {
        "capacity": 0,
        "flow": 0,
        "from": 2,
        "to": 11,
        "value": 0
      }
    ],
    "status": "optimal",
    "total_value_of_fulfilled_projects": 17450
  },
  "statistics": {
    "result": {
      "custom": {
        "available_time_units": 16,
        "excess_time_units": 0,
        "number_of_edges": 25,
        "number_of_fulfilled_projects": 5,
        "number_of_nodes": 12,
        "number_of_projects": 5,
        "number_of_unfilled_projects": 0,
        "number_of_unfulfilled_projects": 0,
        "number_of_workers": 3,
        "required_time_units": 16,
        "unmet_time_units": 0
      },
      "duration": 0.015,
      "value": -17448
    },
    "run": {
      "duration": 0.015
    },
    "schema": "v1"
  }
}

Solution

Field name	Always present	Data type	SI Unit	Description	Example
`flows`	No	`array` of `flow`	NA	A list of all the flows in the solution, including flows to and from the dummy source and
the dummy sink nodes.	See `flow`
`assignments`	No	`array` of `assignment`	NA	A list of actual assignments between workers and projects; translates the flows
into the context of the use case.	See `assignment`
`status`	No	`string`	NA	The status of the solution	`{"status": "optimal"}`
`total_value_of_fulfilled_projects`	No	`int`	NA	The total value of all the projects that could be fully staffed by workers.	`{"value": 123}`

Flow

Field name	Always present	Data type	SI Unit	Description	Example
`from`	No	`int`	NA	Index of start node of the flow.	`{"from": 123}`
`to`	No	`int`	NA	Index of the end node of the flow.	`{"to": 1}`
`flow`	No	`int`	NA	Number of time units in this flow.	`{"flow": 123}`
`capacity`	No	`int`	NA	Original capacity between the start and the end node.	`{"capacity": 123}`
`value`	No	`int`	NA	Project value that is realized with this flow.	`{"value": 123}`

Assignment

Field name	Always present	Data type	SI Unit	Description	Example
`project`	No	`string`	NA	The project id of the project in this assignment.	`{"project": "project_1"}`
`worker`	No	`string`	NA	The worker id of the worker in this assignment.	`{"worker": "worker_1"}`
`value`	No	`int`	NA	The the realized project value of this assignment.	`{"value": 123}`
`time_units`	No	`int`	NA	The utilized time units of the worker to fulfill the indicated project.	`{"capacity": 123}`

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
`number_of_edges`	Yes	`int`	NA	Number of edges in the network that is constructed based on the input.	`{"number_of_edges": 123}`
`number_of_nodes`	Yes	`int`	NA	Number of nodes in the network that is constructed based on the input.	`{"number_of_nodes": 123}`
`number_of_workers`	Yes	`int`	NA	Number of workers in the input.	`{"number_of_workers": "optimal"}`
`number_of_projects`	Yes	`int`	NA	Number of projects in the input.	`{"number_of_projects": 123}`
`available_time_units`	Yes	`int`	NA	Number of time units offered by the workers.	`{"available_time_units": 123}`
`required_time_units`	Yes	`int`	NA	Number of time units required by the projects.	`{"required_time_units": 123}`
`excess_time_units`	Yes	`int`	NA	Number of time units in excess of the demand.	`{"excess_time_units": 123}`
`unmet_time_units`	Yes	`int`	NA	Number of time units that can't be fulfilled by the workers.	`{"unmet_time_units": 123}`
`number_of_fulfilled_projects`	Yes	`int`	NA	Number of projects that could be completely fulfilled by the workers.	`{"number_of_fulfilled_projects": 123}`
`number_of_unfulfilled_projects`	Yes	`int`	NA	Number of projects that could not be completely fulfilled by the workers.	`{"number_of_unfulfilled_projects": 123}`

Run options

These are the default options that are available with cost flow model.

Bash

usage: main.py [-h] [-input INPUT] [-output OUTPUT] [-penalty PENALTY]

Solve cost-flow with OR-Tools.

options:
  -h, --help        show this help message and exit
  -input INPUT      Path to input file. Default is stdin.
  -output OUTPUT    Path to output file. Default is stdout.
  -penalty PENALTY  A penalty added to the edges from dummy source to
                    projects. Default is 3000.

A how-to guide for specifying the input and output schemas in cost-flow.