Lineal Programming Transport Methods

A simple algorithmic implementation of some of the most common lineal programming transport methods and transportation models.

  $ npm install --save transport-methods

API

The public API is as follows:

io.transbordModel(options)

Describes a transbord model from which a valid equivalent transport model can be computed. Returns a valid configuration for transport matrix.

Options

• nodes[] - a node array composing the transbord network.
  • name - identifier to reference to when linking nodes. Required
  • type - any of the following (origin, destination, intermediary). Required
  • input - the whole throughput coming to this node. Required
  • output - the whole throughput coming out from this node. Required
  • next[] - an array of references to other nodes
    • reference another node identifier to reference. Required
    • cost the cost of transbording the current node output to the referenced node input. Required

io.transportMatrix(options)

Describes the complete transport matrix, as specified by the lineal programming transport methods specification. The generated matrix can be computed by any of the allowed transport methods. Returns a TransportMatrix

options

• originations - an array of originations, each origination is an object with the following schema.
  • name - the origination name. Required
  • supply - the supply units available. Required
• destinations - an array of destinations, each destination is an object with the following schema.
  • name - the destination name. Required
  • demand - the demand units. Required
• routes - an array of items which identify the cost of a given route (from a origination to a destination).
  • from - a valid origination name. Any string previously specified at the originations array. Required
  • to - an array with valid destinations.
    • destination - a valid destination name. Any string previously specified at the destinations array. Required
    • cost - a valid number specifying the route cost. Required

About the model

If the transport model is not considered complete (the overall supply is different from the overall demand), additional destinations or originations are added as needed.

TransportMatrix

It represents the logic form of the transport method. Has the ability to compute the best supply/demand distribution based on the transport method specified.

transportMatrix.resolveBy(transportMethod)

• transportMethod - any of the allowed transport methods: [minimumCost, northwestCorner]

Usage

  'use strict';

  const io = require('io-transport-methods');

  const matrix = io.transportMatrix({
    originations: [
      {
        name: 'origination-1',
        supply: 10,
      },
      {
        name: 'origination-2',
        supply: 20,
      },
    ],
    destinations: [
      {
        name: 'destination-1',,
        demand: 15,
      },
      {
        name: 'destination-2',
        demand: 5,
      },
    ],
    routes: [
      {
        from: 'origination-1',
        to: [
          {
            destination: 'destination-1',
            cost: 20,
          }
        ]
      },
      {
        from: 'origination-1',
        to: [
          {
            destination: 'destination-2',
            cost: 10,
          },
        ]
      }
    ],
  });

  matrix
    .resolveBy('minimumCost');

    // {
    //   "summary":360,
    //   "distribution":[
    //     {
    //       "from":"origination-1",
    //       "to":[
    //         {
    //           "destination":"destination-1",
    //           "cost":10,
    //           "units":0
    //         },
    //         {
    //           "destination":"destination-2",
    //           "cost":1,
    //           "units":15
    //         },
    //         {
    //           "destination":"destination-3",
    //           "cost":20,
    //           "units":0
    //         },
    //         {
    //           "destination":"destination-4",
    //           "cost":11,
    //           "units":0
    //         }
    //       ]
    //     },
    //     {
    //       "from":"origination-2",
    //       "to":[
    //         {
    //           "destination":"destination-1",
    //           "cost":12,
    //           "units":0
    //         },
    //         {
    //           "destination":"destination-2",
    //           "cost":7,
    //           "units":0
    //         },
    //         {
    //           "destination":"destination-3",
    //           "cost":9,
    //           "units":15
    //         },
    //         {
    //           "destination":"destination-4",
    //           "cost":20,
    //           "units":10
    //         }
    //       ]
    //     },
    //     {
    //       "from":"origination-3",
    //       "to":[
    //         {
    //           "destination":"destination-1",
    //           "cost":2,
    //           "units":5
    //         },
    //         {
    //           "destination":"destination-2",
    //           "cost":14,
    //           "units":0
    //         },
    //         {
    //           "destination":"destination-3",
    //           "cost":16,
    //           "units":0
    //         },
    //         {
    //           "destination":"destination-4",
    //           "cost":18,
    //           "units":0
    //         }
    //       ]
    //     }
    //   ]
    // }