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Clarke-Wright algorithm, a Capacitated Vehicle Routing Problem solver

Source: R/clarke_wright.R
clarke_wright.Rd

Finds a quasi-optimal solution to the Capacitated Vehicle Routing Problem (CVRP). It is assumed that all demands will be satisfied by a single source.

Usage

clarke_wright(demand, distances, vehicles, restrictions = NULL)

Arguments

demand

A numeric vector consisting of "demands" indexed by sites. The ith entry refers to the demand of site i (and the length of the vector equals the number of sites N with demands). The units of demand values need to match the units of vehicle capacity values. NA values are not allowed.

distances

An object of class dist, created by stats::dist(), with (N + 1) locations describing the distances between individual sites. The first index refers to the source site. The (i+1)th index refers to site i (as defined by demand).

vehicles

A data.frame() describing available vehicle types and their respective capacities. One row per vehicle type. The data frame is expected to have two columns:

  • n - Number of available vehicles. This can be set to NA if the number is "infinite" (i.e. effectively the maximal integer value on your machine.). It is recommended to keep at least one vehicle type as "infinite", otherwise the solver might raise a run time error due to initially not having enough vehicles available (even though the final solution might satisfy the availability restrictions).

  • caps - The vehicle capacity in same units as demand.

The order of the data.frame() is relevant and determines the prioritization of vehicle assignments to runs (in case two or more vehicle types are eligible for assignment the "first" vehicle is chosen). In a typical scenario "more expensive" vehicles should be further down in the list (so the cheaper one is chosen in case there is doubt). Since higher capacity vehicles usually involve higher costs sorting the data frame by capacity is usually a good rule of thumb.

restrictions

An optional data.frame() that allows to define vehicle type restrictions for particular sites in the form of a blacklist. The data frame is expected to have two columns:

  • vehicle - The vehicle type index.

  • site - The site index (i.e. the index of the demand vector)

Each row defines a restriction: vehicle type vehicle can not approach site site. Defaults to NULL, i.e. no restrictions are enforced.

Value

Returns a "heumilkr_solution" object, a data.frame() with one row per site-run combination bestowed with additional attributes. Its columns consist of:

  • site - The site index (i.e. the index of the demand vector) associated to the run.

  • run - Identifies the run the site is assigned to.

  • order - Integer values providing the visiting order within each run.

  • vehicle - The vehicle type index (as provided in vehicles) associated to the run.

  • load - The actual load in units of demand on the particular run.

  • distance - The travel distance of the particular run.

Unless a site demand exceeds the vehicle capacities it is always assigned to only a single run.

Details

See the original paper, Clarke, G. and Wright, J.R. (1964) doi:10.1287/opre.12.4.568 , for a detailed explanation of the Clarke-Wright algorithm.

Examples

demand <- c(3, 2, 4, 2)

positions <-
  data.frame(
    pos_x = c(0, 1, -1, 2, 3),
    pos_y = c(0, 1, 1, 2, 3)
  )

clarke_wright(
  demand,
  dist(positions),
  data.frame(n = NA_integer_, caps = 6)
)
#>   site run order vehicle load distance
#> 1    0   0     0       0    5 4.828427
#> 2    1   0     1       0    5 4.828427
#> 3    2   1     0       0    6 8.485281
#> 4    3   1     1       0    6 8.485281