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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 (i.e. "depot") which is the origin of all runs.

Usage

clarke_wright(
  demand,
  distances,
  vehicles,
  restrictions = data.frame(vehicle = integer(), site = integer())
)

Arguments

demand

A numeric() vector consisting of "demands" indexed by sites. The ith entry refers to the demand of site i that is requested by the source depot (origin). The length of the vector equals the number of sites N. The units of demand values need to match the units of vehicle capacity values. NA values are not allowed. Negative demand values are also allowed and are interpreted as freight that needs to be delivered from a site to the source source depot (origin), i.e. "backhaul". Note that sites with negative demands can only be visited after after sites with positive demand.

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 location. 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 an empty data.frame(), i.e. no restrictions are enforced.

Value

Returns a "heumilkr_solution" object, a named list() of three data.frame()s with names "runs", "sites" and "visits", bestowed with additional attributes.

  • runs: Each record reflects a single run/tour.

    • run - A run identifier.

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

    • max_load - The maximal load of the vehicle on this run. It is always smaller or equal the vehicle capacity.

    • distance - The travel distance of the particular run.

  • sites: Each record reflect a site with demand. Its columns consist of:

    • site - A site identifier.

    • demand - The site demand. This is supplied as an input.

  • visits: Each record reflects a run visit of a particular site. It is implied that each run starts and ends at the origin. Its columns consist of:

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

    • site - The site index (i.e. the index of the (1-indexed) demand vector) associated to the run.

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

    • load - The departing load on site site in units of demand per 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)
)
#> $runs
#>   run vehicle max_load distance
#> 1   0       0        5 4.828427
#> 2   1       0        6 8.485281
#> 
#> $sites
#>   site demand
#> 1    0      3
#> 2    1      2
#> 3    2      4
#> 4    3      2
#> 
#> $visits
#>   run site order load
#> 1   0    0     0    2
#> 2   0    1     1    0
#> 3   1    2     0    2
#> 4   1    3     1    0
#>