The cannery problem

A JuMP implementation of the cannery problem from:

Dantzig, Linear Programming and Extensions, Princeton University Press, Princeton, NJ, 1963.

It was originally contributed by Louis Luangkesorn, January 30, 2015.

using JuMP
import GLPK

function example_cannery()
    # Origin plants.
    plants = ["Seattle", "San-Diego"]
    num_plants = length(plants)
    # Destination markets.
    markets = ["New-York", "Chicago", "Topeka"]
    num_markets = length(markets)
    # Capacity and demand in cases.
    capacity = [350, 600]
    demand = [300, 300, 300]
    # Distance in thousand miles.
    distance = [2.5 1.7 1.8; 2.5 1.8 1.4]
    # Cost per case per thousand miles.
    freight = 90
    cannery = Model()
    set_optimizer(cannery, GLPK.Optimizer)
    # Create decision variables.
    @variable(cannery, ship[1:num_plants, 1:num_markets] >= 0)
    # Ship no more than plant capacity
    @constraint(
        cannery, capacity_con[i = 1:num_plants], sum(ship[i, :]) <= capacity[i]
    )
    # Ship at least market demand
    @constraint(
        cannery, demand_con[j = 1:num_markets], sum(ship[:, j]) >= demand[j]
    )
    # Minimize transporatation cost
    @objective(
        cannery,
        Min,
        sum(
            distance[i, j] * freight * ship[i, j]
            for i = 1:num_plants, j = 1:num_markets
        )
    )
    optimize!(cannery)
    println("RESULTS:")
    for i = 1:num_plants
        for j = 1:num_markets
            println("  $(plants[i]) $(markets[j]) = $(value(ship[i, j]))")
        end
    end
    return
end

example_cannery()

RESULTS:
  Seattle New-York = 50.0
  Seattle Chicago = 300.0
  Seattle Topeka = 0.0
  San-Diego New-York = 250.0
  San-Diego Chicago = 0.0
  San-Diego Topeka = 300.0

View this file on Github.

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