optimization.jl

# Full example here https://github.com/JuliaOpt/JuMP.jl/blob/master/examples/cannery.jl

@variable(cannery, ship[1:num_plants, 1:num_markets] >= 0)

    # Ship no more than plant capacity
    @constraint(cannery, capacity_con[i in 1:num_plants],
        sum(ship[i,j] for j in 1:num_markets) <= capacity[i]
    )

    # Ship at least market demand
    @constraint(cannery, demand_con[j in 1:num_markets],
        sum(ship[i,j] for i in 1:num_plants) >= demand[j]
    )

    # Minimize transporatation cost
    @objective(cannery, Min, sum(distance[i, j] * freight * ship[i, j]
        for i in 1:num_plants, j in 1:num_markets)