Cost Functions

TransportationPlanningOptimization.jl supports two types of cost functions for arcs, each suited to different transportation scenarios.

LinearArcCost

LinearArcCost represents costs that scale proportionally with the volume or size of commodities transported.

Constructor

LinearArcCost(cost_per_unit_size::Float64)

Cost Calculation

The total cost on an arc is computed as:

cost = cost_per_unit_size * total_size_of_commodities

Example

using TransportationPlanningOptimization
using Dates

arc = Arc(;
    origin_id="A",
    destination_id="B",
    cost=LinearArcCost(5.0),
    travel_time=Day(1)
)

BinPackingArcCost

BinPackingArcCost represents discrete costs based on the number of vehicles, containers, or bins needed to transport commodities.

Constructor

BinPackingArcCost(cost_per_bin::Float64, bin_capacity::Int)

Cost Calculation

Commodities are packed into bins using a (1 dimensional) First-Fit Decreasing (FFD) heuristic:

1. Sort commodities by size (largest first)
2. For each commodity, assign it to the first bin with sufficient remaining capacity
3. Open a new bin if no existing bin can fit the commodity

The total cost is:

cost = cost_per_bin * number_of_bins_needed

Example

using TransportationPlanningOptimization
using Dates

arc = Arc(;
    origin_id="A",
    destination_id="B",
    cost=BinPackingArcCost(100.0, 10),
    travel_time=Day(1)
)

Mixed Networks

You can combine both cost types in the same network:

arcs = [
    Arc(; 
        origin_id="Port", 
        destination_id="Warehouse",
        cost=BinPackingArcCost(1000.0, 20),
        travel_time=Week(2)
    ),
    
    Arc(;
        origin_id="Warehouse",
        destination_id="Customer",
        cost=LinearArcCost(15.0),
        travel_time=Day(1)
    ),
]

This flexibility allows modeling realistic multi-modal transportation networks where different segments have different cost structures.

Advanced: Custom Cost Functions

To implement custom cost logic, create a new type that subtypes AbstractArcCostFunction and implement the required interface. See the API reference for details on the cost function interface.