Optimization: Routing

Purpose

This calculator finds the minimum-cost flow from a source node to a target node over a directed network with edge capacities.

It helps you answer a very practical question: if a single direct connection can't (or shouldn't) carry your entire required volume, how should you split it across the available connections so everything still gets through at the lowest possible cost? Instead of guessing which combination of routes to use, you get a ready-to-execute, least-cost dispatch plan.

Background

Problem Domain

Routing optimization here is a minimum-cost flow model, not shortest path alone, because capacities and demanded flow quantity are enforced. This is the same class of problem behind large-scale logistics and network-traffic engines: the cheapest single path is often blocked by capacity, forcing flow to split across multiple routes at once.

Real-World Uses

• Freight routing with lane limits: The cheapest direct lanes may not have enough capacity. Use the model to route required volume through alternate arcs at lowest total transport cost.
• Data/network traffic routing: Link bandwidth is constrained and path costs are non-uniform. Use the model to push feasible minimum-cost flow from origin to destination.
• Multi-hop logistics transfer planning: Shipments may need intermediate nodes because of network topology. Use the model to allocate path flow while satisfying demand and node-balance rules.
• Pipeline/utility dispatch: Target flow must move through a constrained network without breaching segment limits. Use the model to compute least-cost edge-level dispatch quantities.

Inputs

• routing_object: Edge table with columns From, To, Cost, and Capacity. Capacity should use the same quantity unit basis as demand_qty, and Cost is interpreted per one unit of routed flow.
• source_node: Start node that provides net outflow.
• target_node: End node that receives net inflow.
• demand_qty: Required net flow quantity from source_node to target_node. Use the same quantity unit basis as edge Capacity.
• routing_flow_type: Edge flow type. Use continuous for fractional flow or integer for whole-number flow.
• show_zero: Controls output display. Turn on to include zero-flow edges; turn off to show only used edges.

Results

• Summary: High-level routing outcome with Status, Objective, source, target, demand, and total edge flow. This confirms whether required flow is feasible and what minimum transport cost it implies.
• Decision Table: Edge-level dispatch plan (Flow, Capacity, Utilization %, Unit Cost) that shows which arcs carry volume and where network pressure exists.
• Constraint Slack: Slack for edge-capacity and node-conservation constraints, useful for identifying bottleneck links.

Understanding the Calculation

Objective:

• Minimize $\sum_{(i,j)} c_{ij} f_{ij}$.

Constraints:

• Edge cap: $f_{ij} \le \text{Capacity}_{ij}$.
• Flow conservation at each node.
• Source net outflow equals demand_qty; target net inflow equals it.

Example

Default run gives Optimal objective 90 for demand 10 from N1 to N4, using edges:

• N1 -> N3: 10
• N3 -> N4: 10

Interpretation: this path is cheapest while satisfying capacity and flow conservation constraints. If a seemingly obvious direct lane isn't used, check its Capacity — the optimizer routes around any edge, however cheap, the moment it can't carry the required volume.

Important Assumptions and Limitations

• Single source and single target in one solve.
• Linear per-unit edge cost.
• No transit time, reliability, or fixed edge-open costs.