InteractiveMap of Operations Research
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MethodIntermediate04.02
Networks, Games & Systems

Network Optimization

Flows, paths, matchings, and connectivity on graphs.

Overview

Network Optimization focuses on flows, paths, matchings, and connectivity on graphs. In the map of OR, it connects Shortest path, Max flow, Min-cost flow to decisions that must be modeled, solved, explained, and revised as evidence changes.

Many OR problems live on networks: shortest paths, max flow, min-cost flow, assignment, routing. Specialized algorithms scale far beyond generic LP. The practical use case is clearest in Logistics, Telecom, Transit, Supply chains, where the method helps turn constraints and tradeoffs into a decision artifact someone can inspect.

Core ideas

Shortest path

Finds least-cost movement across a graph and is a primitive inside many larger models.

Max flow

Measures throughput under arc capacities and exposes bottlenecks in networks.

Min-cost flow

Combines routing and cost minimization with supply, demand, and capacity balances.

Matching

Pairs entities while respecting compatibility, capacity, or stability rules.

Routing

Routing is a core checkpoint for Network Optimization: define it concretely, attach units or rules where possible, and test whether stakeholders interpret it the same way.

How to use it

  1. 1Start with Logistics: write the decision, time horizon, actors, and objective in operational language.
  2. 2Translate the problem into Shortest path, Max flow, and Min-cost flow; define units and data sources for each one.
  3. 3Build a small instance of Network Optimization that can be solved or simulated by hand inspection before using full production data.
  4. 4Compare the recommendation against a baseline policy, not just against mathematical optimality.
  5. 5Document assumptions, sensitivity results, and the conditions under which the recommendation should be revisited.

Applications

LogisticsTelecomTransitSupply chains
  • Logistics: compare feasible policies, quantify the operating tradeoffs, and make the assumptions behind the recommendation visible.
  • Telecom: compare feasible policies, quantify the operating tradeoffs, and make the assumptions behind the recommendation visible.
  • Transit: compare feasible policies, quantify the operating tradeoffs, and make the assumptions behind the recommendation visible.
  • Supply chains: compare feasible policies, quantify the operating tradeoffs, and make the assumptions behind the recommendation visible.

Common pitfalls

  • Applying Network Optimization because the label sounds appropriate while leaving the actual decision boundary vague.
  • Treating Shortest path as a technical detail instead of a modeling choice that affects the recommendation.
  • Reporting one answer without showing sensitivity to demand, capacity, costs, or behavioral assumptions.
  • Ignoring implementation details such as data quality, explainability, ownership, and how users will override bad recommendations.

Resources