PPolySim OS
Operations & Economics Pack · Multi-Solver

Facility Location

Demand & cost. This multi-solver chains 2 solvers into a single guided workflow — run each step in order and carry the result forward.

Workflow steps
  1. shortest-path
  2. linear-programming
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1

Shortest Path

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Shortest Path (Dijkstra)Live

Controls

Dijkstra's algorithm finds the shortest path from a source (A, blue) to every other node in a weighted graph, always expanding the closest unvisited node next. The number inside each node is its shortest distance from A; the green edges trace the optimal route to your chosen destination. It powers GPS routing, network protocols, and logistics. Click any node to re-target.

Size a graph for the exportable Python solver below — the diagram stays a fixed six-node example.

Presets

▶ Run in Python

Data Inspector

SourceA
DestinationF
Shortest distance11
Graph size6 nodes
Est. edges9 (60%)

Governing equation

Reading this result: Dijkstra grows a set of finalized nodes, each step expanding the nearest unvisited one and relaxing its outgoing edges. Because all weights are non-negative, the first time a node is finalized its distance is already optimal. This configuration describes 6 nodes and about 9 weighted edges (density 60%).

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

2

Linear Programming

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Linear ProgrammingLive

Controls

Presets

Linear programming maximizes a linear objective subject to linear constraints. The constraints carve out a convex feasible region (shaded), and the optimum always sits at a corner. Slide the objective coefficients and watch the optimal vertex jump between corners — the geometric idea behind the simplex algorithm that runs global logistics and finance.

▶ Run in Python

Data Inspector

Optimal x6.00
Optimal y4.00
Objective value26.00

Governing equation

Reading this result: Maximizing 3·x + 2·y lands the optimum at the corner (6.0, 4.0) worth 26.0 — a linear objective over a convex region always peaks at a vertex, so sliding c₁/c₂ just makes the solution hop between corners.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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More in the Operations & Economics pack

Frequently asked questions

What is the Facility Location multi-solver?
Facility Location is a guided workflow that chains 2 individual PolySim solvers into one end-to-end analysis, piping each result into the next step.
Is it free to use?
Yes. Every step runs entirely in your browser using real numerics — no install, no account, no cloud cost. Custom or private solver packs are available as a paid service.