Bid Lattices and the Value of Flexibility:A Granularity Ratio for Capacity Markets

What the math gives to ML

The paper provides a transferable mechanism for systems whose continuous allocation variables are implemented on a discrete lattice: a dimensionless granularity ratio controls the loss caused by discretization. Positive homogeneity shows that, when the objective and constraints scale together, absolute system size matters only through the ratio between one discrete unit and total capacity. In neural networks, this can be used to design and evaluate granularity-aware quantized action heads, mixture-of-experts routing capacities, or structured sparsity masks, with an explicit feasibility-preserving rounding rule and a predicted discretization-error envelope.