Fix a quantity that is data in one model and a decision in another#

This guide shows how to write one specification file (spec) for a quantity such as the size of a plant. In one spec with data attached (model) the solver chooses the quantity, and in another you attach it as data. In a planning study the solver sizes each plant, and in an operational study of the existing fleet you fix each size at today's capacity. You run both from the same spec, so the math cannot drift between them. You need mathspec installed.

Declare the quantity as a variable#

Declare the quantity as a variable, with bounds set to two parameters. Here size is the size of each plant, and rate and stock are the variables that size limits:

dimensions:
  plant: { dtype: str }
  time: { dtype: int }

parameters:
  size_min: { dims: [plant] }
  size_max: { dims: [plant] }
  relmax: { dims: [plant] }

variables:
  size:
    dims: [plant]
    bounds: { lower: size_min, upper: size_max }
  rate: { dims: [plant, time], bounds: { lower: 0 } }
  stock: { dims: [plant], bounds: { lower: 0 } }

Write every rule against the variable#

Write each limit that the size sets as a constraint against size:

constraints:
  rate_max:
    dims: [plant, time]
    expression: rate - relmax * size <= 0
  stock_max:
    dims: [plant]
    expression: stock <= size

rate_max is one constraint whether the solver chooses size or you attach it as data. stock_max limits the stock of each plant to its size. stock_max is a constraint and not a bound, because mathspec refuses upper: size in the bounds of a variable.

Even where you fix size with equal bounds (pin it), a product of size and another variable, such as an on/off binary, is quadratic.

Pin the variable in the data#

Where you attach the quantity as data, pin the variable. Attach the same value to size_min and size_max for each plant whose size is fixed. Where the two bounds differ, the solver chooses the size between them.

Check the spec#

Put the two fences in one file, spec.yaml, and run check on it:

python -m mathspec check spec.yaml

import mathspec as ms

for note in ms.advice('spec.yaml'):
    print(note)

The command and the Python loop print nothing, because mathspec accepts the spec and has no remark to make about it (advice). You then use the same file as the spec of both models.