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Objective

In any Mat-dp system, there must be an objective to be achieved.
One may wish to maximise the runs of a certain process, and/or minimise the runs of another.

An objective function in Mat-dp core is expressed very similarly to a constraint expression: an objective helps to find an 'optimal' valid means of operation, while a constraint defines what is valid in the first place.

Explanation

An objective function will always aim to minimise its result.

Below is an example of a minimisation objective function:

objective = 5 * coal_power_plant + gas_power_plant + 4 * oil_power_plant

Lets take one section of the function: 5 * coal_power_plant
The process variable coal_power_plant by itself contributes +1 to the value of the objective function each time it 'runs'.
5 * is a multiplier to the runs of process variable coal_power_plant - this is typically called a 'weighting'.
As a consequence of the 5 * weighting, during Measurement the solution will favour reducing runs of the coal_power_plant five times more than runs of the gas_power_plant.

Worked Example

An objective makes the most sense in the context of an optimisation problem.

Below is an optimisation problem concerning how to provide a power grid with sufficient kwh of electricity, while minimizing CO2 release. The constraints involve not exceeding the capacity of each plant, while still meeting the demand of the grid.

There exists the following processes:

  • A coal power plant, producing 100kwh for every 1 tonnes of CO2.
  • A gas power plant, producing 100kwh for every 0.6 tonnes of CO2.
  • An organic waste power plant, producing 100kwh for every 0.8 tonnes of CO2.
  • The atmosphere, which consumes any produced CO2.
  • The Energy grid, which consumes any produced electricity.
    In a MAT-DP Core system, any produced resource must be eventually consumed - unless otherwise specified.

The following constraints:

  • The coal power plant cannot produce more than 2,000kwh/day.
  • The gas power plant cannot produce more than 1,500kwh/day.
  • The organic waste power plant cannot produce more than 1,000kwh/day.
  • The combined output of all three power plants must meet the needs of the grid: 2,200kwh/day.

The optimisation objective of:

  • Minimise the amount of CO2 produced by the system.

Here is a diagram to help illustrate the situation:

Let's break this problem into code:

from mat_dp_core import Resources, Processes, GeConstraint, LeConstraint, Measure

r = Resources()
electricity = r.create("electricity", "kwh")
carbon_dioxide = r.create("CO2", "tonnes")

p = Processes()
coal_plant = p.create("Coal Power Plant", (carbon_dioxide, 1), (electricity, 100))
gas_plant = p.create("Gas Power Plant", (carbon_dioxide, 0.6), (electricity, 100))
organic_plant = p.create("Organic Mass Power Plant", (carbon_dioxide, 0.8), (electricity, 100))
environment = p.create("The Atmosphere", (carbon_dioxide, -1))
grid = p.create("The Energy Grid", (electricity, -100))

coal_capacity = LeConstraint("Coal Plant Capacity 2,000kwh", coal_plant, 20)
gas_capacity = LeConstraint("Gas Plant Capacity 1,500kwh", gas_plant, 15)
organic_capacity = LeConstraint("Organic Plant Capacity 1,000kwh", organic_plant, 10)
grid_needs = GeConstraint("Grid Requirement of 2,200kwh", grid, 22)

# Objective function:
# objective = 1 * coal_plant + 0.8 * organic_plant + 0.6 * gas_plant
# Is equivalent to:
objective = environment

It may seem odd that environment's runs alone are equivalent to the weighted runs of each power plant. Keep in mind that the system will always aim to reach net nil resources; if the power plants are the only producers of CO2, then the only consumer (environment) encapsulates all of their production in its runs.
More complicated examples can be found in the cookbook.

Please read on to the measure section to see this problem completed.