InvestParameters

[InvestParameters][flixopt.interface.InvestParameters] model investment decisions in optimization problems, enabling both binary (invest/don't invest) and continuous sizing choices with comprehensive cost modeling.

Investment Decision Types

FlixOpt supports two main types of investment decisions:

Binary Investment

Fixed-size investment creating a yes/no decision (e.g., install a 100 kW generator):

$$\label{eq:invest_binary} v_\text{invest} = s_\text{invest} \cdot \text{size}_\text{fixed} $$

With:

$v_\text{invest}$ being the resulting investment size
$s_\text{invest} \in {0, 1}$ being the binary investment decision
$\text{size}_\text{fixed}$ being the predefined component size

Behavior:

$s_\text{invest} = 0$: no investment ($v_\text{invest} = 0$)
$s_\text{invest} = 1$: invest at fixed size ($v_\text{invest} = \text{size}_\text{fixed}$)

Continuous Sizing

Variable-size investment with bounds (e.g., battery capacity from 10-1000 kWh):

$$\label{eq:invest_continuous} s_\text{invest} \cdot \text{size}_\text{min} \leq v_\text{invest} \leq s_\text{invest} \cdot \text{size}_\text{max} $$

With:

$v_\text{invest}$ being the investment size variable (continuous)
$s_\text{invest} \in {0, 1}$ being the binary investment decision
$\text{size}_\text{min}$ being the minimum investment size (if investing)
$\text{size}_\text{max}$ being the maximum investment size

Behavior:

$s_\text{invest} = 0$: no investment ($v_\text{invest} = 0$)
$s_\text{invest} = 1$: invest with size in $[\text{size}\text{min}, \text{size}\text{max}]$

This uses the bounds with state pattern described in Bounds and States.

Optional vs. Mandatory Investment

The mandatory parameter controls whether investment is required:

Optional Investment (mandatory=False, default): $$\label{eq:invest_optional} s_\text{invest} \in {0, 1} $$

The optimization can freely choose to invest or not.

Mandatory Investment (mandatory=True): $$\label{eq:invest_mandatory} s_\text{invest} = 1 $$

The investment must occur (useful for mandatory upgrades or replacements).

Effect Modeling

Investment effects (costs, emissions, etc.) are modeled using three components:

Fixed Effects

One-time effects incurred if investment is made, independent of size:

$$\label{eq:invest_fixed_effects} E_{e,\text{fix}} = s_\text{invest} \cdot \text{fix}_e $$

With:

$E_{e,\text{fix}}$ being the fixed contribution to effect $e$
$\text{fix}_e$ being the fixed effect value (e.g., fixed installation cost)

Examples:

Fixed installation costs (permits, grid connection)
One-time environmental impacts (land preparation)
Fixed labor or administrative costs

Specific Effects

Effects proportional to investment size (per-unit costs):

$$\label{eq:invest_specific_effects} E_{e,\text{spec}} = v_\text{invest} \cdot \text{spec}_e $$

With:

$E_{e,\text{spec}}$ being the size-dependent contribution to effect $e$
$\text{spec}_e$ being the specific effect value per unit size (e.g., €/kW)

Examples:

Equipment costs (€/kW)
Material requirements (kg steel/kW)
Recurring costs (€/kW/year maintenance)

Piecewise Effects

Non-linear effect relationships using piecewise linear approximations:

$$\label{eq:invest_piecewise_effects} E_{e,\text{pw}} = \sum_{k=1}^{K} \lambda_k \cdot r_{e,k} $$

Subject to: $$ v_\text{invest} = \sum_{k=1}^{K} \lambda_k \cdot v_k $$

With:

$E_{e,\text{pw}}$ being the piecewise contribution to effect $e$
$\lambda_k$ being the piecewise lambda variables (see Piecewise)
$r_{e,k}$ being the effect rate at piece $k$
$v_k$ being the size points defining the pieces

Use cases:

Economies of scale (bulk discounts)
Technology learning curves
Threshold effects (capacity tiers with different costs)

See Piecewise for detailed mathematical formulation.

Retirement Effects

Effects incurred if investment is NOT made (when retiring/not replacing existing equipment):

$$\label{eq:invest_retirement_effects} E_{e,\text{retirement}} = (1 - s_\text{invest}) \cdot \text{retirement}_e $$

With:

$E_{e,\text{retirement}}$ being the retirement contribution to effect $e$
$\text{retirement}_e$ being the retirement effect value

Behavior:

$s_\text{invest} = 0$: retirement effects are incurred
$s_\text{invest} = 1$: no retirement effects

Examples:

Demolition or disposal costs
Decommissioning expenses
Contractual penalties for not investing
Opportunity costs or lost revenues

Total Investment Effects

The total contribution to effect $e$ from an investment is:

$$\label{eq:invest_total_effects} E_{e,\text{invest}} = E_{e,\text{fix}} + E_{e,\text{spec}} + E_{e,\text{pw}} + E_{e,\text{retirement}} $$

Effects integrate into the overall system effects as described in Effects, Penalty & Objective.

Integration with Components

Investment parameters modify component sizing:

Without Investment

Component size is a fixed parameter: $$ \text{size} = \text{size}_\text{nominal} $$

With Investment

Component size becomes a variable: $$ \text{size} = v_\text{invest} $$

This size variable then appears in component constraints. For example, flow rate bounds become:

$$ v_\text{invest} \cdot \text{rel}_\text{lower} \leq p(t) \leq v_\text{invest} \cdot \text{rel}_\text{upper} $$

Using the scaled bounds pattern from Bounds and States.

Cost Annualization

Important: All investment cost values must be properly weighted to match the optimization model's time horizon.

For long-term investments, costs should be annualized:

$$\label{eq:annualization} \text{cost}_\text{annual} = \frac{\text{cost}_\text{capital} \cdot r}{1 - (1 + r)^{-n}} $$

With:

$\text{cost}_\text{capital}$ being the upfront investment cost
$r$ being the discount rate
$n$ being the equipment lifetime in years

Example: €1,000,000 equipment with 20-year life and 5% discount rate $$ \text{cost}_\text{annual} = \frac{1{,}000{,}000 \cdot 0.05}{1 - (1.05)^{-20}} \approx €80{,}243/\text{year} $$

Implementation

Python Class: [InvestParameters][flixopt.interface.InvestParameters]

Key Parameters:

fixed_size: For binary investments (mutually exclusive with continuous sizing)
minimum_size, maximum_size: For continuous sizing
mandatory: Whether investment is required (default: False)
effects_of_investment: Fixed effects incurred when investing (replaces deprecated fix_effects)
effects_of_investment_per_size: Per-unit effects proportional to size (replaces deprecated specific_effects)
piecewise_effects_of_investment: Non-linear effect modeling (replaces deprecated piecewise_effects)
effects_of_retirement: Effects for not investing (replaces deprecated divest_effects)

See the [InvestParameters][flixopt.interface.InvestParameters] API documentation for complete parameter list and usage examples.

Used in:

[Flow][flixopt.elements.Flow] - Flexible capacity decisions
[Storage][flixopt.components.Storage] - Storage sizing optimization
[LinearConverter][flixopt.components.LinearConverter] - Converter capacity planning
All components supporting investment decisions

Examples

Binary Investment (Solar Panels)

solar_investment = InvestParameters(
    fixed_size=100,  # 100 kW system
    mandatory=False,  # Optional investment (default)
    effects_of_investment={'cost': 25000},  # Installation costs
    effects_of_investment_per_size={'cost': 1200},  # €1200/kW
)

Continuous Sizing (Battery)

battery_investment = InvestParameters(
    minimum_size=10,  # kWh
    maximum_size=1000,
    mandatory=False,  # Optional investment (default)
    effects_of_investment={'cost': 5000},  # Grid connection
    effects_of_investment_per_size={'cost': 600},  # €600/kWh
)

With Retirement Costs (Replacement)

boiler_replacement = InvestParameters(
    minimum_size=50,  # kW
    maximum_size=200,
    mandatory=False,  # Optional investment (default)
    effects_of_investment={'cost': 15000},
    effects_of_investment_per_size={'cost': 400},
    effects_of_retirement={'cost': 8000},  # Demolition if not replaced
)

Economies of Scale (Piecewise)

battery_investment = InvestParameters(
    minimum_size=10,
    maximum_size=1000,
    piecewise_effects_of_investment=PiecewiseEffects(
        piecewise_origin=Piecewise([
            Piece(0, 100),    # Small
            Piece(100, 500),  # Medium
            Piece(500, 1000), # Large
        ]),
        piecewise_shares={
            'cost': Piecewise([
                Piece(800, 750),  # €800-750/kWh
                Piece(750, 600),  # €750-600/kWh
                Piece(600, 500),  # €600-500/kWh (bulk discount)
            ])
        },
    ),
)

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InvestParameters

Investment Decision Types

Binary Investment

Continuous Sizing

Optional vs. Mandatory Investment

Effect Modeling

Fixed Effects

Specific Effects

Piecewise Effects

Retirement Effects

Total Investment Effects

Integration with Components

Without Investment

With Investment

Cost Annualization

Implementation

Examples

Binary Investment (Solar Panels)

Continuous Sizing (Battery)

With Retirement Costs (Replacement)

Economies of Scale (Piecewise)

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InvestParameters

Investment Decision Types

Binary Investment

Continuous Sizing

Optional vs. Mandatory Investment

Effect Modeling

Fixed Effects

Specific Effects

Piecewise Effects

Retirement Effects

Total Investment Effects

Integration with Components

Without Investment

With Investment

Cost Annualization

Implementation

Examples

Binary Investment (Solar Panels)

Continuous Sizing (Battery)

With Retirement Costs (Replacement)

Economies of Scale (Piecewise)