Hi there,

I’m trying to formulate an optimization model that maximizes profit while dealing with the transportation of raw supplies and production of goods. The profit calculation is lengthy and depends upon both decision variables. So, instead of including it in the Objective statement, I defined a function that takes as inputs the decision variables and performs the calculations necessary for profit. However, I receive the following error:

MethodError: Cannot `convert`

an object of type AffExpr to an object of type Float64

Here is my MWE:

```
using CSV, DataFrames, JuMP, Gurobi
# Load input data
df = DataFrame(a = rand(5),b = rand(5))
# Number of municipalities
n = nrow(df)
# Manure generated
S = df[!, 1]
# Initialize model
model = Model(Gurobi.Optimizer)
# Load parameters
param = 5
# Decision Variables
@variable(model, x[1:n, 1:2], Bin) # Biomethane (1) and Electricity (2) production in muni i
@variable(model, y[1:n,1:n] >= 0) # Manure transported (kg/day) from muni i to j
# Here is a function to calculate the network wide profit from the production of Biomethane and/or Electricity.
# Profit is defined as revenue from Biomethane and Electricity minus infrastructure and transportation costs.
# This function is designed to be called in the objective function.
function network_profit(df::DataFrame, y::Matrix{VariableRef}, x::Matrix{VariableRef})
# Some logic to calculate profit based on manure amount and decision (either biomethane or electricity)
# Return calculated profit
n = nrow(df)
# initialize manure column ("ArgumentError: Cannot assign to non-existent column")
df[!, :manure_supply_kg_day] = df[!,1]
for i in 1:n
for j in 1:n
if i != j # Avoid subtracting or adding when the source and destination are the same
# Subtract resources sent from municipality 'i' to 'j'
df[i, :manure_supply_kg_day] -= y[i,j]
# Add resources received by municipality 'i' from 'j'
df[i, :manure_supply_kg_day] += y[j,i]
end
end
end
# digester size
df[!, :digester_size_m3] = df[!, :manure_supply_kg_day] ./ 1000 .* 17
# 1000...manure density? ; 17...digestion time?
# digester capital cost
df[!, :digester_capital_cost_USD] = param .* (df[!, :digester_size_m3] ./ param) .^ param
# annualized digester capital cost (USD/yr)
df[!, :annualized_digester_capital_cost_USD_yr] = df[!, :digester_capital_cost_USD] .* (param / 100)
# digester O&M (USD/yr)
df[!, :digester_OM_USD_yr] = df[!, :digester_capital_cost_USD] .* param
# biogas production (m3/day)
df[!, :biogas_production_m3_day] = df[!, :manure_supply_kg_day] .* df[!, 2]
# Apply muni specific CH4 yield to the transported manure
# Add methane for incoming manure and subtract methane for outgoing manure,
# while taking into account the specific CH4 yield of the municipality where the manure originates.
# initialize methane column ("ArgumentError: cannot assign to a non-existent column")
df[!, :methane_production_m3_day] = zeros(nrow(df))
for i in 1:n
for j in 1:n
if i != j # Avoid subtracting or adding when the source and destination are the same
# Subtract resources sent from municipality 'i' to 'j'
df[i, :methane_production_m3_day] -= y[i,j] * df[i, 2]
# Add resources received by municipality 'i' from 'j'
df[i, :methane_production_m3_day] += y[j,i] * df[i, 2]
end
end
end
# Biomethane calculations
# daily biomethane production (m3/day)
df[!, :daily_biomethane_production_m3_day] = df[!, :methane_production_m3_day] ./ 0.94
# 0.94
# hourly biomethane production (m3/hr)
df[!, :hourly_biomethane_production_m3_hr] = df[!, :daily_biomethane_production_m3_day] ./ 24
# biomethane capital cost (USD)
df[!, :biomethane_capital_cost_USD] = df[!, :hourly_biomethane_production_m3_hr] .* param
# daily biomethane revenue (USD/day)
df[!, :daily_biomethane_revenue_USD_day] = df[!, :daily_biomethane_production_m3_day] .* param
# annual biomethane revenue (USD/day)
df[!, :annual_biomethane_revenue_USD_yr] = df[!, :daily_biomethane_revenue_USD_day] .* 365
# annualized biomethane capital cost (USD/yr)
df[!, :annualized_biomethane_capital_cost_USD_yr] = df[!, :biomethane_capital_cost_USD] .* (param / 100)
# biomethane O&M (USD/yr)
df[!, :biomethane_OM_USD_yr] = df[!, :daily_biomethane_production_m3_day] .* param .* 365
# annual biomethane cost
df[!, :annual_biomethane_cost] = df[!, :annualized_biomethane_capital_cost_USD_yr] .+ df[!, :biomethane_OM_USD_yr]
# annual biomethane profit
df[!, :annual_biomethane_profit] = df[!, :annual_biomethane_revenue_USD_yr] .- df[!, :annual_biomethane_cost]
# Electricity calculations
# daily electricity generated (MWh/day)
df[!, :daily_electricity_generated_MWh_day] = df[!, :methane_production_m3_day] .* param .* 0.0105
# daily electricity revenue (USD/day)
df[!, :daily_electricity_revenue_USD_day] = df[!, :daily_electricity_generated_MWh_day] .* param
# annual electricity revenue (USD/yr)
df[!, :annual_electricity_revenue_USD_yr] = df[!, :daily_electricity_revenue_USD_day] .* 365
# electricity capital cost (USD)
df[!, :electricity_capital_cost_USD] = param .* (df[!, :daily_electricity_generated_MWh_day] ./ 24)
# annualized electricity capital cost (USD/yr)
df[!, :annualized_electricity_capital_cost_USD_yr] = df[!, :electricity_capital_cost_USD] .* (param / 100)
# electricity O&M (USD/yr)
df[!, :electricity_OM_USD_yr] = df[!, :electricity_capital_cost_USD] .* (param / 100)
# annual electricity cost
df[!, :annual_electricity_cost] = df[!, :annualized_electricity_capital_cost_USD_yr] .+ df[!, :electricity_OM_USD_yr]
# annual electricity profit
df[!, :annual_electricity_profit] = df[!, :annual_electricity_revenue_USD_yr] .- df[!, :annual_electricity_cost]
# Aggregate calculations
# infrastructure cost ($ annualized)
df[!, :infrastructure_cost_USD_annualized] = df[!, :annualized_digester_capital_cost_USD_yr] .+ df[!, :digester_OM_USD_yr] .+ df[!, :annualized_biomethane_capital_cost_USD_yr] .+ df[!, :biomethane_OM_USD_yr] .+ df[!, :annualized_electricity_capital_cost_USD_yr] .+ df[!, :electricity_OM_USD_yr]
# annual energy revenue (USD/yr)
df[!, :annual_energy_revenue_USD_yr] = df[!, :annual_biomethane_revenue_USD_yr] .+ df[!, :annual_electricity_revenue_USD_yr]
# biogas GHG savings
df[!, :annual_biogas_GHG_savings] = df[!, :methane_production_m3_day] .* param .* param .* 365
# manure collection emissions (kg/yr)
df[!, :manure_collection_emissions_kg_yr] = df[!, 1] .* (param .+ param) .* 365
# annual GHG offset (kg/yr)
df[!, :annual_GHG_savings_kg_yr] = df[!, :annual_biogas_GHG_savings] .- df[!, :manure_collection_emissions_kg_yr]
# annual GHG offset (MM kg/yr)
df[!, :annual_GHG_savings_MM_kg_yr] = df[!, :annual_GHG_savings_kg_yr] ./ 1000000
# Aggregate calculations for Optimization
# Initialize values
biometh_rev = 0
elect_rev = 0
biometh_inf = 0
elect_inf = 0
biometh_rev = sum(df[!, :annual_biomethane_revenue_USD_yr] .* x[:,1])
elect_rev = sum(df[!, :annual_electricity_revenue_USD_yr] .* x[:,2])
df[!, :elect_infrastructure_cost_USD_annualized] = df[!, :annualized_digester_capital_cost_USD_yr] .+ df[!, :digester_OM_USD_yr] .+ df[!, :annualized_electricity_capital_cost_USD_yr] .+ df[!, :electricity_OM_USD_yr]
df[!, :biometh_infrastructure_cost_USD_annualized] = df[!, :annualized_digester_capital_cost_USD_yr] .+ df[!, :digester_OM_USD_yr] .+ df[!, :annualized_biomethane_capital_cost_USD_yr] .+ df[!, :biomethane_OM_USD_yr]
biometh_inf = sum(df[!, :biometh_infrastructure_cost_USD_annualized] .* x[:,1])
elect_inf = sum(df[!, :elect_infrastructure_cost_USD_annualized] .* x[:,2])
network_profit = biometh_rev + elect_rev - biometh_inf - elect_inf
return network_profit
end
# Objective
@objective(model, Max, network_profit(df, y, x))
# Constraints
# Material Balance: do not export more manure than available in each muni
for i=1:n
@constraint(model, sum(y[i,j] for j=1:n) <= S[i])
end
# Processing: each muni can process either Biomethane (1) or Electricity (2)
for j=1:n
@constraint(model, sum(x[i,1] + x[i,2] for i=1:n) <= 1)
end
optimize!(model)
```