python DEA: by-product NDDF DEA模型

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by-product DEA模型取消了常用的DEA模型中的弱处置性（weak disposability）,可以用来模拟副产品与主产品相关性不强的情景。

如，在电力生产中，若安装了APCD，则空气污染物的产生与电力生产量就不具有强的相关性，应当采用by-product模型。

#!/usr/bin/env python
# coding: utf-8import numpy as np
import pandas as pd
import pulpclass DEAProblem:"""Help on class DEAProblemDEAProblem(inputs, outputs, bad_outs, weight_vector, directional_factor=None, returns='CRS',in_weights=[0, None], out_weights=[0, None],badout_weights=[0, None])DEAProblem solves DEA model using directional distance function.Parameters:inputs: input data, DataFrame dataoutputs: output data, DataFrame databad_outs: undesirable output data, DataFrame dataweight_vector: weights for individual inputs and outputs. List data"""def __init__(self,n_inputs,p_inputs,outputs,bad_outs,weight_vector,directional_factor=None,returns="CRS",in_weights=[0, None],out_weights=[0, None],badout_weights=[0, None],):self.n_inputs = n_inputsself.p_inputs = p_inputsself.outputs = outputsself.bad_outs = bad_outsself.returns = returnsself.weight_vector = (weight_vector  # weight vector in directional distance function)self.J, self.nI = self.n_inputs.shape  # no of DMUs, non-polluting inputs_, self.pI = self.p_inputs.shape  # no of polluting inputs_, self.R = self.outputs.shape  # no of outputs_, self.S = self.bad_outs.shape  # no of bad outputsself._ni = range(self.nI)  # iterate over non-polluting inputsself._pi = range(self.pI)  # iterable over polluting inputsself._r = range(self.R)  # outputsself._s = range(self.S)  # bad_outputself._j = range(self.J)  # DMUsif directional_factor == None:self.gx1 = self.n_inputsself.gx2 = self.p_inputsself.gy = self.outputsself.gb = self.bad_outselse:self.gx1 = directional_factor[: self.nI]self.gx2 = directional_factor[: (self.nI + self.pI)]self.gy = directional_factor[(self.nI + self.pI) : ((self.nI + self.pI) + self.J)]self.gy = directional_factor[((self.nI + self.pI) + self.J) :]self._in_weights = in_weights  # input weight restrictionsself._out_weights = out_weights  # output weight restrictionsself._badout_weights = badout_weights  # bad output weight restrictions# creates dictionary of pulp.LpProblem objects for the DMUsself.dmus = self._create_problems()def _create_problems(self):"""Iterate over the DMU and create a dictionary of LP problems, onefor each DMU."""dmu_dict = {}for j0 in self._j:dmu_dict[j0] = self._make_problem(j0)return dmu_dictdef _make_problem(self, j0):"""Create a by-product technology model. Reference: doi.org/10.1111/deci.12421"""# Set up pulpprob = pulp.LpProblem("".join(["DMU_", str(j0)]), pulp.LpMaximize)self.weights_1 = pulp.LpVariable.dicts("Weight_non_polluting", (self._j), lowBound=self._in_weights[0])  # define the weight for non-pulluting unit in the by-product technology modelself.weights_2 = pulp.LpVariable.dicts("Weight_polluting", (self._j), lowBound=self._in_weights[0])  # define the weight for pulluting unit in the by-product technology model#         self.betax1 = pulp.LpVariable.dicts(#             "scalingFactor_nx", (self._ni), lowBound=0, upBound=1#         ) # scaling factor for non-polluting inputs#         self.betax2 = pulp.LpVariable.dicts(#             "scalingFactor_px", (self._pi), lowBound=0, upBound=1#         ) # scaling factor for polluting inputsself.beta = pulp.LpVariable("scalingFactor", lowBound=0)  # scaling factor#         self.betab = pulp.LpVariable.dicts(#             "scalingFactor_b", (self._s), lowBound=0, upBound=1#         ) # scaling factor for undesirable factor# Set up objective functionprob += pulp.lpSum(self.beta)# Set up constraintsfor ni in self._ni:prob += (pulp.lpSum([(self.weights_1[j0] * self.n_inputs.values[j0][ni])for j0 in self._j])<= self.n_inputs.values[j0][ni])for pi in self._pi:prob += (pulp.lpSum([(self.weights_1[j0] * self.p_inputs.values[j0][pi])for j0 in self._j])<= self.p_inputs.values[j0][pi])# strong disposability for desirable output in non-pulluting processfor r in self._r:prob += (pulp.lpSum([(self.weights_1[j0] * self.outputs.values[j0][r])for j0 in self._j])>= self.outputs.values[j0][r] + self.beta * self.gy.values[j0][r])for pi in self._pi:prob += (pulp.lpSum([(self.weights_2[j0] * self.p_inputs.values[j0][pi])for j0 in self._j])>= self.p_inputs.values[j0][pi])# strong disposability for undesirable output in polluting processfor s in self._s:prob += (pulp.lpSum([(self.weights_2[j0] * self.bad_outs.values[j0][s])for j0 in self._j])<= self.bad_outs.values[j0][s] - self.beta * self.gb.values[j0][s])# Set returns to scaleif self.returns == "VRS":prob += sum([self.weights_1[j] for j in self.weights_1]) == 1prob += sum([self.weights_2[j] for j in self.weights_2]) == 1return probdef solve(self):"""Iterate over the dictionary of DMUs' problems, solve them, and collatethe results into a pandas dataframe."""sol_status = {}sol_weights = {}sol_efficiency = {}for ind, problem in list(self.dmus.items()):problem.solve(pulp.PULP_CBC_CMD(msg=0))sol_status[ind] = pulp.LpStatus[problem.status]sol_weights[ind] = {}for v in problem.variables():sol_weights[ind][v.name] = v.varValuesol_efficiency[ind] = pulp.value(problem.objective)
#             for name, c in list(problem.constraints.items()):
#                 print(name, ":", c, "\t", c.pi, "\t\t", c.slack)return sol_status, sol_efficiency, sol_weights

使用的案例可以见我的Github

代码相关的文章工作还在进行中，代码有用的话，请考虑引用我的论文~

Cite my works

F. Yang, H. Lee. An innovative provincial CO2 emission quota allocation scheme for Chinese low-carbon transition. Technological forecast and social change. 2022. In press.

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python DEA: by-product NDDF DEA模型

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