An environmental protection industry sewage treatment capacity prediction method and system based on big data

Abstract

The present application relates to the field of environmental protection industry wastewater treatment technology, and discloses a kind of environmental protection industry wastewater treatment capacity prediction method and system based on big data, initial data is collected from the data source of multiple parties of industrial enterprises, municipal pipe network and meteorological department, and the initial data collected is integrated;Data cleaning is carried out on the integrated data, and abnormal values and missing values in the data are removed, and target features are extracted from the preprocessed data;The target feature is used as the input of the LSTM model, and the output is the wastewater treatment capacity prediction value in the future period;According to the prediction result, the optimal equipment start-stop, load distribution scheme is solved, and the resource allocation is optimized;The present application considers the influence of various factors on wastewater treatment capacity, improves the accuracy and reliability of prediction, and provides strong support for the planning and management of environmental protection industry.

Description

Technical Field

[0001] This invention relates to the field of wastewater treatment technology in the environmental protection industry, specifically to a method and system for predicting wastewater treatment volume in the environmental protection industry based on big data. Background Technology

[0002] With the acceleration of urbanization and rapid industrial development, the prediction of wastewater treatment volume is crucial for the planning and management of the environmental protection industry. Accurate wastewater treatment volume prediction can help wastewater treatment plants rationally plan the operation of treatment equipment, optimize resource allocation, and reduce treatment costs. It also helps environmental protection departments formulate effective pollution control policies. However, current wastewater treatment volume prediction methods often only consider a single data source, such as historical data from municipal pipe networks, ignoring the impact of industrial wastewater discharge and meteorological factors on wastewater treatment volume, resulting in low prediction accuracy. Furthermore, traditional prediction models typically employ simple statistical methods or time series models, which are ill-suited for handling complex multi-source data and nonlinear relationships, failing to meet the needs of practical applications. Summary of the Invention

[0003] The purpose of this invention is to solve the above problems by designing a method and system for predicting wastewater treatment volume in the environmental protection industry based on big data.

[0004] The first aspect of this invention provides a method for predicting wastewater treatment volume in the environmental protection industry based on big data, the method comprising the following steps:

[0005] Initial data was collected from multiple sources, including industrial enterprises, municipal pipelines, and meteorological departments, and then integrated.

[0006] The integrated data is cleaned to remove outliers and missing values, and the target features are extracted from the preprocessed data.

[0007] The target features are used as input to the LSTM model, and the output is a predicted value of wastewater treatment volume over a future period of time.

[0008] Based on the prediction results, the optimal equipment start-up and shutdown and load allocation schemes are solved to optimize resource allocation.

[0009] Optionally, in a first implementation of the first aspect of the present invention, the step of collecting initial data from multiple data sources, including industrial enterprises, municipal pipelines, and meteorological departments, and integrating the collected initial data, includes:

[0010] Establish multi-source data acquisition interfaces to collect production data, water consumption, and wastewater discharge from industrial enterprise production management systems;

[0011] Utilize IoT sensors to acquire sewage flow and water quality data from municipal pipeline monitoring systems;

[0012] Rainfall, temperature, humidity, and wind speed data are obtained from meteorological departments through open meteorological data interfaces;

[0013] The initial data collected is converted into a new format. ETL tools are used to extract and transform data from multiple sources and load it into a distributed data warehouse, forming integrated data that includes timestamps and data source identifiers.

[0014] Optionally, in a second implementation of the first aspect of the present invention, the step of cleaning the integrated data to remove outliers and missing values ​​includes:

[0015] The box plot method based on IQR calculates the first quartile Q1 and the third quartile Q3 in the integrated data, identifies outlier data points that are less than Q1-1.5×IQR or greater than Q3+1.5×IQR, and marks them as outliers. Outliers are then processed by linear interpolation based on the preceding and following data.

[0016] For missing values, based on the time series correlation of the data, interpolation methods based on trend and seasonal terms are used to fill in the missing values, resulting in preprocessed data.

[0017] Optionally, in a third implementation of the first aspect of the present invention, the step of extracting target features from the preprocessed data includes:

[0018] In the preprocessed data, the wastewater treatment volume data is used as the target variable, and the remaining data are used as candidate feature variables.

[0019] The mutual information method is used to calculate the mutual information value between each candidate feature variable and the target variable in turn. The mutual information values ​​of each candidate feature are sorted to form a candidate feature sequence based on the size of the mutual information values.

[0020] From the candidate feature sequence, select the top N candidate features as the target features, where N is the threshold number of features.

[0021] Optionally, in the fourth implementation of the first aspect of the present invention, the step of using the target features as input to the LSTM model and outputting a predicted value of wastewater treatment volume over a future period includes:

[0022] Construct an LSTM model, which consists of an input layer, multiple LSTM hidden layers, and an output layer;

[0023] The target features are received through the input layer and divided into a sequence input according to the time step.

[0024] The LSTM units in the hidden layer capture long-term time dependencies and complex nonlinear patterns in wastewater treatment data through the coordinated operation of forget gates, input gates, and output gates.

[0025] The output layer maps the output of the hidden layer to the predicted wastewater treatment volume over a future period through a fully connected layer.

[0026] Optionally, in the fifth implementation of the first aspect of the present invention, the Adam optimization algorithm is used to train the LSTM model, and the loss function is a weighted sum of mean squared error and mean absolute error.

[0027] During training, the 5-fold cross-validation method is used to evaluate the model's performance and the hyperparameters are dynamically adjusted. Training is stopped when the loss no longer decreases after 10 consecutive training epochs, and the final LSTM model is obtained. The hyperparameters include the learning rate, the number of hidden layer units, and the training batch size.

[0028] Optionally, in a sixth implementation of the first aspect of the present invention, the step of solving for the optimal equipment start-up and shutdown and load allocation scheme and optimizing resource allocation based on the prediction results includes:

[0029] Based on the predicted wastewater treatment volume, the equipment operating cost, energy consumption, treatment capacity limitations, and predicted water volume are transformed into linear constraints and objective functions.

[0030] The optimal equipment start-up and shutdown times and load allocation scheme are obtained by using a mixed-integer linear programming algorithm.

[0031] A second aspect of this invention provides a wastewater treatment volume prediction system for the environmental protection industry based on big data, the system comprising:

[0032] The data integration module is used to collect initial data from multiple data sources, including industrial enterprises, municipal pipelines, and meteorological departments, and to integrate the collected initial data.

[0033] The data processing module is used to clean the integrated data, remove outliers and missing values, and extract target features from the preprocessed data.

[0034] The model output module is used to take the target features as input to the LSTM model and output the predicted value of sewage treatment volume over a future period of time.

[0035] The optimization configuration module is used to solve for the optimal equipment start-up and shutdown and load distribution scheme based on the prediction results, thereby optimizing resource allocation.

[0036] The technical solution provided by this invention collects initial data from multiple data sources, including industrial enterprises, municipal pipe networks, and meteorological departments, and integrates the collected initial data. The integrated data is then cleaned to remove outliers and missing values, and target features are extracted from the preprocessed data. These target features are used as input to an LSTM model, which outputs a predicted wastewater treatment volume over a future period. Based on the prediction results, the optimal equipment start-up and shutdown and load allocation schemes are solved to optimize resource allocation. This invention considers the impact of multiple factors on wastewater treatment volume, improving the accuracy and reliability of predictions and providing strong support for the planning and management of the environmental protection industry. Attached Figure Description

[0037] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention.

[0038] Figure 1 A flowchart illustrating a big data-based wastewater treatment volume prediction method for the environmental protection industry, provided in an embodiment of the present invention.

[0039] Figure 2 This is a schematic diagram of the structure of the wastewater treatment volume prediction system for the environmental protection industry based on big data, provided in an embodiment of the present invention. Detailed Implementation

[0040] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a particular order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” or “having,” and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, apparatus, product, or device that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or devices.

[0041] For ease of understanding, the specific process of the embodiments of the present invention is described below. Please refer to [link / reference]. Figure 1 The flowchart of the wastewater treatment volume prediction method for the environmental protection industry based on big data provided in this embodiment of the invention includes the following steps:

[0042] Step 101: Collect initial data from multiple data sources, including industrial enterprises, municipal pipelines, and meteorological departments, and integrate the collected initial data.

[0043] In this embodiment, a multi-source data acquisition interface is established to collect production data, water consumption, and drainage volume from the industrial enterprise production management system; wastewater flow and water quality data are obtained from the municipal pipeline monitoring system using IoT sensors; rainfall, temperature, humidity, and wind speed data are obtained from the meteorological department through the meteorological data open interface; the initial data collected is format-converted, and the multi-source data is extracted and converted using ETL tools and loaded into a distributed data warehouse to form integrated data containing timestamps and data source identifiers.

[0044] Step 102: Clean the integrated data to remove outliers and missing values, and extract target features from the preprocessed data.

[0045] In this embodiment, all data for each data feature, such as industrial enterprise drainage volume, municipal pipe network sewage flow, and rainfall, are arranged in ascending order of value. In this ordered data sequence, the first quartile Q1 and the third quartile Q3 are determined by calculating the data position. Specifically, the data sequence is divided into four equal parts. Q1 is the data located at the 25th percentile. If the position is not an integer, it is determined by the weighted average of adjacent data. Q3 is the data located at the 75th percentile. This provides a key benchmark for subsequent outlier judgment.

[0046] Based on the calculated Q1 and Q3, the interquartile range (IQR) is calculated (IQR = Q3 - Q1). Then, the outlier range is determined to be data points that are less than Q1 - 1.5 × IQR or greater than Q3 + 1.5 × IQR. All data for each data feature are traversed, and data within the outlier range are marked as outliers. For the marked outliers, a linear interpolation method based on the preceding and following data is used for processing. Taking the abnormal sewage flow data at a certain moment as an example, the normal flow data at the adjacent moments before and after this moment are used to estimate a reasonable flow value through linear calculation, and this value is used to replace the outlier.

[0047] To address missing values ​​in the data, a seasonal decomposition method is employed based on the time-series correlation of the data. First, the time-series data is decomposed into trend, seasonal, and random components. Historical data is analyzed to determine the seasonal cycle of the data, such as daily, weekly, or monthly cycles. By statistically analyzing data patterns within the same seasonal cycle and combining this with the current data's trend component, the trend and seasonal characteristic values ​​corresponding to the missing values ​​are estimated. Finally, the estimated values ​​of the trend and seasonal components are combined to obtain the interpolation results for the missing values, completing the data imputation and resulting in complete and accurate preprocessed data.

[0048] In this embodiment, wastewater treatment volume data is explicitly designated as the target variable in the preprocessed data, while the remaining data are used as candidate feature variables. All data is checked to ensure that the data types are consistent and meet the requirements of subsequent calculations. If there are data format issues, appropriate conversions are performed to ensure that the candidate feature variables and the target variable are computable.

[0049] The mutual information method is used to calculate the mutual information value between each candidate feature variable and the wastewater treatment volume in turn. In the mutual information calculation process, the joint probability distribution and the marginal probability distribution of the candidate feature variable and the target variable are first statistically analyzed. The dependency between the two variables is measured by the probability distribution. The higher the dependency, the greater the mutual information value. This calculation process will traverse all candidate feature variables to obtain the mutual information value result corresponding to each candidate feature and the target variable.

[0050] The mutual information values ​​of each candidate feature are sorted from largest to smallest to form a candidate feature sequence based on the mutual information value, so that features with a greater potential impact on wastewater treatment volume prediction are placed at the beginning of the sequence, and features with a smaller impact are placed at the end.

[0051] Set a threshold N for the number of features to be selected. From the sorted candidate feature sequence, select the top N candidate features as the key features to be used as the final model input, and discard the remaining candidate features. This completes the feature extraction work based on mutual information from the preprocessed data, and obtains a feature set for subsequent model construction and training.

[0052] Step 103: Use the target features as input to the LSTM model and output the predicted wastewater treatment volume for a future period of time.

[0053] In this embodiment, the model is defined as consisting of an input layer, multiple LSTM hidden layers, and an output layer. The input layer is responsible for receiving the target feature data after feature extraction. This data covers key information such as time features, industrial enterprise features, municipal pipeline network features, and meteorological features. Multiple LSTM hidden layers are connected in sequence, and each layer contains a certain number of LSTM units. The number of units is determined according to the complexity of the data. The multi-layer structure enhances the model's ability to capture deep patterns in the data. The output layer is connected to the last LSTM hidden layer and adopts a fully connected layer form to transform the information processed by the hidden layer into specific predicted values ​​of sewage treatment volume.

[0054] After receiving the target features, the input layer segments the feature data according to a preset time step to form continuous time series segments. For example, if the time step is set to 24, the feature data of every 24 consecutive moments are combined into a sequence input. This division method enables the model to predict the future sewage treatment volume based on the feature change trend over a period of time, which is in line with the logic of using past data to infer the future in time series prediction and lays the foundation for the subsequent hidden layer to capture time dependencies.

[0055] Each LSTM hidden layer contains a forget gate, an input gate, and an output gate. These three gates work together to filter and pass information. The forget gate decides which historical information to discard based on the current input and the cell state at the previous time step, such as filtering out early data that is irrelevant to the current prediction. The input gate determines which new information needs to be stored in the cell state, such as the key change of a recent surge in rainfall. The output gate determines the information to be output to the next time step based on the current cell state and the input information. Through this gating mechanism, the LSTM unit can effectively preserve important long-term temporal dependencies and handle complex nonlinear patterns in the data, avoiding the gradient vanishing or exploding problems of traditional recurrent neural networks.

[0056] The fully connected layer of the output layer integrates the feature vector output by the last LSTM hidden layer and maps it to the predicted value of sewage treatment volume in the future through linear transformation and activation function. For example, if it is necessary to predict the sewage treatment volume in the next 24 hours, the output layer will output the prediction results for 24 times. Each result is an estimate of the sewage treatment volume at that time. The fully connected layer adjusts the weight parameters to ensure that the output prediction value is consistent with the changing trend of the actual sewage treatment volume, and finally obtains the prediction data that can be used for subsequent equipment scheduling.

[0057] In this embodiment, before training the LSTM model, the Adam optimization algorithm is selected as the optimization tool for the model parameters. This algorithm can effectively improve the efficiency and stability of model training by adaptively adjusting the learning rate of each parameter. At the same time, the loss function is set as a weighted sum of mean squared error and mean absolute error. The mean squared error is mainly used to amplify the impact of larger errors on model training, while the mean absolute error can more robustly reflect the overall deviation between the predicted value and the true value. By setting reasonable weights for the two, the loss function is made to better fit the actual needs of sewage treatment volume prediction, providing an accurate optimization direction for model training.

[0058] The preprocessed dataset is randomly divided into 5 subsets of similar size. Each subset is used as a validation set, and the other 4 subsets are merged as a training set. The model is trained and validated 5 times. During each training process, the parameters of the LSTM model are updated using the training set, and the predictive performance of the model is evaluated using the validation set. The results of each validation are recorded. By combining the average performance of the 5 validations, the evaluation bias caused by the division of a single dataset is avoided, and the generalization ability of the model is reflected more objectively.

[0059] Based on the evaluation results of 5-fold cross-validation, the hyperparameters of the model are dynamically adjusted. The hyperparameters include the learning rate, the number of hidden layer units, and the training batch size. If the validation loss decreases slowly during model training, the learning rate can be increased appropriately. If the model shows signs of overfitting, the number of hidden layer units can be reduced. If the memory usage is too high or the model convergence is unstable during training, the training batch size can be adjusted. After each adjustment, the model is retrained and cross-validated until a combination of hyperparameters that improves validation performance is found.

[0060] During model training, the loss of the validation set is continuously monitored. If the validation loss does not decrease within 10 consecutive training cycles, the model is considered to have reached the optimal training state, and the training process is stopped. At this point, the parameter configuration of the current model is saved to obtain the final LSTM model. This model avoids the overfitting problem caused by overtraining and maintains good prediction performance.

[0061] Step 104: Based on the prediction results, solve for the optimal equipment start-up and shutdown and load allocation scheme to optimize resource allocation.

[0062] In this embodiment, based on the predicted wastewater treatment volume and the actual operation of the wastewater treatment plant, the equipment operating cost, energy consumption, treatment capacity limitations, and predicted water volume are quantified and transformed into mathematical expressions. The equipment operating cost includes equipment depreciation, maintenance costs, and labor costs; energy consumption includes electricity and chemical consumption, all converted into specific values. The treatment capacity limitations specify the maximum treatment flow rate and load limit for each treatment unit, such as bar screens, sedimentation tanks, and aeration tanks. The predicted water volume serves as the basic data, and the objective function is set to minimize the total operating cost. Linear constraints include that the treatment flow rate of each device must not exceed its maximum treatment capacity, the start-up and shutdown status of the equipment must remain consistent within the same time period, and the treatment load must match the predicted water volume.

[0063] The transformed linear constraints and objective function are constructed into a mixed-integer linear programming model, where the start-up and shutdown states of equipment are represented by binary variables (0 for stop and 1 for operation), and the processing load allocation is represented by continuous variables. Professional linear programming tools such as CPLEX and Gurobi are used to call the mixed-integer linear programming algorithm to solve the model. The algorithm traverses the feasible solution space and, under the premise of satisfying all constraints, finds the solution that minimizes the objective function value. This solution corresponds to specific equipment start-up and shutdown times (e.g., which equipment is turned on or off during which time period) and load allocation schemes (e.g., the proportion of processing flow handled by each equipment). After solving, the output optimal solution can be directly used to guide the equipment operation scheduling of the wastewater treatment plant, achieving efficient resource allocation.

[0064] Please see Figure 2 A schematic diagram of the structure of the wastewater treatment volume prediction system for the environmental protection industry based on big data provided in this embodiment of the invention. The system includes:

[0065] The data integration module is used to collect initial data from multiple data sources, including industrial enterprises, municipal pipelines, and meteorological departments, and to integrate the collected initial data.

[0066] The data processing module is used to clean the integrated data, remove outliers and missing values, and extract target features from the preprocessed data.

[0067] The model output module is used to take the target features as input to the LSTM model and output the predicted value of sewage treatment volume over a future period of time.

[0068] The optimization configuration module is used to solve for the optimal equipment start-up and shutdown and load distribution scheme based on the prediction results, thereby optimizing resource allocation.

[0069] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for predicting wastewater treatment volume in the environmental protection industry based on big data, characterized in that, The method includes the following steps: Initial data was collected from multiple sources, including industrial enterprises, municipal pipelines, and meteorological departments, and then integrated. The integrated data is cleaned to remove outliers and missing values, and the target features are extracted from the preprocessed data. The target features are used as input to the LSTM model, and the output is a predicted value of wastewater treatment volume over a future period of time. Based on the prediction results, the optimal equipment start-up and shutdown and load allocation schemes are determined to optimize resource allocation. The initial data is collected from multiple data sources, including industrial enterprises, municipal pipelines, and meteorological departments. The collected initial data is then integrated, including: Establish multi-source data acquisition interfaces to collect production data, water consumption, and wastewater discharge from industrial enterprise production management systems; Utilize IoT sensors to acquire sewage flow and water quality data from municipal pipeline monitoring systems; Rainfall, temperature, humidity, and wind speed data are obtained from meteorological departments through open meteorological data interfaces; The initial data collected is converted into a new format. ETL tools are used to extract and transform data from multiple sources and then load it into a distributed data warehouse to form integrated data containing timestamps and data source identifiers. The process of using target features as input to an LSTM model and outputting a predicted wastewater treatment volume over a future period includes: Construct an LSTM model, which consists of an input layer, multiple LSTM hidden layers, and an output layer; The target features are received through the input layer and divided into a sequence input according to the time step. The LSTM units in the hidden layer capture long-term time dependencies and complex nonlinear patterns in wastewater treatment data through the coordinated operation of forget gates, input gates, and output gates. The output layer maps the output of the hidden layer to the predicted wastewater treatment volume over a future period through a fully connected layer; The process of solving for the optimal equipment start-up and shutdown and load allocation scheme based on the prediction results, and optimizing resource allocation, includes: Based on the predicted wastewater treatment volume, the equipment operating cost, energy consumption, treatment capacity limitations, and predicted water volume are transformed into linear constraints and objective functions. The optimal equipment start-up and shutdown times and load allocation scheme are obtained by using a mixed-integer linear programming algorithm. The extraction of target features from the preprocessed data includes: In the preprocessed data, the wastewater treatment volume data is used as the target variable, and the remaining data are used as candidate feature variables. The mutual information method is used to calculate the mutual information value between each candidate feature variable and the target variable in turn. The mutual information values ​​of each candidate feature are sorted to form a candidate feature sequence based on the size of the mutual information values. From the candidate feature sequence, select the top N candidate features as the target features, where N is the threshold number of features.

2. The method for predicting wastewater treatment volume in the environmental protection industry based on big data as described in claim 1, characterized in that, The process of cleaning the integrated data to remove outliers and missing values ​​includes: The box plot method based on IQR calculates the first quartile Q1 and the third quartile Q3 in the integrated data, identifies outlier data points that are less than Q1-1.5×IQR or greater than Q3+1.5×IQR, and marks them as outliers. Outliers are then processed by linear interpolation based on the preceding and following data. For missing values, based on the time series correlation of the data, interpolation methods based on trend and seasonal terms are used to fill in the missing values, resulting in preprocessed data.

3. The method for predicting wastewater treatment volume in the environmental protection industry based on big data as described in claim 1, characterized in that, The LSTM model was trained using the Adam optimization algorithm, and the loss function was a weighted sum of mean squared error and mean absolute error. During training, the 5-fold cross-validation method is used to evaluate the model's performance and the hyperparameters are dynamically adjusted. Training is stopped when the loss no longer decreases after 10 consecutive training epochs, and the final LSTM model is obtained. The hyperparameters include the learning rate, the number of hidden layer units, and the training batch size.

4. A wastewater treatment volume prediction system for the environmental protection industry based on big data, characterized in that, The system includes: The data integration module is used to collect initial data from multiple data sources, including industrial enterprises, municipal pipe networks, and meteorological departments, and integrate the collected initial data: It establishes a multi-source data acquisition interface to collect production data, water consumption, and wastewater discharge from industrial enterprise production management systems; it uses IoT sensors to obtain sewage flow and water quality data from municipal pipe network monitoring systems; and it obtains rainfall, temperature, humidity, and wind speed data from meteorological departments through an open meteorological data interface. The module then converts the format of the collected initial data, uses ETL tools to extract and transform the data from multiple sources, and loads it into a distributed data warehouse, forming integrated data containing timestamps and data source identifiers. The data processing module is used to clean the integrated data, remove outliers and missing values, and extract target features from the preprocessed data: wastewater treatment volume is used as the target variable, and the remaining data are used as candidate feature variables; the mutual information method is used to calculate the mutual information value between each candidate feature variable and the target variable, and the mutual information values ​​of each candidate feature are sorted to form a candidate feature sequence based on the magnitude of the mutual information values; from the candidate feature sequence, the top N candidate features are selected as the target features, where N is a threshold for the number of features; The model output module takes the target features as input to the LSTM model and outputs predicted wastewater treatment volume over a future period. It constructs an LSTM model, which includes an input layer, multiple hidden LSTM layers, and an output layer. The input layer receives the target features and divides them into a sequence input based on time steps. The LSTM units in the hidden layers, through the collaborative work of forget gates, input gates, and output gates, capture long-term temporal dependencies and complex nonlinear patterns in the wastewater treatment volume data. The output layer maps the output of the hidden layers to predicted wastewater treatment volume over a future period through a fully connected layer. The optimization configuration module is used to solve for the optimal equipment start-up and shutdown and load allocation scheme based on the prediction results, and optimize resource allocation: based on the predicted sewage treatment volume, the equipment operating cost, energy consumption, treatment capacity limit and predicted water volume are transformed into linear constraints and objective functions; a mixed integer linear programming algorithm is used to solve for the optimal equipment start-up and shutdown time and load allocation scheme.

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