Correction: Developing mathematical models and intelligent sustainable supply chains by uncertain parameters and algorithms

Massoumeh Nazari; Mahmoud Dehghan Nayeri; Kiamars Fathi Hafshjani; Massoumeh Nazari; Mahmoud Dehghan Nayeri; Kiamars Fathi Hafshjani

doi:10.3934/math.20241230

AIMS Mathematics

2024, Volume 9, Issue 9: 25223-25231. doi: 10.3934/math.20241230

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Correction

Correction: Developing mathematical models and intelligent sustainable supply chains by uncertain parameters and algorithms

1.
Department of Industrial Management, Islamic Azad University, Tehran South Branch, Faculty of Management, Tehran, Iran
2.
Department of Industrial Management, Tarbiat Modares University, Faculty of Management and Economics, Tehran, Iran
Correction of: AIMS Mathematics 9: 5204-5233.

Received: 27 August 2024 Revised: 27 August 2024 Accepted: 28 August 2024 Published: 29 August 2024

Citation: Massoumeh Nazari, Mahmoud Dehghan Nayeri, Kiamars Fathi Hafshjani. Correction: Developing mathematical models and intelligent sustainable supply chains by uncertain parameters and algorithms[J]. AIMS Mathematics, 2024, 9(9): 25223-25231. doi: 10.3934/math.20241230

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A correction on

Developing mathematical models and intelligent sustainable supply chains by uncertain parameters and algorithms

by Massoumeh Nazari, Mahmoud Dehghan Nayeri and Kiamars Fathi Hafshjani. AIMS Mathematics, 2024, 9(3): 5204–5233. DOI: 10.3934/math.2024252

The authors would like to revise a small mistake in Figure 1 by changing the direction of the fifth elbow arrow from h to j, and add the artificial intelligence codes to Appendix section of the published paper ^[1]. The updated Figure 1 and Appendix are as follows,

Figure 1. Conceptual models.

DownLoad: Full-Size Img PowerPoint

Appendix

A.1. The shipping cost parameter from the polymer material supplier to the factory

T = tonndata(y, true, false);

trainFcn = 'trainlm';

feedbackDelays = 1:3;

hiddenLayerSize = 25;

net = narnet(feedbackDelays, hiddenLayerSize, 'open', trainFcn);

net.input.processFcns = {'removeconstantrows', 'mapminmax'};

[x, xi, ai, t] = preparets(net, {}, {}, T);

net.divideFcn = 'dividerand';

net.divideMode = 'time';

net.divideParam.trainRatio = 70/100;

net.divideParam.valRatio = 10/100;

net.divideParam.testRatio = 20/100;

net.performFcn = 'mse';

net.plotFcns = {'plotperform', 'plottrainstate', 'ploterrhist', ... 'plotregression', 'plotresponse', 'ploterrcorr', 'plotinerrcorr'};

[net, tr] = train(net, x, t, xi, ai);

y = net(x, xi, ai);

e = gsubtract(t, y);

performance = perform(net, t, y)

trainTargets = gmultiply(t, tr.trainMask);

valTargets = gmultiply(t, tr.valMask);

testTargets = gmultiply(t, tr.testMask);

trainPerformance = perform(net, trainTargets, y)

valPerformance = perform(net, valTargets, y)

testPerformance = perform(net, testTargets, y)

view(net)

netc = closeloop(net);

netc.name = [net.name ' - Closed Loop'];

view(netc)

[xc, xic, aic, tc] = preparets(netc, {}, {}, T);

yc = netc(xc, xic, aic);

closedLoopPerformance = perform(net, tc, yc)

[x1, xio, aio, t] = preparets(net, {}, {}, T);

[y1, xfo, afo] = net(x1, xio, aio);

[netc, xic, aic] = closeloop(net, xfo, afo);

[y2, xfc, afc] = netc(cell(0, 5), xic, aic);

nets = removedelay(net);

nets.name = [net.name ' - Predict One Step Ahead'];

view(nets)

[xs, xis, ais, ts] = preparets(nets, {}, {}, T);

ys = nets(xs, xis, ais);

stepAheadPerformance = perform(nets, ts, ys)

if (false)

genFunction(net, 'myNeuralNetworkFunction');

y = myNeuralNetworkFunction(x, xi, ai);

end

if (false)

genFunction(net, 'myNeuralNetworkFunction', 'MatrixOnly', 'yes');

x1 = cell2mat(x(1, :));

xi1 = cell2mat(xi(1, :));

y = myNeuralNetworkFunction(x1, xi1);

end

if (false)

gensim(net);

end

A.2. The shipping costs from the factory to the distributors of automotive plastic accessories

T = tonndata(y, true, false);

trainFcn = 'trainlm';

feedbackDelays = 1:3;

hiddenLayerSize = 20;

net = narnet(feedbackDelays, hiddenLayerSize, 'open', trainFcn);

net.input.processFcns = {'removeconstantrows', 'mapminmax'};

[x, xi, ai, t] = preparets(net, {}, {}, T);

net.divideFcn = 'dividerand';

net.divideMode = 'time';

net.divideParam.trainRatio = 85/100;

net.divideParam.valRatio = 5/100;

net.divideParam.testRatio = 10/100;

net.performFcn = 'mse';

net.plotFcns = {'plotperform', 'plottrainstate', 'ploterrhist', ... 'plotregression', 'plotresponse', 'ploterrcorr', 'plotinerrcorr'};

[net, tr] = train(net, x, t, xi, ai);

y = net(x, xi, ai);

e = gsubtract(t, y);

performance = perform(net, t, y)

trainTargets = gmultiply(t, tr.trainMask);

valTargets = gmultiply(t, tr.valMask);

testTargets = gmultiply(t, tr.testMask);

trainPerformance = perform(net, trainTargets, y)

valPerformance = perform(net, valTargets, y)

testPerformance = perform(net, testTargets, y)

view(net)

netc = closeloop(net);

netc.name = [net.name ' - Closed Loop'];

view(netc)

[xc, xic, aic, tc] = preparets(netc, {}, {}, T);

yc = netc(xc, xic, aic);

closedLoopPerformance = perform(net, tc, yc)

[x1, xio, aio, t] = preparets(net, {}, {}, T);

[y1, xfo, afo] = net(x1, xio, aio);

[netc, xic, aic] = closeloop(net, xfo, afo);

[y2, xfc, afc] = netc(cell(0, 5), xic, aic);

nets = removedelay(net);

nets.name = [net.name ' - Predict One Step Ahead'];

view(nets)

[xs, xis, ais, ts] = preparets(nets, {}, {}, T);

ys = nets(xs, xis, ais);

stepAheadPerformance = perform(nets, ts, ys)

if (false)

genFunction(net, 'myNeuralNetworkFunction');

y = myNeuralNetworkFunction(x, xi, ai);

end

if (false)

genFunction(net, 'myNeuralNetworkFunction', 'MatrixOnly', 'yes');

x1 = cell2mat(x(1, :));

xi1 = cell2mat(xi(1, :));

y = myNeuralNetworkFunction(x1, xi1);

end

if (false)

gensim(net);

end

A.3. The shipping costs from the distributors of automotive plastic accessories to the customers of plastic car accessories

T = tonndata(y, true, false);

trainFcn = 'trainlm';

feedbackDelays = 1:3;

hiddenLayerSize = 27;

net = narnet(feedbackDelays, hiddenLayerSize, 'open', trainFcn);

net.input.processFcns = {'removeconstantrows', 'mapminmax'};

[x, xi, ai, t] = preparets(net, {}, {}, T);

net.divideFcn = 'dividerand';

net.divideMode = 'time';

net.divideParam.trainRatio = 85/100;

net.divideParam.valRatio = 10/100;

net.divideParam.testRatio = 5/100;

net.performFcn = 'mse';

net.plotFcns = {'plotperform', 'plottrainstate', 'ploterrhist', ... 'plotregression', 'plotresponse', 'ploterrcorr', 'plotinerrcorr'};

[net, tr] = train(net, x, t, xi, ai);

y = net(x, xi, ai);

e = gsubtract(t, y);

performance = perform(net, t, y)

trainTargets = gmultiply(t, tr.trainMask);

valTargets = gmultiply(t, tr.valMask);

testTargets = gmultiply(t, tr.testMask);

trainPerformance = perform(net, trainTargets, y)

valPerformance = perform(net, valTargets, y)

testPerformance = perform(net, testTargets, y)

view(net)

netc = closeloop(net);

netc.name = [net.name ' - Closed Loop'];

view(netc)

[xc, xic, aic, tc] = preparets(netc, {}, {}, T);

yc = netc(xc, xic, aic);

closedLoopPerformance = perform(net, tc, yc)

[x1, xio, aio, t] = preparets(net, {}, {}, T);

[y1, xfo, afo] = net(x1, xio, aio);

[netc, xic, aic] = closeloop(net, xfo, afo);

[y2, xfc, afc] = netc(cell(0, 5), xic, aic);

nets = removedelay(net);

nets.name = [net.name ' - Predict One Step Ahead'];

view(nets)

[xs, xis, ais, ts] = preparets(nets, {}, {}, T);

ys = nets(xs, xis, ais);

stepAheadPerformance = perform(nets, ts, ys)

if (false)

genFunction(net, 'myNeuralNetworkFunction');

y = myNeuralNetworkFunction(x, xi, ai);

end

if (false)

genFunction(net, 'myNeuralNetworkFunction', 'MatrixOnly', 'yes');

x1 = cell2mat(x(1, :));

xi1 = cell2mat(xi(1, :));

y = myNeuralNetworkFunction(x1, xi1);

end

if (false)

gensim(net);

end

A.4. The shipping costs from the customers of plastic car accessories to the recycling center

T = tonndata(x4, false, false);

trainFcn = 'trainlm';

feedbackDelays = 1:3;

hiddenLayerSize = 42;

net = narnet(feedbackDelays, hiddenLayerSize, 'open', trainFcn);

net.input.processFcns = {'removeconstantrows', 'mapminmax'};

[x, xi, ai, t] = preparets(net, {}, {}, T);

net.divideFcn = 'dividerand';

net.divideMode = 'time';

net.divideParam.trainRatio = 75/100;

net.divideParam.valRatio = 15/100;

net.divideParam.testRatio = 10/100;

net.performFcn = 'mse';

net.plotFcns = {'plotperform', 'plottrainstate', 'ploterrhist', ... 'plotregression', 'plotresponse', 'ploterrcorr', 'plotinerrcorr'};

[net, tr] = train(net, x, t, xi, ai);

y = net(x, xi, ai);

e = gsubtract(t, y);

performance = perform(net, t, y)

trainTargets = gmultiply(t, tr.trainMask);

valTargets = gmultiply(t, tr.valMask);

testTargets = gmultiply(t, tr.testMask);

trainPerformance = perform(net, trainTargets, y)

valPerformance = perform(net, valTargets, y)

testPerformance = perform(net, testTargets, y)

view(net)

netc = closeloop(net);

netc.name = [net.name ' - Closed Loop'];

view(netc)

[xc, xic, aic, tc] = preparets(netc, {}, {}, T);

yc = netc(xc, xic, aic);

closedLoopPerformance = perform(net, tc, yc)

[x1, xio, aio, t] = preparets(net, {}, {}, T);

[y1, xfo, afo] = net(x1, xio, aio);

[netc, xic, aic] = closeloop(net, xfo, afo);

[y2, xfc, afc] = netc(cell(0, 5), xic, aic);

nets = removedelay(net);

nets.name = [net.name ' - Predict One Step Ahead'];

view(nets)

[xs, xis, ais, ts] = preparets(nets, {}, {}, T);

ys = nets(xs, xis, ais);

stepAheadPerformance = perform(nets, ts, ys)

if (false)

genFunction(net, 'myNeuralNetworkFunction');

y = myNeuralNetworkFunction(x, xi, ai);

end

if (false)

genFunction(net, 'myNeuralNetworkFunction', 'MatrixOnly', 'yes');

x1 = cell2mat(x(1, :));

xi1 = cell2mat(xi(1, :));

y = myNeuralNetworkFunction(x1, xi1);

end

if (false)

gensim(net);

end

A.5. The shipping costs from the recycling center to the factory

T = tonndata(x5, false, false);

feedbackDelays = 1:3;

hiddenLayerSize = 38;

net = narnet(feedbackDelays, hiddenLayerSize, 'open', trainFcn);

net.input.processFcns = {'removeconstantrows', 'mapminmax'};

[x, xi, ai, t] = preparets(net, {}, {}, T);

net.divideFcn = 'dividerand';

net.divideMode = 'time';

net.divideParam.trainRatio = 45/100;

net.divideParam.valRatio = 35/100;

net.divideParam.testRatio = 20/100;

net.performFcn = 'mse';

net.plotFcns = {'plotperform', 'plottrainstate', 'ploterrhist', ... 'plotregression', 'plotresponse', 'ploterrcorr', 'plotinerrcorr'};

[net, tr] = train(net, x, t, xi, ai);

y = net(x, xi, ai);

e = gsubtract(t, y);

performance = perform(net, t, y)

trainTargets = gmultiply(t, tr.trainMask);

valTargets = gmultiply(t, tr.valMask);

testTargets = gmultiply(t, tr.testMask);

trainPerformance = perform(net, trainTargets, y)

valPerformance = perform(net, valTargets, y)

testPerformance = perform(net, testTargets, y)

view(net)

netc = closeloop(net);

netc.name = [net.name ' - Closed Loop'];

view(netc)

[xc, xic, aic, tc] = preparets(netc, {}, {}, T);

yc = netc(xc, xic, aic);

closedLoopPerformance = perform(net, tc, yc)

[x1, xio, aio, t] = preparets(net, {}, {}, T);

[y1, xfo, afo] = net(x1, xio, aio);

[netc, xic, aic] = closeloop(net, xfo, afo);

[y2, xfc, afc] = netc(cell(0, 5), xic, aic);

nets = removedelay(net);

nets.name = [net.name ' - Predict One Step Ahead'];

view(nets)

[xs, xis, ais, ts] = preparets(nets, {}, {}, T);

ys = nets(xs, xis, ais);

stepAheadPerformance = perform(nets, ts, ys)

if (false)

genFunction(net, 'myNeuralNetworkFunction');

y = myNeuralNetworkFunction(x, xi, ai);

end

if (false)

genFunction(net, 'myNeuralNetworkFunction', 'MatrixOnly', 'yes');

x1 = cell2mat(x(1, :));

xi1 = cell2mat(xi(1, :));

y = myNeuralNetworkFunction(x1, xi1);

end

if (false)

gensim(net);

end

The changes have no material impact on the conclusion of this article. The original manuscript will be updated ^[1].

Conflict of interest

The authors declare no conflicts of interest.

References

[1]	M. Nazari, M. D. Nayeri, K. F. Hafshjani, Developing mathematical models and intelligent sustainable supply chains by uncertain parameters and algorithms, AIMS Math., 9 (2024), 5204–5233.https://doi.org/10.3934/math.2024252 doi: 10.3934/math.2024252

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通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

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AIMS Mathematics

Correction: Developing mathematical models and intelligent sustainable supply chains by uncertain parameters and algorithms

Related Papers:

A correction on

Appendix

A.1. The shipping cost parameter from the polymer material supplier to the factory

A.2. The shipping costs from the factory to the distributors of automotive plastic accessories

A.3. The shipping costs from the distributors of automotive plastic accessories to the customers of plastic car accessories

A.4. The shipping costs from the customers of plastic car accessories to the recycling center

A.5. The shipping costs from the recycling center to the factory

Conflict of interest

References

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AIMS Mathematics

Correction: Developing mathematical models and intelligent sustainable supply chains by uncertain parameters and algorithms

Related Papers:

A correction on

Appendix

A.1. The shipping cost parameter from the polymer material supplier to the factory

A.2. The shipping costs from the factory to the distributors of automotive plastic accessories

A.3. The shipping costs from the distributors of automotive plastic accessories to the customers of plastic car accessories

A.4. The shipping costs from the customers of plastic car accessories to the recycling center

A.5. The shipping costs from the recycling center to the factory

Conflict of interest

References

Reader Comments

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