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Bi-objective optimization of a supply chain: identification of the key impact category and green management

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In the present work, a bi-objective optimization model is proposed for the green management of the supply chain of fresh fruit considering transportation costs, and environmental impact categories given by the ReCiPe methodology. The ε-constraint method is used to convert the bi-objective function into a single-objective optimization problem and it is applied to two case studies to test the model in a tomato supply chain, providing a set of Pareto solutions. Results showed that the most affected environmental impact category is “climate change” from the emission of greenhouse gases and that there are greater CO2 emissions at the stage of transportation from producers to warehouses. Solutions obtained by the proposed approach provided useful information such as the best operating points for the green management of the supply chain. Moreover, the model can be used in similar situations for regional development.

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Best practical option


Scenario 1


Scenario 2

f N :

Nadir point

f U :

Utopia point


Greenhouse gases


Green supply chain management


Life cycle assessment


Life cycle impact assessment


Linear programming

MK k :

Supermarket k


Mixed integer linear programming


Multi-objective optimization


Non-methane volatile organic compounds

Pi :

Producer i


Supply chain


Supply chain management

W j :

Warehouse j

F :

Multiobjective function

f 1 :

Economic function

f 2 :

Environmental function

i :

Index of producer i

j :

Index of warehouse j

k :

Index of supermarket k

b i :

Minimum amount must deliver

ca jk :

Transportation cost from warehouse j to supermarket k

cp ij :

Transportation cost from producer i to warehouse j

dm k :

Supermarket k total demand

da j :

Warehouse j demand

ecoPW ij :

Impact (kg) from producer i to warehouse j

ecoW jk :

Impact (kg) from warehouse j to supermarket k

sa j :

Quantities offered by the warehouse

sp i :

Producer i production capacity

tp ij :

Distance from producer i to warehouse j

tw jk :

Distance from warehouse j to supermarket k

ε :

Épsilon for constrained objective functions

x 1ij :

Total distributed from producer i to warehouse j

x 2jk :

Total distributed from warehouse j to supermarket k


Agricultural land occupation (m2a)


Climate change (kg CO2-eq)


Fossil depletion (kg oil-eq)


Freshwater ecotoxicity (kg 1,4-DC)


Freshwater eutrophication (kg 1,4-DC)


Human toxicity (kg 1,4-DC)


Ionising radiation (kg U235-eq)


Marine ecotoxicity (kg 1,4-DC)


Marine eutrophication (kg N-eq)


Metal depletion (kg Fe-eq)


Natural land transformation (m2a)


Ozone depletion (kg CFC-11)


Particulate matter (kg PM10-eq)


Photochemical oxidant (kg NMVOC)


Terrestrial acidification (kg SO2-eq)


Terrestrial ecotoxicity (kg 1,4-DC)


Urban land occupation (m2a)


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The authors are thankful for the financial support from Coordination for the Improvement of Higher Education Personnel—Process 88881.171419/2018-01—CAPES (Brazil) and the National Council for Scientific and Technological Development (Brazil).

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Correspondence to Rodrigo Camilo.

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Appendix A: State of art

See Table 4.

Table 4 Contributions on green management supply chain

Appendix B: Pareto fronts obtained by optimizing the cost function and restricting to the impact categories M3, M6, M7, M10 and M17, respectively

The blue points comprise the Pareto Front, the green triangle represents the Utopia Point, the purple diamond indicates the Nadir Point, and the letter “x” shows the Knee Point.

See Figs. 8, 9, 10, 11 and 12.

Fig. 8

Pareto fronts for the fossil depletion category are shown in a for C1 and in b for C2

Fig. 9

Pareto fronts for the human toxicity category are shown in a for C1 and in b for C2

Fig. 10

Pareto fronts for the ionizing radiation category are shown in a for C1 and in b for C2

Fig. 11

Pareto fronts for the metal depletion category are shown in a for C1 and in b for C2

Fig. 12

Pareto fronts for the urban land occupation category are shown in a for C1 and in b for C2

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Camilo, R., Bonfim-Rocha, L., Macowski, D.H. et al. Bi-objective optimization of a supply chain: identification of the key impact category and green management. Braz. J. Chem. Eng. (2020).

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  • Linear programming
  • ε-constraint
  • Transportation stage
  • Greenhouse gases
  • Climate change