Sustainable Optimization of Food Networks in Disenfranchised

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Sustainable Optimization of Food Networks in Disenfranchised Communities Sergio Ivan Martínez-Guido, J. Betzabe González-Campos, Mahmoud M El-Halwagi, and José María Ponce-Ortega ACS Sustainable Chem. Eng., Just Accepted Manuscript • DOI: 10.1021/ acssuschemeng.7b01703 • Publication Date (Web): 16 Aug 2017 Downloaded from http://pubs.acs.org on August 22, 2017

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ACS Sustainable Chemistry & Engineering

Sustainable Optimization of Food Networks in Disenfranchised Communities

Sergio Iván Martínez-Guidoa, J. Betzabe GonzálezCamposb, Mahmoud M. El-Halwagi,c,d José María PonceOrtega*a a

Chemical Engineering Department, Universidad Michoacana de San

Nicolás de Hidalgo, Av. Francisco J. Mujica, S/N, Ciudad Universitaria, Edificio V1, Morelia, Michoacán 58060, México b

Institute for Chemical and Biological Researches, Universidad

Michoacana de San Nicolás de Hidalgo, Av. Francisco J. Mujica S/N, Ciudad Universitaria, Edificio B1, Morelia, Michoacán 58060, México c

Chemical Engineering Department, Texas A&M University,0386 Spence St, College Station TX, 77843, USA d

Department of Chemical and Materials Engineering, Faculty of

Engineering, King Abdulaziz University, P. O. Box 80204, Jeddah, 21589, Saudi Arabia

*E-mail: [email protected] Tel.: +52 (443) 3223500, ext. 1277 Fax: +52 (443) 3273584

ACS Paragon Plus Environment


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Abstract With the growing concerns about food security around the world, there is a need to develop sustainable strategies and proactive measures especially in developing countries with disenfranchised communities. These strategies must account for the specific nature and resources of each community and should be integrated with the need for economic growth. This work presents a conceptual framework and a mathematical programming model for the strategic planning of a sustainable food assistance program to satisfy the nutritional needs of disenfranchised communities while taking into account the objective of economic growth and the constraints of local resources. A case study from Mexico is presented as an example of applying the proposed approach. Fourteen municipalities with the lowest human development index are considered. The results show that it is possible to satisfy the nutritional needs while simultaneously improving the local economy of these disenfranchised communities.

Keywords: Suitable nutrition; Social development; Food networks; Strategic planning.


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Introduction The deficiency in providing sufficient needs of nutrients for impoverished communities is a problem that is closely related to food supply security and economic disenfranchisement. Around the world, 159 million children under the age of five suffer from nutritional stunting, while 50 million children of the same age group have low weight compared to their normal-weight counterparts.1 In 2016, the Food and Agriculture

Organization

reported

that

795

million

people

worldwide

are

undernourished and 98% of them are in developing regions (see Figure 1 for regional distribution). Therefore, governments around the world have applied actions to mitigate this problem by mainly focusing on food aid, subsidy, and assistance programs. Several concerns have been raised with respect to the sustainability of these programs and their effectiveness in addressing the more underlying problem of the lack of economic growth and reliable food supply. The food supply problem must be analyzed taking into account all the steps involved in the supply chain while focusing on economic, social, political and environmental benefits. Consideration should also be given to community development, local resources, supply and demand, food production, and distribution centers.2 Additionally, the quality, safety, health and nutritional aspects in diets should be addressed3 while creating a symbiosis network between the demand and sustainable production and distribution of food4. The analogy between food supply chains and industrial supply chains offers valuable lessons and efficient tools. The supply chains of different industrial processes have been analyzed through various optimization models addressing a broad range of case studies. For example, Guillén-Gosálbez and Grossmann5 proposed a global optimization approach for the environmentally conscious design of chemical supply chains. These environmental objectives may be reconciled with other sustainability objectives through the use of multi-dimensional metrics.6 Bowling et al.7 presented a systematic approach for the optimal production planning and facility location of a biorefinery system, including the selection of feedstock, distributed preprocessing hubs and centralized processing facilities to obtain the optimal supply chain, size, operational strategies and location. These mathematical models applied to different industrial processes can be the basis to provide food supply chain models. In this context, Santibañez-Aguilar et al.8 developed a mathematical programming model for the optimal planning of supply chains associated with the management of municipal



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solid waste. Arredondo-Ramírez et al.9 presented an optimization approach for the shale gas exploitation including the infrastructure development in Mexico. Yue et al.10 included the life cycle optimization for bioethanol supply chain in UK. El-Halwagi et al.11 developed an optimization formulation for including economic, environmental, and safety considerations in the design of biorefining supply chains. López-Díaz et al.12 proposed a mathematical model for the supply chain of biorefineries accounting for the interactions with the surrounding watershed. Martínez-Guido et al.13 analyzed the reconfiguration of a sugar cane industry to an integrated biorefinery. Noureldin and ElHalwagi14 and El-Halwagi15 introduced systematic approaches for the integration of hydrocarbon processing supply chains and industrial cities. Garcia and You16 analyzed the water-energy-food nexus through the entire supply chain. Galán-Martín et al.17 proposed a multi-objective optimization model for an integral agricultural network. Regarding food networks, Sgarbossa and Russo18 integrated the recovered waste from the meat industry with the objective of enhancing self-sufficiency and sustainability. Other works have been focused on proposing a food system to maintain the safety and quality of food.19 The transportation problem,20 land-network,21 planning production and distribution,22 and zero-packaging23 have been evaluated as strategies of food supply improvement, involving environmental, economic and social aspects. It should be noted that none of the above mentioned works have addressed the food supply network in disenfranchised communities to satisfy the nutritional needs through the available resources and accounting for the commercial interaction between different disenfranchised communities. The food supply chains around the world consume 20-35% of the global energy on a life cycle basis.24 This corresponds to about 15% of the greenhouse gas emissions (GHGE) in the world.3 It should be noticed that one third of the produced food is lost or wasted.25 Moreover, the global population increases at a rate of approximately 1.18% per year,26 which means a greater demand for food, water, energy, and land,19 In addition, the current challenges of climate change, public health, and farming wastes are closely tied to food security and supply chains. Consequently, the analysis of food supply chains is a source of growing concern worldwide. Some investigations have focused on the localization of production sites involving environmental and economic aspects27 as well as the product quality and safety28 to reduce the cost29 and the


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associated emissions from some processing products.30 Other works have focused on the integration of new technologies31 and management32 to obtain sustainable farms33. Also, there have been reported some mathematical models for planning agricultural systems. This way, Mosleh et al.33 reported a study taking into account suitable cultivable lands and water resources to improve cropping systems in a province of Iran. Jana et al.34 proposed a mathematical model to account for the uncertainties associated to the agriculture in India. Galán-Martín et al.35 developed a multi-stage linear programming model to determine the optimal planning for different crops for Spain. Other approaches for optimizing the agricultural activity have focused on the environmental aspect,36 resource management37 and localization;38 however, none of them has focused on undernourished communities. In several developing countries, various forms of subsidies and other aid strategies have been implemented to satisfy the basic food needs of impoverished communities especially the ones that are mostly concentrated in rural areas. Typically, these programs are inefficient in tackling the underlying economic growth problems and do not take into consideration the complex nature of the entire food supply chains39 or the local resources40,

19

. In addition, these governmental programs only consider the

distribution of specific food products to disenfranchised people independently of their location, age and overall needs, and do not take into account specific nutritional needs for the people of different regions and age groups. To overcome these limitations, this work proposes a general multi-objective optimization formulation for food supply chain planning to satisfy specify nutritional needs of disenfranchised communities while considering the location, age and population of the implicated regions. The proposed model takes into account the integration of the available resources in each considered community, as well as the potential distribution of food products to the different involved communities to satisfy the entire nutritional needs of the population. Cultivation, harvesting and transportation of food products are considered in the optimization model, and the objectives for the proposed approach incorporate the simultaneous minimization of the total cost and the total environmental impact as well as the maximization of job creation in the entire supply chain, to satisfy the nutritional needs of people from these disenfranchised communities. An optimization formulation is proposed to guide the decision makers in creating sustainable strategies for food security to satisfy the specific nutritional needs



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in places with low Human Development Index (HDI), investing in local resources, and accounting for economic, environmental and social objectives. The interaction between the three main entities (harvesting sites, hub/processing plants and consumers) involved in the food supply chain as shown in Figure 2.

Addressed Problem The addressed problem in this work is stated as follows. Given the nutritional needs based on the population of a set of disenfranchised communities located in the same region. A disenfranchised community corresponds to a municipality with a high poverty index. The people leaving in a disenfranchised community have low economic incomes, do not have access to good elementary education, health care services, security, food supply, basic domestic utilities (water, electricity, heating and cooling) and an adequate housing. Also there are given the available resources of each community, including cultivating land, weather conditions, available fresh water and installed infrastructure to produce food products. Furthermore, the infrastructure for transporting the food products and raw materials is needed. Then, the problem consists in determining the way to satisfy the nutritional needs of people of these disenfranchised communities at the minimum net annual cost accounting for their own resources and the commercial interaction between these communities, through the trade of food products and raw materials to improve the sustainability of the food supply chain. The model is based on the superstructure shown in Figure 2, it includes mass balances for the raw materials in the different communities, the balances for the products and for transportation activities to satisfy the nutritional needs of people in these communities. The objective function consists in minimizing the total annual costs, which includes all the costs for raw materials production, production of food products, distribution of raw materials and products as well as the external purchase of food products, minus the sale of food products to other communities.

Mathematical Model This paper proposes the superstructure shown in Figure 2, which first presents the available animal and vegetable productions in each selected site. Also, animal food can be bought from external sellers or obtained from cultivating sites. After producing the animal and vegetal food, the products can be sent in three different ways: a) directly to the final consumers in the same location to satisfy nutrient demands in the current


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time period, b) to other community, c) to hubs where the products can be stored and distributed to other communities in different time periods or to sell to external consumers. The mathematical model is based on mass balances over the superstructure previously described, and using the symbols presented in the nomenclature section. Then, the model formulation is stated as follows. Mass balance of raw materials The raw material balances are divided into two groups (vegetal and animal products). Vegetal products Equation (1) shows the balance for the yield obtained from each raw material

( r ) , in each municipality harvesting site ( m1) , produced in a period of time ( t) . The

(

total raw material produced RM rveg ,m 1,t

) is equal to the yield ( β (

HS r , m1, t

) multiplied by the

)

occupied area for each product in each municipality Arused , m1,t . used RM rveg = βrHS , m1,t Ar , m1,t , ∀ r ∈ R, m1∈ M 1, t ∈T ,m1,t

(1)

The considered products depend on the availability in each community, accounting for the available land, water and weather conditions. For example, the vegetable products can be beans, corn, green tomatoes, red tomatoes, oats, chili, mango, avocado, sugar cane, onion and wheat. Area balance

(

)

First, the total area of land used for cultivation Arused accounts for the current , m1,t cultivated area

(A

current r , m1,t

)

plus the new needed area to cultivate additional vegetables

(A ). new r , m1,t

Current new Arused ,m1,t = Ar , m1,t + Ar ,m1,t ∀ r ∈R, m1∈M1, t ∈T

(2)

Furthermore, the total cultivated area must be lower than the maximum available

(

)

−Veg in the municipality ArTot . , m1,t

Tot −Ve Arused , m1,t ≤ Ar , m1,t ∀ m1∈ M 1, t ∈T


(3)


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Animal products The production of each type of animals (for example poultry, cattle and swain) in each municipality during the period of time t ( NAra ,m1,t ) is equal to the available (or required) food

(θ

)

YPA ra , m1,t

( Af

UAF ra , m1,t

)

to feed the animal ( ra ) multiplied by the growth yield

plus the amount of bought animals from other sites

(

( Na

AP ra , m1,t

)

minus the

)

amount of animals sold to other municipalities Narasale,m1,t . UAF AP sale NAra,m1,t = θraYPA , m1,t Af ra ,m1,t + Nara , m1,t − Nara ,m1,t , ∀ ra ∈ Ra, m1∈ M 1, t ∈T

(

The food used to feed animals Af raUAF , m1,t food

( Af

CAF ra , m1,t

(4)

) accounts for the amount of cultivated

) , which are crop wastes that can be used as animal food (chaff and (

stubble) plus the amount of animal food that can be purchased from other sites Af raPAF , m1,t

)

. CAF PAF AfraUAF ,m1,t = Af ra ,m1,t + Af ra , m1,t ∀ ra∈ Ra, m1∈M1, t ∈T

(

(5)

)

The cultivated animal food Af raCAF can be defined like grazing, which means , m1,t that the crop residues can be used as food for the animals, which is equal to animal yield

(θ

YPA ra ,m1,t

( RM

)

multiplied by the cultivated area

veg r , m1,t

)

(A

UAF ra , m1,t

)

plus the harvested vegetables

(

multiplied by the fraction used to feed animals φraRPA , r , m1,t

)

(i.e., waste like

corn residues used to feed chickens). YPA UAF RPA veg Af raCAF , m1,t = θ ra , m1,t Ara , m1, t + ∑ (φra , r , m1,t RM r , m1,t ) ∀ ra ∈ Ra, m1∈ M 1, t ∈T

(6)

r

(

The area used to cultivate animal food AraUAF , m1,t

(

)

has to be constrained by the

)

maximum available land for this activity AraTAF , m1,t . TAF AraUAF ,m1,t ≤ Ara,m1,t ∀ ra∈Ra, m1∈M1, t ∈T

(7)

Eggs, meat and milk production The animal products (eggs, meat and milk) account for the yield factor of each

(

)

product λ pa ,ra,m1,t multiplied by the number of produced animals ( NAra ,m1,t ) .


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FpaANP ,m1,t = NAra,m1,t λpa,ra,m1,t ∀ pa∈PA, ra∈RA, m1∈M1, t ∈T

(8)

Product distribution The balances for the different products are stated as follows. Vegetables

(

The produced vegetables RM rveg ,m 1,t



∑F 

vegeH r ,m1,m2,t

over the time period t 

m2



∑F 

veg Pr r , m1, m3,t

the consumers 

m3

)

are equal to those received from the hubs

  plus the amount of vegetables that can be sent to 

 . 

vegMar RM rveg = ∑ FrvegH ,m1,m2,t + ∑ Fr ,m1,m3,t , ∀ r ∈R,m1∈M1, t ∈T ,m1,t m2

(9)

m3

The vegetable balance in the hub states that the amount of stored vegetables

(S

vegS r , m 2,t

)

(S

vegetable − stored r , m 2,t −1

is equal to the amount of vegetables stored in a previous time period



) plus the amount received from harvesting sites  ∑ F

vegH r ,m1,m2,t

m1



∑F 

vegHtM r ,m2,m3,t

amount of vegetables sent to the consumers 

m3

(F

vegetable − hub − sale r , m 2,t

  minus the 

  and the one sold 

).

vegSD vegH vegHtM vegHtSa SrvegS ,m2,t = Sr ,m2,t −1 + ∑ Fr ,m1,m2,t − ∑ Fr ,m2,m3,t − Fr ,m2,t , m1

(10)

m3

∀r∈R,m2 ∈M 2, t ∈T

(

The amount of vegetables in the markets FrvegM , m3,t



∑F 

vegHtM r ,m2,m3,t

received from the hubs 

m2



∑F 

vegM r , m1, m3,t

sites 

m1

)

  plus the ones received directly from harvesting 

 vegPu  plus the amount of vegetables purchased from other sites ( Fr ,m3,t ) . 

vegHStM vegHtM vegPu FrvegM ,m3,t = ∑ Fr ,m1, m3,t + ∑ Fr , m 2,m3,t + Fr ,m3,t , ∀ r ∈ R, m3 ∈M 3, t ∈T m1

is equal to the vegetables

m2

Animal products


(11)


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The animal products need preprocessing and/or packing, therefore, the first

(

)

balance includes the amount of animal products in the hub Fpaani,mP1,t , the one existing in



∑F 

aniHStH pa,m1,m2,t

the hub 

m2

  aniHStM   and the one that is sent to the markets  ∑ Fpa,m1,m3,t  .   m3 

aniHStM Fpaani,mP1,t = ∑ FpaaniHStH , m1, m 2,t + ∑ Fpa , m1,m 3,t , ∀ pa ∈ PA, m1 ∈ M 1, t ∈T m2

(12)

m3

(

)

aniS The animal product in the hub includes the amount stored Spa, m 2,t , which is

equal to the amount that was stored in a previous time period



∑F 

aniHStH pa, m1,m2,t

amount received from the production sites 

m1



∑F 

aniHtM pa,m2,m3,t

market 

m3

(S

aniSD pa , m 2,t −1

)

plus the

  minus the amount sent to the 

 aniHSA  and the one sold ( Fpa,m 2,t ) . 

aniSD aniHStH aniHtM aniHSA Spa,aniSm2,t = Spa ,m2,t−1 +∑Fpa,m1,m2,t −∑Fpa,m2,m3,t − Fpa,m2,t ,∀ pa∈PA,m2∈M2, t ∈T m1

(13)

m3

(

)

Equation (14) shows the animal product balance in the markets Fpa,aniM m 3,t , where the amount of animal product in the market is equal to the flux that is received from the



∑F 

aniHtM pa,m2,m3,t

hubs 

m2

  , and the flux that is received directly from the harvesting site  

∑F 

aniHStM pa,m1,m3,t

without treatment 

m1

(F

aniPU pa, m 3,t

  , plus the amount of purchased animal product 

).

aniHStM aniHtM aniPU Fpa,aniM m3,t = ∑Fpa,m1,m3,t + ∑Fpa,m2,m3,t + Fpa,m3,t , ∀ pa∈PA,m3∈M 3, t ∈T m1

(14)

m2

It should be noticed that food decay was considered in the proposed model. For this reason, there are hubs, which have several functions, including treating and packaging the food to reduce this problem for each product. Also, food decay was considered in the transportation process, involving the associated costs for refrigeration when it is needed. Demands


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For the product demand, the six groups of food proposed by “The healthy eating plate”, shown in Figure 3, were selected. This corresponds to the Official Mexican Norm performed by the basic health service to promote a healthy nutrition. From each of these six groups, the main micro and macro nutrients were obtained, creating a new division of twelve groups (carbohydrates, fats, fiber, cholesterol, calcium, n-3 and n-6 fatty acids polyunsaturated, proteins, lipids, vitamins, animal protein and iron). These twelve groups are effective to know the amount of micro and macro nutrients needed in a healthy diet. From these parameters, it is possible to determine the amount of needed products. Then, the demand for each group age can be determined as follows:42

Dnut ,m3,t = Pem3,tGEnut , ∀nut ∈NUT , m3∈M 3, t ∈T The demands

(F

vegM r , m 3,t

(ξ

vegn nut , r

(D

nut , m3,t

),

(15)

in terms of the vegetables and animal food

, Fpa,aniM m 3,t ) , are multiplied by the nutriment factor demanded by the population

anin , ξ nut ,pa ) :

vegn aniM anin Dnut ,m3,t ≥ ∑FrvegM ,m3,t ξnut ,r +∑Fpa,m3,tξnut ,pa +, ∀nut ∈NUT, m3∈M3, t ∈T r

(16)

pa

Costs Vegetables production

(

)

(

)

The cost generated by the vegetables due to the raw material production Crveg , m1,t

(

)

is equal to the produced vegetables RM rveg multiplied by the unit crop cost σ rveg , m1,t , m1,t : veg veg Crveg ,m1,t = RMr,m1,tσr,m1,t , ∀r∈R, m1∈M1, t ∈T

(17)

Animal purchase

(

)

There is a cost associated to the purchase of animals CraaniPU , m1,t , which is equal to the number of purchased animals

(

( NA

PU ra , m1,t

)

multiplied by the corresponding unit

)

animal cost σ raaniPU , m1,t : PU aniPU CraaniPU ,m1,t = NAra,m1,tσra,m1,t , ∀ra∈RA, m1∈M1, t ∈T


(18)


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Animal food

(

)

There is a cost associated to feed the animals CraanifCU , m1,t , which depends on the

(

)

(

)

unit factor σ raanifCU as well as the cultivated animal food AFraanifCU : , m1,t , m1,t anifCU anifCU CraanifCU ,m1,t = AFra,m1,t σ ra,m1,t , ∀ ra∈RA, m1∈M1, t ∈T

(19)

When the cultivated animal food is not enough, the food for the animals must be purchased

(C

anifPU ra , m1,t

),

(σ

which is equal to the unit cost

(

anifPU ra , m1,t

)

multiplied by the

)

purchased animal food AFraanifPU , m1,t : anifPU anifPU CraanifPU ,m1,t = AFra,m1,t σra,m1,t , ∀ra∈RA, m1∈M1, t ∈T

(20)

(

)

ani Pr Furthermore, the production of the animal food has an associated cost C pa , m1,t ,

(

which takes into account the produced animals Fpaani,mPr1,t

(σ

ani Pr pa , m1,t

)

multiplied by the unit cost

):

ani Pr ani Pr ani Pr Cpa ,m1,t = Fpa,m1,tσpa,m1,t , ∀ pa∈PA, m1∈M1,t∈T

(21)

It is worth noting that natural and processed food were considered as optimization options accounting for their availability and unit costs. The optimization model selects the used food to feed animals in each municipality based on the cost and environmental impact. Transportation cost The transportation of raw materials and products has an associated cost. This way, the vegetables are produced in the harvesting sites and then they can be transported to the hub (where they receive a treatment or packing process and then they are sent to the markets) or they can be directly transported to the markets (without any treatment process). Figure 4 shows these transportation options. Similarly, the animal products can be sent directly to the markets or to the processing hubs. The transportation costs account for the unit transportation factor that is directly related to the involved distances.


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This way, the transportation cost for vegetables from cultivation sites to the hubs

(C ) vegTr r,t

is related to the unit transportation cost

(

(σ

vegTrH r, m1,m 2,t

)

times the amount of

)

vegH transported vegetables Fr ,m1,m 2,t : vegTrH Cr,vegTr = ∑∑ FrvegH , m1, m 2,tσ r, m1,m 2,t , ∀ r ∈ R , t ∈T t

(22)

m1 m 2

(

) ):

The transportation cost for vegetables from cultivation sites to markets Cr,vegTrM t

(

)

(

vegTrM vegHStM depends on the unit transportation cost σ r,m1,m3,t and the transported amount Fr ,m1,m3,t vegTrM Cr,vegTrM = ∑∑ FrvegHStM t ,m1, m3,t σ r,m1,m3,t , ∀ r ∈ R, t ∈T

(23)

m1 m3

(

)

vegTrHtM The transportation cost for vegetables from hubs to markets Cr,t is related

(

)

vegHtM to the transported amount Fr ,m2,m3,t , which is multiplied by the unit transportation cost

(σ

):

vegTrHtM r,m2,m3,t

vegTrHtM C r,vegTrHtM = ∑ ∑ FrvegHtM t , m 2, m 3,t σ r, m 2,m 3,t , ∀ r ∈ R , t ∈T

(24)

m2 m3

Similarly for the animal products, where the animal transportation cost from

(

)

(

)

aniTrH aniHstH production to markets Cpa,t depends on the transported amount Fpa,m1,m2,t and the

(

)

aniTrH unit transportation cost σ pa,m1,m2,t :

aniTrH C pa = ,t

∑∑F

aniHstH pa , m 1, m 2 , t

aniTrH σ pa , m 1, m 2 , t , ∀ pa ∈ PA , t ∈ T

(25)

m1 m 2

(

aniTrM The transportation cost for animals from hubs to markets C pa ,t

multiplying the transported amount

(σ

aniTrM pa ,m 2, m3,t

(F

aniHtM pa,m2,m3,t

)

) is obtained

by the unit transportation cost

):

aniTrM aniTrM C pa = ∑∑ FpaaniHtM ,t , m 2, m 3,tσ pa , m 2, m 3,t , ∀ pa ∈ PA, t ∈T

(26)

m 2 m3

Finally, the transportation cost for the animal products from the production site

(

)

aniTrHstM to the final markets Cpa is stated as follows: ,t



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aniTrHstM aniTrHstM C pa = ∑ ∑ FpaaniHStM ,t , m1, m 3,t σ pa , m1, m 3,t , ∀ pa ∈ PA, t ∈T

Page 14 of 51

(27)

m1 m 3

Cost for storage Another activity implied in the supply chain is the storage of both types of food products (animal and vegetables); these can be stored when the production is greater than the market demand in the corresponding time period. This activity generates a storage cost, which is related to the conservation of the products.

(

)

(

)

vegs First, the vegetable storage cost Cr ,m 2,t

(

)

considers the stored vegetables in a

vegS vegs hub Sr ,m 2,t multiplied by the unit factor σ r ,m2,t :

vegS vegs Crvegs , m 2,t = Sr ,m 2,tσ r , m 2,t , ∀ r ∈ R, m2∈M 2, t ∈T

(28)

(

)

anis Similarly for the storage of animal products Cpa,m 2,t :

anis aniS anis Cpa, m 2,t = S pa, m 2,tσ pa, m 2,t , ∀ pa ∈ PA, m 2∈ M 2, t ∈T

(29)

Cost generated by the purchase of products

(C

vegPU r , m3,t

The cost for the purchased vegetables

(

)

(

)

depends on the purchased

)

vegPU vegPU amount Fr ,m3,t times the unit price σ r ,m3,t :

vegPU vegPU CrvegPU , m 3,t = Fr , m 3,t σ r , m 3,t , ∀ r ∈ R, m3∈ M 3, t ∈T

(30)

(

aniPU Similarly, the cost for the purchased animals C pa ,m3,t

(

)

(

) depends on the amount

)

aniPU aniPU of purchased animal Fpa,m3,t ) and the unit cost σ pa,m3,t :

aniPU aniPU aniPU Cpa ,m3,t = Fpa,m3,tσ pa,m3,t , ∀ pa∈PA, m3∈M 3, t ∈T

(31)

Sales

(

)

vegSA The profit obtained for the sale of vegetables Cr,m2,t depends on the amount of

(

)

(

)

vegSA vegSA sold vegetables Fr ,m2,t and the unit sale cost σ r ,m 2,t :

vegSA vegSA Cr,vegSA m2,t = Fr ,m2,tσr ,m2,t , ∀r ∈R, m2∈M 2, t ∈T


(32)

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(

aniSA Similarly, the profit for the sale of animal products C pa,m2,t

(

)

(

)

depends on the

)

aniHSA aniSA amount of sold animals Fpa,m2,t and the unit sale price σ pa , m 2,t :

aniSA aniHSA aniSA Cpa ,m2,t = Fpa,m2,t σ pa,m2,t , ∀ pa∈PA, m2∈M 2, t ∈T

(33)

Total annual cost The total annual cost (TAC) incorporates the total costs associated in the food supply chain minus the income obtained from the sale of products, whereas the demand is satisfied in all the involved communities. aniPU anifCU anifPU TAC = ∑∑∑ Crveg , m1,t + ∑∑∑ Cra , m1,t + ∑∑∑ Cra , m1,t + ∑∑∑ Cra , m1,t + r

∑∑∑ C pa m1

+ ∑∑ C

+ ∑∑∑∑ C

vegPU r , m 3,t

t

m1

vegTrH r,t

t

pa m 2 m 3

t

m3

ra

r

aniTrM pa ,t

∑∑∑ C r

t

ani Pr pa , m1,t

t

∑∑ C pa

m1

t

ra

+ ∑∑ C r

t

aniTrHtM pa ,m 2 ,m 3,t

t

m1

vegTrM r,t

t

+ ∑∑ C r

+ ∑∑∑ C r

ra

m2

m1

t

vegS r , m 2,t

pa

+ ∑∑∑ C pa m 2

t

t

aniTrH + ∑∑ C pa + ,t

vegTrHsTM r,t

t

aniS pa, m 2,t

+

t

aniPU vegSA aniSA + ∑∑∑ Cpa, m 3,t − ∑∑∑ Cp, m 2,t − ∑∑∑ Cpa, m 2,t pa m 3

t

p

m2

t

pa m 2

t

(34) Objective Function The objective function includes the minimization of the total annual cost as follows: Objective Function = min TAC

(35)

The proposed model is a Linear Programming (LP) problem, which was coded in the software GAMS43, and solved in an Intel ® Xenon ® processor at 2.40 GHz and 8 GB of RAM. It should be noticed that the sustainability of the system is considered accounting for economic, environmental and social aspects in the proposed optimization model. First, the objective function is to determine the minimum cost to satisfy the nutrimental needs of disenfranchised communities involving the economic point of view. The social aspect was accounted for because the model involves to improve the local economy of the considered disenfranchised communities, involving local resources and to interact each other. Furthermore, the people of these disenfranchised communities can be benefited because through a better nutrition, they can get better health and education. Furthermore, the environment was considered, because in the proposed model, the



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available resources in the considered communities have been considered without considering an overexploitation of the natural reserves. In the proposed optimization model, binary variables are not needed for selecting the existence of hubs, because for this specific case, when a community produces an excess of animal or vegetable food, then there is needed a hub for processing, storing and distributing the access of food. Then, the cost for the hub only involves the amount of processed food. Binary variables can be included to reduce or control the number of hubs in the optimal solution, which can be easily included in the optimization model.

Case Study Particularly, in urban zones of Mexico there are approximately 7.25% of children between 5 and 14 years old with a deficit of nutrients, this percentage is duplicated in rural zones44. Moreover, 85% of the municipalities in Mexico are rural zones42. To address this problem, the Mexican government distributes basic meals to the most affected zones; however, this alternative requires a huge governmental inversion, not just for the purchase of products but also for distribution from urban zones, which affects simultaneously from the economic and the environmental points of view because of the emissions and monocultures in the same place causing soil wear and water pollution. The State of Michoacán in Mexico has been selected as case study in this work because it is one of the most disenfranchised states of Mexico (Figure 5). It has 113 municipalities, where 64% of the population lives under poverty conditions45. 14 municipalities with the lowest scores of HDI with major nutritional deficiencies are identified and have been selected for this study. The sustainability metric used for each municipality is the HDI, which is defined as the average of the human development of three factors, including human health, knowledge and standard of living.46 These dimensions (metrics) are measured through indirect factors, which are shown in Figure 6. The HDI does not reflect inequalities, poverty, human security and empowerment; however, the HDI is an indirect measurement of this as it can be seen in Figure 7. Hence, the HDI results were added to the poverty analysis, showing that there is a direct association between the municipalities with a great percentage of people living under poverty and the lowest HDI scores.


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Data for the case study The municipalities with the lowest HDI were selected; afterwards, for each considered municipality a distribution for the population based on age groups was performed, taken into account the report by INEGI42. Table 1 shows the considered age groups; meanwhile Table 2 presents the age groups distribution in each selected site. Additionally, Table 3 was generated using the approach reported by Bourges et al.47 for the nutritional needs of different age groups. Also, an analysis to identify the economic actives in each municipality was performed, which includes agriculture, cattle raising, available agricultural land, available fresh water and water conditions as it can be seen in Table 4. It should be noticed that the optimization model is general and it can consider different types of animals, for the presented case study, based on the available options, poultry, cattle and swain were considered. This way, the different types of food to feed these animals were considered in the model. The uncertainty may affect drastically the proposed mode. For example, the unit costs for raw material and products have involved a lot of uncertainty. Also, the production is highly affected by weather conditions. In this first model, average values for the involved parameters were considered accounting for statistical data bases.

Results The proposed mathematical model for the addressed case study is a LP formulation, which has 169,938 constraints and 650,418 continuous variables. The model was coded in the software GAMS and it takes 2.62 seconds of CPU time using the solver CPLEX43. First, the problem for minimizing the total annual cost was considered, the design configuration of this supply chain suggests that the production of vegetables is enough to satisfy the basic nutritional demands (Point A of Figure 8); however, this solution does not achieve a balanced diet, and it would represent a total change in dietary habits of the population, which makes this alternative impractical and difficult to implement. Thus, a constraint for the animal ingestion was considered, ensuring this way a healthy and balanced diet (see Figure 8). Hence, for the other analyzed scenarios, the TAC increases proportionally to the tonnes of animal products supplied (Points B, C and D of Figure 8). Then, each solution of this Figure 8 is discussed in detail. Solution A



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The solution of Scenario A generates a TAC of USD$-224,475, the negative value is given by Equation40, where the TAC is equal to the cost minus the sales; therefore, a positive net profit by the sale of the extra production is obtained. Table 5 shows the details about the satisfied nutritional demand in all the selected zones by each group of considered nutrients (carbohydrates, fiber, vegetal fats, polyunsaturated fatty acids (n-6) and (n-8), cholesterol, vegetal protein, animal protein, calcium, animal fat, iron and magnesium). Then, in the second row of Table 5, the tonnes of nutrients obtained from the production of vegetables are shown, similarly the third row presents the tonnes of nutrients from animal food production, which in this case are equal to zero (the solution for the minimum TAC does not consider nutrients from animal source food) because vegetables are cheaper. Afterwards, the global balance is presented in the fourth row of Table 5, which corresponds to the subtraction of the nutrients demand minus the nutrient production; in this case, if the global balance shows a negative value, it means that the demand has been satisfied (the numeric value shows the amount of tonnes that could be sold to external buyers); on the other hand, if the value is positive, it means that the nutrients demand has not been satisfied, the numeric value shows the amount of missing tonnes by each unsatisfied nutrient (cholesterol, animal protein and animal fats). In this scenario A, the sales between the selected zones are not activated due to the transportation cost represents a high increase in the TAC. This way, Young and Dhanda25 reported that local food just represents 7% of the total consumed in disenfranchised communities, while 93% comes from external industrial zones. Thus, it involves only the production, and local intake represents an alternative to the municipality economic development. 4,058,958 tonnes of vegetable products are used to satisfy the demand (avocado, beans, chili, corn, green tomatoes, mango, oats, onion, pumpkin, red tomatoes, sorghum, sugar cane and wheat) as Figure 9 shows. Solutions of scenarios B, C and D For the Scenarios B, C and D, the same amount of vegetable products are harvested; however, as the global balance of Table 5 shows, three parameters are unsatisfied (animal protein, fats and cholesterol). To fulfill this problem, the animal food production was added as a constraint, taking into account the animal products supply shown by Figure 10, while the total cost of each type of animal product is shown in Table 6.


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From these constrains, the global balances shown in Table 7 were obtained for the Scenarios B, C and D (and evaluated in the same way as in Table 5). In the Scenario B, the nutrient demand from animal proteins and fats is unsatisfied (see the global balance of Scenario B in Table 7), with a lack of 325 and 423 tonnes, respectively, while the cholesterol demand is satisfied. In the Scenarios C and D, all the nutrient groups are achieved; this means that the optimal solution is found between these two limit points, taking into account that an optimal solution for this study is to achieve a balanced diet and nutrition security. Figure 11 shows the production cost comparison between vegetable and animal products; in all scenarios B, C and D, the vegetable production remains constant, however it represents 97% of production cost in Scenario B, while for Scenarios C and D the production costs are 94% and 92%, respectively. It should be noted that even when the vegetables production represents more than 90% of the cost, it denotes higher yield and profit; because the profitability of vegetables, in the Scenario A, it is possible to obtain earnings even if there are only considering vegetable nutrients, therefore, the animal food production is used just to satisfy some nutrient demands that only can be obtained from animal source food. In all the scenarios, the transportation costs between the selected sites were included; this is because the local production has the capacity to satisfy the internal demand. Figures 12 and 13 show the configuration of the food supply chain, where the animal and vegetable productions are identified as

( RM ) veg

r ,m 1,t

and

( NA ) ra ,m1,t

for the

distribution fluxes ( m1) to represent the analyzed zone.

Conclusions This paper has presented a conceptual framework and an optimization formulation for planning a sustainable food network in disenfranchised zones. The proposed model incorporates the specific nutritional needs and local resources for the targeted region and integrates it with the broader supply chain. Food growth, harvesting, transportation, and usage are modeled as part of the supply chain. Economic and environmental objectives are addressed and reconciled through an optimization approach. Analogies between industrial and food supply chains are used to develop computationally efficient formulations and solution approaches.



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A case study has been solved for 14 Mexican communities (in the State of Michoacán) with high rates of nutritional deficiencies. Important factors such as yield and capacity production, healthy and balanced diet, resource efficiency and design configuration have been included in the mathematical model to provide a realistic basis for the food supply optimization. The results indicate that it is possible to satisfy the nutritional needs of disenfranchised communities using local resources that are integrated with the broader supply chains while enhancing the sustainability and economic growth of these communities. It is recommended to include different environmental and social objectives, as well as to account for the involved uncertainty in a future work.

AUTHOR INFORMATION Corresponding Author *Ponce-Ortega José M. Tel. +52 443 3223500. Ext. 1277. Fax. +52 443 3273584. E-mail: [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENT The authors acknowledge the financial support from the Mexican Council for Science and Technology (CONACyT).

Nomenclature Index L

Type of processed food (1= cheese, 2= bred, 3= chicken meat, 4=beef, 5= pork meat, 6= ham, 7= milk, 8=protein, 9= tortillas, 10=sugar)

m1

Harvesting sites (municipalities) included in the analysis (Municipalities selected 1-14)

m2

Hub located in each municipality (1-14)

m3

Population to feed in each municipality (1-14)


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Np

Population age groups, all the intervals are considered in years (2-3, 4-8, 9-13 (boys and girls), 14-18 (boys and girls), 19-30 (Women and men), 31-50 (Women and men), more than 51 (Women and men), the pregnancy and nursling are divided in three groups))

Nut

Nutrient package (oils, fruits, vegetables, dairy products, beans and meat).

Pa

Type of animal product (1= meat, 2= milk, 3= eggs)

R

Type of raw material (1= beans, 2= corn, 3= green tomato, 4= red tomato, 5= sorghum, 6= oats, 7= chili, 8= avocado, 9= pumpkin, 10= mango, 11= onion, 12= wheat and 13= sugar cane)

Ra

Type of animal (1=chicken, 2= caw, 3=pig)

T

Period of time considered, one period takes one week (Periods 1-52)

Variables

Arused , m1,t

Land used for agriculture (km2)

Arnew , m1,t

New area designated to cultivation (km2)

2 AraanifU ,m1,t Area used for animal feed (km )

Af raUAF , m1,t

Tonnes of animal food used to feed (tonnes)

AfraCAF ,m1,t

Tonnes of animal food cultivated, residues from the crops (tonnes)

AfraPAF , m1,t

Tonnes of animal food purchased from other sites (tonnes)

AFraCAF ,m1,t

Amount of cultivated animal food (tonnes)

AFraPAF ,m1,t

Amount of purchased animal food (tonnes)

CraaniPU , m1,t

Generated cost by the animal purchase (USD$)

Crveg ,m1,t

Total production cost of the vegetal raw material (USD$)

CraanifPU ,m1,t

Purchased animal food cost (USD$)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

CraanifCU ,m1,t Production animal food cost (USD$) ani Pr C pa , m1,t

Production cost of animal food (USD$)

aniTrH Cpa ,t

Cost by the animal product transportation to the hub (USD$)

aniTrM C pa ,t

Cost by the animal product transportation to the market from hub (USD$)

aniTrHstM Cpa ,t

Cost by the animal product transportation to the market from harvesting

sites (USD$)

CrvegTr ,t

Cost by vegetable transportation to the hub (USD$)

CrvegTrM ,t

Cost by vegetable transportation to the market (USD$)

Cr,vegTrHtM t

Cost by vegetable transportation from the hub to the market (USD$)

anis C pa , m 2,t

Crvegs ,m2,t aniSA C pa , m 2,t

Cost by the animal product storage (USD$) Cost by the vegetable product storage (USD$) Earnings by the animal product sales (USD$)

CrvegSA ,m2,t

Earnings by the vegetable product sales (USD$)

Dnut ,m3,t

Nutritional demand (tonne of each food group)

Fpaani,mP1,t

Animal food produced (tonnes)

Fpa,aniM m3,t

Animal product sent to the markets (tonnes)

FpaaniHStH ,m1,m2,t

Animals sent to the hub (tonnes)

FpaaniHtM ,m 2, m3,t

Animals sent to the market from the hub (tonnes)

FpaaniHStM ,m1,m3,t

Animals sent directly to the market (tonnes)

Fpa,aniHSA m2,t

Animals sold (tonnes)


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Fpaani,mPU3,t

Animal products purchased (tonnes)

Frveg ,m1,t

Total tonnes of vegetables produced (tonnes)

FrvegH , m1, m 2,t

Vegetables sent to the hubs (tonnes)

FrvegMar ,m1, m3,t

Vegetables distributed directly to the population (tonnes)

FrvegPU , m3,t

Vegetable products purchased from other producers (tonnes)

FrvegHtM ,m2, m3,t

Vegetables sent from the hub to the market (tonnes)

FrvegHStM , m1,m3,t

Vegetable products sent from the harvesting site to the market (tonnes)

FrvegHSA ,m 2,t

Vegetables sold in the market (tonnes)

NAra,m1,t

Number of animals produced in each site (number)

NaraAP,m1,t

Number of bought animals from other municipality (animals)

Narasale,m1,t

Number of sold animals to other municipalities (animals)

RM rveg ,m1,t

Tonnes of vegetable raw material (fresh food)

aniS Spa, m2,t

Animal product stored in the hub (tonnes)

aniSD S pa ,m2,t −1

Animal product stored in the hub in the previous time period (tonnes)

SrvegS , m 2,t

Vegetables stored (tonnes)

SrvegSD , m 2,t −1

Vegetables stored in previous period of time (tonnes)

TAC

Total annual cost (USD$)

Parameters

AraUAF ,m1,t

Area used to feed the animals (km2)

ArCurrent ,m1,t

Current area designated to the harvesting of each crop (km2)



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−Ve ArTot ,m1,t

Limit for the used area in each municipality (km2)

2 AraTAF ,m1,t Available area for the animal feed (km )

GEnut

Nutrient group (type)

Pem3,t

Inhabitants (number)

βrHS , m1,t

Yield factor of each cultivated crop (tonnes/km)

θraYPA,m1,t

Yield factor of produced animals (animals/tonnes food)

anin ξnut ,pa

Amount of needed animal nutrients (tonnes)

vegn ξnut ,r

Amount of needed vegetable nutrients (tonnes)

φraRPA , r , m1,t

Yield of raw material residues (tonnes/tonnes)

λpa,ra,m1,t

Yield factor of produced animals (tonnes/amount of animal)

σ raaniPU , m1,t

Unit animal purchased cost (USD$/animal)

ani Pr σ pa , m1,t

Price of animal production (USD$/animal)

Pr σ rveg ,m1,t

Unit vegetable production cost (USD$/tonnes)

aniTrH σ pa ,m1,m2,t

Animal product price transportation from the harvesting sites to the hub

(USD$/tonnes) aniTrM σ pa ,m2,m3,t

Animal product price transportation from the hub to the market

(USD$/tonnes) aniTrHstM σ pa ,m1,m3,t

Animal product price transportation from the harvesting site to the

market (USD$/tonnes)

σ rvegTrH , m1, m 2,t

Vegetable price transportation from the harvesting sites to the hub

(USD$/tonnes)


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σ rvegTrM , m1,m3,t

Vegetable price transportation from the harvesting sites to the market

(USD$/tonnes)

σ raanifCU ,m1,t

Unit animal food cost (USD$/tonnes)

σ raanifPU ,m1,t

Unit animal purchased food cost (USD$/tonnes)

anis σ pa ,m 2,t

Price for the animal products storage (USD$/tonnes)

σ rvegs , m2,t

Price for the vegetable products storage (USD$/tonnes)

aniSA σ pa , m 2,t

Unit price for animal product sales (USD$/tonnes)

σ rvegSA , m 2,t

Unit price for vegetable sales (USD$/tonnes)

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(17) Galán-Martín, A.; Pavel, V.; Assumpción, A.; Jiménez-Esteller, L.; GuillénGosálbez, G. Multi-objective optimization of rainfed and irrigated agricultural areas considering production and environmental criteria a case study of wheat production in Spain. J. Cleaner Prod. 2017, 140(2): 816-830. (18) Sgarbossa, F.; Russo, I. A proactive model in sustainable food supply chain:

insight from a case study. Int. J. Prod. Econ. 2017, 183(1):596-606. (19) Wang, J.; Yue, H. Food safety pre-warning system based on data mining for sustainable food supply chain. Food Control. 2017, 73(1):223-229. (20) Yu, F.; Xue, L.; Sun, C.; Zhang, C. Product transportation distance based supplier selection in sustainable supply chain network. J. Cleaner Prod. 2016, 137(1): 29-39. (21) Accorsi, R.; Cholette, S.; Manzini, R.; Pini, C.; Penazzi, S. The land-network problem: ecosystem carbon balance in planning sustainable agro-food supply chains. J. Cleaner Prod. 2016, 112(1): 158-171. (22) Catalá, L, P.; Moreno, S.; Blanco, A. M.; Bandoni, A. A bi-objective optimization model for tactical planning in the pome fruit industry supply chain. Comput. Electronics Agri. 2016, 130(1): 128-141. (23) Beitzen-Heineke, E. F.; Balta-Ozkan, N.; Reefke; H. The prospects of zeropackaging grocery stores to improve the social and environmental impacts of the food supply chain. J. Cleaner Prod. 2017, 140(1): 1528-1541. (24) Garnett, T. Where are the best opportunities for reducing greenhouse gas emissions in the food system (including the food chain)? Food Policy. 2011, 36(1): s23-s32. (25) Young, T. S.; Dhanda, K. K. Sustainability: Essentials for business. SAGE Publications, Los Angeles CA. United States of America. 2012 (26) The World Bank (2015) Population growth (annual %). Available on: http://data.worldbank.org/indicator/SP.POP.GROW (Accessed May 2017) ( (27) Nicholson, C. F.; He, X.; Gómez, M. I.; Gao, H. O.; Hill, E. Environmental and economic impacts of localizing food systems: The case of dairy supply chains in the Northeastern United States. Environ. Sci. Technol. 2015, 49(1): 1200512014. (28) Bala, B. K.; Alias, E. F.; Arshad, F. M.; Noh, K. M.; Hadi, A. H. A. Modelling of food security in Malaysia. Simulat. Model. Prac. Theo. 2014, 47(1): 152164.



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(29) Manzini, R.; Accorsi, R. The new conceptual framework for food supply chain assessment. J. Food Eng. 2013, 115(1): 251-263. (30) Özbayrak, M.; Papadopoulou, T.; Akgun, M. Systems dynamics modelling of a manufacturing supply chain system. Simulat. Model. Prac. Theo. 2007, 15(10): 1338-1355. (31) Ma, L.; Wang, F.; Zhang, W.; Ma, W.; Velthof, G.; Qin, W.; Oenema, O. Environmental assessment of management options for nutrient flows in the food Chain in China. Environ. Sci. Technol. 2013, 47(1): 7260-7268. (32) Soysal, M.; Bloemhof-Ruwaard, J. M.; Van der Vorst, J. G. A. J. Modelling food logistics networks with emission consideration: The case of an international beef supply chain. Int. J. Prod. Econ. 2014, 152(1):57-70 (33) Mosleh, Z.; Salehi, M. H.; Fasakhodi, A. A.; Jafari, A.; Mehnatkesh, A.; Borunjeni, E.; Sustainable allocation of agricultural lands and water resources using suitability analysis and mathematical multi-objective programming. Geoderma. 2017, 303(1):52-59 (34) Jana, P. K.; Sharma, D. K.; Chakraborty, B. A hybrid probabilistic fuzzy goal programming approach for agricultural decision making. Int. J. Prod. Econ. 2016, 173(1): 134-141 (35) Galán-Martín, A.; Pozo, C.; Guillén-Gosálbez, G.; Antón-Vallejo, A.; JiménezEsteller, L. Multi-stage linear programming model for optimizing cropping plan decisions under the new Common Agricultural Policy. Land Use Policy. 2015, 48(1):515-524 (36) Rubio-Castro, E.; Ponce-Ortega, J.M.; Cervantes-Gaxiola, M.E.; HernándezCalderón, O.M.; Ortiz-del-Castillo, J.R.; Milán-Carrillo, J.; HernándezMartínez, J.F.; Meza-Contreras, J.A. Optimal design of integrated agricultural water networks. Comput. Chem. Eng. 2016, 84(1): 63-82 (37) Ma, L.; Wang, F.; Zhang, W.; Ma, W.; Velthof, G.; Qin, W.; Oenema, O.; Zhang, F. Environmental assessment of management options for nutrient flows in the food chain in China. Environ. Sci. Technol. 2013, 47(13): 7260-7268 (38) Nicholson, C.F.; He, X.; Gómez, M.I.; Gao, H.O.; Hill, E. Environmental and economic impacts of localizing food systems: The case of dairy supply chains in the Northeastern U.S. Environ. Sci. Technol. 2015, 49(20): 12005-12014


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(39) Van der-Vorst, J.; Tromp, S. O.; Van der Zee, D. J. Simulation modelling for food supply chain redesign; integrated decisions making on product quality, sustainability and logistics. Int. J. Prod. Res. 2009, 47(23): 6611-6631. (40) Tao, Q.; Huang, Z.; Gu, C.; Zhang, C. Optimization of green agri-food supply chain network using particle swarm optimization algorithm. Comput. Eng. Network. 2014, 277(1): 91-98. (41) Banasik, A.; Kanellopoulos, A.; Claassen, G. D. H.; Bloemhof-Ruwaard, J. M.; Van der Vorst, J. G. A. Assessing alternative production options for ecoefficient food supply chains using multi-objective optimization. Ann. Oper. Res. 2016, 1(1): 1-22. (42) INEGI (National Institute of Statistics and Geography. Mexico in numbers): National Information by state and municipalities. 2012. Mexico City. http://www.inegi.org.mx/ (Accessed May 2017) (43) Brooke, A.; Kendrick, D.; Meeruas, A.; Raman, R. GAMS-Language guide, GAMS Development Corp: Washington DC., 2017. (44) UNICEF (United Nations Children´s Fund) (2016) Health and nutrition. Available on: http://www.unicef.org/mexico/spanish/17047.htm (Accessed May 2017). (45) CONEVAL (National Assessment of Social Development Policy) (2012) Puberty 2010 State information: Michoacán 2010-2012. Available on: http://www.coneval.org.mx/InformesPublicaciones/Documents/folletos_pobrez ayrezagosocial/michoacan_pob_rez_soc.pdf (Accessed January 2017) (46) UNDP

(United

Development

Nations Index

Development

Programme)

(HDI).

(2016)

Available

http://hdr.undp.org/en/content/human-development-index-hdi

Human on: (Accessed

January 2017) (47) ourges, H.; Casanueva, E.; Rosado, J. L. Intake recommendations for the Mexican population. Medica Panamericana, Mexico City. 2009. (48) NOM-043-SSA2-2005 (Official Mexican Norm), Basic security services. Promotion and education to health in relation to the food. Mexico City, 2006. http://www.promocion.salud.gob.mx/dgps/descargas1/programas/2_norma_ofi cial_mexicana_nom_043_SSA2_2005.pdf (Accessed January 2017)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Tables

Table 1. Population range in each municipality.

Group

Age (years)

Preschool

2 to 3

Scholars

4 to 8

Girls

9 to 13

Boys

9 to 13

Group

14 to 18

Boys

14 to 18

Group

Adults

Women

Teens Girls

Age (years)

Men

Period 1º Quarter

19 to 30

Pregnancy 2º Quarter

31 to 50

3º Quarter

More than 51

1º Quarter

19 to 30

2º Quarter

31 to 50

Nursling

More than 51


3º Quarter

Page 31 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Table 2. Population distribution in the selected municipalities (%). Children Municipalities

Girls

Boys

Girls

Boys

Women

Men

Women

Men

Women

Men

0-1

2 to 3

4 to 8

9 to 13

9 to 13

14 to 18

14 to 18

19 to 30

19 to 30

31 to 50

31 to 50

more than 51

more than 51

Charapan

0,93

1,87

11,21

5,99

5,29

2,52

2,41

6,31

6,05

19,84

15,18

12,51

9,88

Churintzio

1,74

3,49

8,72

5,90

4,55

4,92

3,79

11,92

9,17

13,57

10,44

12,31

9,49

Churumuco

0,99

2,00

11,97

5,93

6,04

2,22

2,24

5,57

5,60

17,75

17,60

11,12

10,97

Huaniqueo

1,40

2,81

7,02

4,87

3,53

4,06

2,94

11,60

8,41

17,95

13,00

12,99

9,41

Nahuatzen

0,91

1,83

10,95

5,40

5,55

4,27

3,80

10,66

9,50

6,15

5,34

18,74

16,92

Nocupétaro

1,06

2,14

12,79

7,23

5,56

2,18

2,18

5,44

5,46

17,40

16,30

11,43

10,84

Susupuato

0,93

1,89

11,31

6,00

5,31

2,34

2,10

5,81

5,24

18,45

17,76

11,55

11,32

Tacámbaro

1,00

2,01

12,06

6,00

6,06

4,20

3,90

10,50

9,76

5,80

5,20

17,61

15,89

Tangamandapio

2,74

5,49

13,71

8,97

7,49

7,47

6,24

14,99

12,51

6,15

5,14

4,96

4,14

Tiquicheo

0,80

1,61

9,66

4,85

4,81

2,21

2,13

5,52

5,34

19,11

19,17

12,37

12,41

Tumbiscatío

1,03

2,05

12,31

5,42

6,89

2,26

2,13

5,64

5,33

17,19

17,67

10,86

11,23

Turicato

2,91

5,83

14,57

9,35

8,13

7,80

6,75

13,86

12,04

3,72

3,23

6,31

5,49

Tuzantla

2,98

5,96

14,90

9,21

8,67

7,67

7,23

13,80

13,00

1,38

1,29

7,16

6,74

Tzitzio

0,91

1,84

10,98

5,80

5,19

2,04

2,10

5,09

5,23

17,94

18,75

11,88

12,26



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Page 32 of 51

Table 3. Nutritional needs (tonnes/person*y). Fatty acids Sex

Age range

Carbohydrates

Fiber

Fats

Fatty acids

polyunsaturated polyunsaturated Cholesterol (n-3)

(n-6)

Proteins

Any

0 to 1

0.000539

0.000133

0.000217

0.0000308

0.0000035

8.75E-07

0.00007

Any

2 to 3

0.00091

0.000133

0.00021

0.0000322

0.0000322

8.75E-07

0.0000091

Any

4 to 8

0.00091

0.000175

0.000245

0.000049

0.000049

8.75E-07

0.000133

Girls

9 to 13

0.00091

0.000182

0.000245

0.00007

0.00007

8.75E-07

0.000238

Boys

9 to 13

0.00091

0.000217

0.000245

0.000084

0.000084

8.75E-07

0.000238

Girls

14 to 18

0.00091

0.000182

0.000245

0.00007

0.00007

8.75E-07

0.000322

Boys

14 to 18

0.00091

0.000266

0.000245

0.000077

0.000077

8.75E-07

0.000364

Women

19 to 30

0.00091

0.000175

0.00021

0.000084

0.000084

8.75E-07

0.000322

Men

19 to 30

0.00091

0.000266

0.00021

0.000119

0.000119

8.75E-07

0.000392

Women

31 to 50

0.00091

0.000175

0.00021

0.000084

0.000084

8.75E-07

0.000322

Men

31 to 50

0.00091

0.000266

0.00021

0.000119

0.000119

8.75E-07

0.000392

Women

more than 51

0.00091

0.00021

0.00021

0.000077

0.000077

8.75E-07

0.000322

Men

more than 51

0.00091

0.00021

0.00021

0.000098

0.000098

8.75E-07

0.000392


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Table 4. Agricultural land in each municipality (km2). Municipality

Current area Available area Maximum area

Charapan

117

77,33

194,33

Churintzio

74,06

54,63

128,69

Churumuco

186,71

223

409,71

Huaniqueo

74,25

70,91

145,16

Nahuatzen

138,11

29,71

167,82

Nocupétaro

38,32

266,07

304,39

Susupuato

91,03

75,69

166,72

Tacámbaro

341,35

72,08

413,43

Tangamandapio

138,26

61,98

200,24

Tiquicheo

120,81

365,54

486,35

Tumbiscatío

63,48

1252,44

1315,92

Turicato

314,91

630,61

945,52

Tuzantla

138,46

363,4

501,86

Tzitzio

21,32

402,79

424,11



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Page 34 of 51

Table 5. Nutritional demand and input from animal and vegetable products in Scenario A (tonnes/y)

Polyunsaturated Concept

Carbohyd

Fiber

rates Demand

12049

2729

Vegetal

fatty acids

Magnesi Cholest

Vegetal

Animal

Calci

Animal

fat

(n-6)

(n-8)

erol

protein

protein

um

fat

2368

1097

113

12

3159

788

12

572

Iron

um

2,E-

4

01 Vegetal

2293853

69427

29869

29869

8

152408

0

1538

0

75

2108

57

input Animal

1272

0

0

0

0

0

0

0

0

0

0

0

0

-2281804

-

-67059

-28772

-29756

4

-149249

788

-1526

592

-74

-2104

input Global balance

1245 29


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Table 6. Cost of animal products for different scenarios (USD/y). Product

A

B

C

D

Chicken

0

2,511,600

5,023,200

6,362,720

Caw

0

1,092,000

2,184,000

2,766,400

Pig

0

1,310,400

2,620,800

3,319,680



Table 7. Satisfied nutrient demand in Scenarios B, C and D (tonnes/y). Carboh Type of nutrient

Fiber

ydrates

Vegeta

Polyunsaturated

Cholester

Vegetal

Animal

l fat

fatty acids

ol

protein

protein

(n-6) Demand

12049

2729

2368

1097

Calcium

Animal

Iron

fat

esium

(n-8) 113

Magn

12

3159

788

12

572

2,E-

4

01 Scenario Global Balance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Page 36 of 51

B Scenario C Scenario D

-

-

2281870

124529

-

-

2281937

124529

-

-

2281972

124529

-67059

-28772 -29756

-1

-149249

325

-1528

423

-74

-2104

-67059

-28772 -29756

-6

-149249

-138

-1530

-8

-75

-2105

-67059

-28772 -29756

-9

-149249

-385

-1531

-57

-75

-2105


Page 37 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Caption for Figures: Figure 1. Undernourishment distribution in developing regions. Figure 2. Proposed superstructure for the sustainable food supply chain. Figure 3. Healthy eating plate (Healthy eating pyramid).47 Figure 4. Distribution of products. Figure 5. Location for the addressed case study. Figure 6. HDI dimensions. Figure 7. HDI for the municipalities of the State of Michoacan. Figure 8. Effect of animal food consumption increase on cost. Figure 9. Distribution of vegetable products. Figure 10. Animal products supply for different scenarios. Figure 11. Production cost of vegetable and animal nutrients for different scenarios. Figure 12. Diagram configuration of food supply chain for Scenarios A (above) and B (below). Figure 13. Diagram configuration of food supply chain for Scenarios C (Above) and D (below).



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Africa 27% 39%

Asia Latin America and Caribbean

11% 23%

Oceania

Figure 1. Undernourishment distribution in developing regions.


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2. Proposed superstructure for the sustainable food supply chain.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Oils

Fruit Grains Vegetables Dairy products Beans and meat

Figure 3. Healthy eating plate (Healthy eating pyramid).47


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4. Distribution of products.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Michoacán

Mexico Pacific Ocean

Golf of Mexico

Figure 5. Location for the addressed case study.


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Education dimension • Assessed by life expectancy at birth

Health dimension

• Years of schooling for adults aged 25 years • Expected years of schooling for children of school entering age

Figure 6. HDI dimensions.


• Measured by gross national income per capita Standar living dimension


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 44 of 51

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Health index

Education index

Percapita income index

HDI

Figure 7. HDI for the municipalities of the State of Michoacan.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Animal protein supplied ton/y

Page 45 of 51

200 180 160 140 120 100 80 60 40 20 0

D C

B

A

USD/y

Cost of food supply

Figure 8. Effect of animal food consumption increase on cost.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Sugar cane 4% Wheat 3%

Beans 4% Corn 8%

Green tomatoes 6%

Red tomatoes 11%

Onion 37%

Mango 1% Pumpkin 4%

Oats 12%

Sorghum 4%

Avocado 2%

Chili 4%

Figure 9. Distribution of vegetable products.


Page 46 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Ton/y

Page 47 of 51

3000 2500 2000 1500 1000 500 0

2766

Chicken Caw Pig

2184 1092

0 A

B

C

D

Scenario

Figure 10. Animal products supply for different scenarios.



200000000 Production cost (USD/Y)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 48 of 51

160000000 120000000 Vegetal

80000000

Animal 40000000 0 B

C Scenario

D

Figure 11. Production cost of vegetable and animal nutrients for different scenarios.


Page 49 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Figure 12. Diagram configuration of food supply chain for Scenarios A (above) and B (below).



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Figure 13. Diagram configuration of food supply chain for Scenarios C (above) and D (below)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


For Table of Content Use Only

Synopsis: A mathematical optimization approach was proposed for sustainable food networks in disenfranchised communities.


Sustainable Optimization of Food Networks in Disenfranchised

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