Sustainable Optimization of Food Networks in Disenfranchised

Research Article pubs.acs.org/journal/ascecg

Sustainable Optimization of Food Networks in Disenfranchised Communities Sergio Iván Martínez-Guido,† J. Betzabe González-Campos,‡ Mahmoud M. El-Halwagi,§,∥ and José María Ponce-Ortega*,† †

Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Av. Francisco J. Mujica, S/N, Ciudad Universitaria, Edificio V1, Morelia, Michoacán 58060, México ‡ 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 § Chemical Engineering Department, Texas A&M University, 0386 Spence Street, College Station, Texas 77843, United States ∥ Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia 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, whereas 50 million children of the same age group have low weight compared to their normalweight 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 food.4 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 Received: May 29, 2017 Revised: August 15, 2017 Published: August 16, 2017

Figure 1. Undernourishment distribution in developing regions. © 2017 American Chemical Society

8895

DOI: 10.1021/acssuschemeng.7b01703 ACS Sustainable Chem. Eng. 2017, 5, 8895−8907

Research Article

ACS Sustainable Chemistry & Engineering

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

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 ́ et al.12 the design of biorefining supply chains. López-Diaz proposed a mathematical model for the supply chain of biorefineries accounting for the interactions with the ́ surrounding watershed. Martinez-Guido et al.13 analyzed the reconfiguration of a sugar cane industry to an integrated biorefinery. Noureldin and El-Halwagi14 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-Martiń et al.17 proposed a multiobjective optimization model for an integral agricultural network.

environmental objectives may be reconciled with other sustainability objectives through the use of multidimensional 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 ́ et al.9 presented an municipal solid waste. Arredondo-Ramirez optimization approach for the shale gas exploitation including the infrastructure development in Mexico. Yue et al.10 included 8896


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ACS Sustainable Chemistry & Engineering 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 abovementioned 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 noted 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 associated emissions from some processing products.30 Other works have focused on the integration of new technologies31 and management32 to obtain sustainable farms.33 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 with the agriculture in India. Galán-Martiń et al.35 developed a multistage 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 resources.40,41,19 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 multiobjective 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 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.

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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 living 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.

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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 the animal and vegetal food are produced, 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 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 8897


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UAF The area used to cultivate animal food (Ara,m1,t ) has to be constrained by the maximum available land for this activity (ATAF ra,m1,t).

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 veg HS raw material produced (RMr,m1,t ) is equal to the yield (βr,m1,t ) multiplied by the occupied area for each product in each municipality (Aused r,m1,t). HS used RMrveg , m1, t = βr , m1, t A r , m1, t ,

TAF A raUAF , m1, t ≤ A ra , m1, t ,

ANP Fpa , m1, t = NA ra , m1, t λpa , ra , m1, t ,

∀ pa ∈ PA , ra ∈ RA , m1 ∈ M1, t ∈ T (1)

Pr sent to the consumers (∑m3 Frveg , m1, m3, t ).

RMrveg , m1, t =

amount of vegetables sent to the consumers (∑m3 FrvegHtM , m2, m3, t ) and the one sold (Fvegetable−hub−sale ). r,m2,t

(3)

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 (Af UAF ra,m1,t) to feed the animal (ra) multiplied YPA by the growth yield (θra,m1,t ) plus the amount of bought animals AP from other sites (Nara,m1,t ) minus the amount of animals sold to other municipalities (Nasale ra,m1,t).

vegSD SrvegS , m2, t = Sr , m2, t − 1 +

−

FrvegHtSa , m2, t ,

m3

∀ r ∈ R , m2 ∈ M 2, t ∈ T

(10)

The amount of vegetables in the markets (FvegM r,m3,t) is equal to the vegetables received from the hubs (∑m2 FrvegHtM , m2, m3, t ) plus the ones received directly from harvesting sites (∑m1 FrvegM , m1, m3, t ) plus the amount of vegetables purchased from other sites (FvegPu r,m3,t).

(4)

FrvegM , m3, t =

UAF (Af ra,m1,t )

The food used to feed animals accounts for the amount of cultivated food (Af CAF ), which are crop wastes that ra,m1,t can be used as animal food (chaff and stubble) plus the amount of animal food that can be purchased from other sites (Af PAF ra,m1,t).

vegHtM vegPu ∑ FrvegHStM , m1, m3, t + ∑ Fr , m2, m3, t + Fr , m3, t , m1

m2

∀ r ∈ R , m3 ∈ M 3, t ∈ T

(11)

Animal Products. The animal products need preprocessing and/or packing, therefore, the first balance includes the amount P of animal products in the hub (Fani pa,m1,t), the one existing in the aniHStH hub (∑m2 F pa , m1, m2, t ) and the one that is sent to the markets

Af raUAF = Af raCAF + AfraPAF , , m1, t , m1, t , m1, t (5)

aniHStM (∑m3 F pa , m1, m3, t ).

The cultivated animal food (Af CAF ra,m1,t) can be defined like grazing, which means that the crop residues can be used as food YPA for the animals, which is equal to animal yield (θra,m1,t ) UAF multiplied by the cultivated area (Ara,m1,t) plus the harvested vegetables (RMveg r,m1,t) multiplied by the fraction used to feed animals (ϕRPA ra,r,m1,t) (i.e., waste like corn residues used to feed chickens).

aniP F pa , m1, t =

aniHStM ∑ F paaniHStH , m1, m2, t + ∑ F pa , m1, m3, t , m2

m3

∀ pa ∈ PA , m1 ∈ M1, t ∈ T

(12)

The animal product in the hub includes the amount stored (SaniS pa,m2,t), which is equal to the amount that was stored in a aniSD previous time period (Spa,m2,t−1 ) plus the amount received from aniHStH the production sites (∑m1 Fpa, m1, m2, t ) minus the amount sent to

∑ (ϕraRPA RMrveg , m1, t ), , r , m1, t r

∀ ra ∈ Ra , m1 ∈ M1, t ∈ T

vegHtM ∑ FrvegH , m1, m2, t − ∑ Fr , m2, m3, t m1

UAF AP sale NA ra , m1, t = θraYPA , m1, t Af ra , m1, t + Nara , m1, t − Nara , m1, t ,

UAF Af raCAF = θraYPA , m1, t A ra , m1, t + , m1, t

(9)

The vegetable balance in the hub states that the amount of stored vegetables (SvegS r,m2,t) is equal to the amount of vegetables stored in a previous time period (Svegetable−stored ) plus the amount r,m2,t−1 received from harvesting sites (∑m1 FrvegH , m1, m2, t ) minus the

Furthermore, the total cultivated area must be lower than the maximum available in the municipality (ATot−Veg r,m1,t ).

∀ ra ∈ Ra , m1 ∈ M1, t ∈ T

m3

∀ r ∈ R , m1 ∈ M1, t ∈ T

(2)

∀ ra ∈ Ra , m1 ∈ M1, t ∈ T

vegMar ∑ FrvegH , m1, m2, t + ∑ Fr , m1, m3, t , m2

∀ r ∈ R , m1 ∈ M1, t ∈ T

∀ m1 ∈ M1, t ∈ T

(8)

Product Distribution. The balances for the different products are stated as follows. Vegetables. The produced vegetables (RMveg r,m1,t) are equal to those received from the hubs over the time period t (∑m2 FrvegeH , m1, m2, t ) plus the amount of vegetables that can be

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 used cultivation (Ar,m1,t ) accounts for the current cultivated area current (Ar,m1,t ) plus the new needed area to cultivate additional new vegetables (Ar,m1,t ).

Tot − Ve A rused , m1, t ≤ A r , m1, t ,

(7)

Eggs, Meat and Milk Production. The animal products (eggs, meat and milk) account for the yield factor of each product (λpa,ra,m1,t) multiplied by the number of produced animals (NAra,m1,t).

∀ r ∈ R , m1 ∈ M1, t ∈ T

Current new A rused , m1, t = A r , m1, t + A r , m1, t ,

∀ ra ∈ Ra , m1 ∈ M1, t ∈ T

aniHtM aniHSA the market (∑m3 F pa , m2, m3, t ) and the one sold (Fpa,m2,t ).

(6) 8898


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ACS Sustainable Chemistry & Engineering aniS aniSD Spa, m2, t = Spa , m2, t − 1 +

m1

−

aniHSA Fpa, m2, t ,

to the produced vegetables (RMveg r,m1,t) multiplied by the unit crop cost (σveg ): r,m1,t

aniHStH aniHtM ∑ Fpa, m1, m2, t − ∑ F pa , m2, m3, t m3

∀ pa ∈ PA , m2 ∈ M 2, t ∈ T

veg veg Crveg , m1, t = RM r , m1, t σr , m1, t ,

(13)

(17)

Equation 14 shows the animal product balance in the aniM markets (Fpa,m3,t ), where the amount of animal product in the market is equal to the flux that is received from the hubs aniHtM (∑m2 Fpa, m2, m3, t ), and the flux that is received directly from the

Animal Purchase. There is a cost associated with the aniPU purchase of animals (Cra,m1,t ), which is equal to the number of purchased animals (NAPU ra,m1,t) multiplied by the corresponding unit animal cost (σaniPU ra,m1,t):

aniHStM harvesting site without treatment (∑m1 Fpa, m1, m3, t ), plus the aniPU ). amount of purchased animal product (Fpa,m3,t aniM Fpa, m3, t =

PU aniPU CraaniPU , m1, t = NA ra , m1, t σra , m1, t ,

∀ ra ∈ RA , m1 ∈ M1, t ∈ T

aniHStM aniHtM aniPU ∑ Fpa, m1, m3, t + ∑ Fpa, m2, m3, t + Fpa, m3, t , m1

(18)

Animal Food. There is a cost associated with feed the CU anif CU animals (Canif ra,m1,t ), which depends on the unit factor (σra,m1,t ) as anif CU well as the cultivated animal food (AFra,m1,t ):

m2

∀ pa ∈ PA , m3 ∈ M 3, t ∈ T

∀ r ∈ R , m1 ∈ M1, t ∈ T

(14)

It should be noted 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. 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.48

anifCU anifCU CraanifCU , m1, t = AFra , m1, t σra , m1, t ,

∀ ra ∈ RA , m1 ∈ M1, t ∈ T (19)

When the cultivated animal food is not enough, the food for the PU animals must be purchased (Canif ra,m1,t ), which is equal to the unit anif PU cost (σra,m1,t ) multiplied by the purchased animal food PU (AFanif ra,m1,t ): anifPU anifPU CraanifPU , m1, t = AFra , m1, t σra , m1, t ,

∀ ra ∈ RA , m1 ∈ M1, t ∈ T (20)

Furthermore, the production of the animal food has an associated cost (CaniPr pa,m1,t), which takes into account the produced aniPr animals (FaniPr pa,m1,t) multiplied by the unit cost (σpa,m1,t): ani Pr ani Pr ani Pr C pa , m1, t = F pa , m1, t σpa , 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.

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

From each of these six groups, the main micro and macro nutrients were obtained, creating a new division of 12 groups (carbohydrates, fats, fiber, cholesterol, calcium, n-3 and n-6 fatty acids polyunsaturated, proteins, lipids, vitamins, animal protein and iron). These 12 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, t GEnut , ∀ nut ∈ NUT , m3 ∈ M 3, t ∈ T

(15)

The demands (Dnut,m3,t), in terms of the vegetables and aniM animal food (FvegM r,m3,t, Fpa,m3,t), are multiplied by the nutriment anin factor demanded by the population (ξvegn nut,r, ξnut,pa): Dnut , m3, t ≥

vegn aniM anin ∑ FrvegM , m3, t ξnut , r + ∑ Fpa, m3, t ξnut ,pa + , r

pa

∀ nut ∈ NUT , m3 ∈ M 3, t ∈ T

(16)

Costs. Vegetables Production. The cost generated by the vegetables due to the raw material production (Cveg r,m1,t) is equal

Figure 4. Distribution of products. 8899


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Cost Generated by the Purchase of Products. The cost for the purchased vegetables (CvegPU r,m3,t ) depends on the purchased vegPU amount (FvegPU r,m3,t ) times the unit price (σr,m3,t ):

This way, the transportation cost for vegetables from cultivation sites to the hubs (CvegTr r,t ) is related to the unit transportation cost (σvegTrH r,m1,m2,t) times the amount of transported vegetables (FvegH r,m1,m2,t): CrvegTr ,t

=

∑∑

vegTrH FrvegH , m1, m2, t σr, m1,m2, t ,

vegPU vegPU CrvegPU , m3, t = Fr , m3, t σr , m3, t ,

(30) aniPU Similarly, the cost for the purchased animals (Cpa,m3,t ) aniPU depends on the amount of purchased animal (Fpa,m3,t) and aniPU the unit cost (σpa,m3,t ):

m1 m2

(22)

The transportation cost for vegetables from cultivation sites to markets (CvegTrM ) depends on the unit transportation cost r,t vegTrM (σr,m1,m3,t ) and the transported amount (FvegHStM r,m1,m3,t): CrvegTrM = ,t

vegTrM ∑ ∑ FrvegHStM , m1, m3, t σr, m1,m3, t ,

aniPU aniPU aniPU C pa , m3, t = F pa , m3, t σpa , m3, t ,

vegSA Sales. The profit obtained for the sale of vegetables (Cr,m2,t ) vegSA depends on the amount of sold vegetables (Fr,m2,t) and the unit sale cost (σvegSA r,m2,t):

(23)

The transportation cost for vegetables from hubs to markets vegHtM (CvegTrHtM ) is related to the transported amount (Fr,m2,m3,t ), r,t vegTrHtM which is multiplied by the unit transportation cost (σr,m2,m3,t ): =

∑∑

vegTrHtM FrvegHtM , m2, m3, t σr, m2,m3, t ,

vegSA vegSA Cr,vegSA m2, t = Fr , m2, t σr , m2, t ,

(32)

∀ r ∈ R, t ∈ T (24)

aniSA aniHSA aniSA C pa , m2, t = Fpa, m2, t σpa , m2, t ,

Similarly, for the animal products, where the animal aniTrH transportation cost from production to markets (Cpa,t ) aniHstH depends on the transported amount (Fpa,m1,m2,t) and the unit aniTrH transportation cost (σpa,m1,m2,t ):

(33)

m1 m2

TAC =

(25)

∑ ∑ ∑ Crveg, m1, t + ∑ ∑ ∑ CraaniPU , m1, t r

The transportation cost for animals from hubs to markets aniTrM (Cpa,t ) is obtained multiplying the transported amount aniHtM (Fpa,m2,m3,t) by the unit transportation cost (σaniTrM pa,m2,m3,t): aniTrM C pa ,t

=

∑∑

+ + +

(26)

=

∑∑

+ + +

(27)

+

+

t

t

∑ ∑ ∑ CraanifPU , m1, t m1

t

∑ ∑ Cr,vegTrH t r

r aniTrH C pa ,t

+

t

pa

∑∑∑∑

t

∑ ∑ CpaaniTrM ,t

t

t

aniTrHtM C pa ,m2,m3, t

+

t

∑ ∑ ∑ CrvegS , m2, t r

m2

t

aniS vegPU ∑ ∑ ∑ Cpa, m2, t + ∑ ∑ ∑ Cr , m3, t t

r

m3

t

aniPU vegSA ∑ ∑ ∑ Cpa, m3, t − ∑ ∑ ∑ Cp, m2, t m3

t

∑∑∑ pa m2

p

m2

t

aniSA Cpa, m2, t

(34)

t

Objective Function. The objective function includes the minimization of the total annual cost as follows: ObjectiveFunction = min TAC

(35)

The proposed model is a linear programming (LP) problem, which was coded in the software GAMS,43 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

∀ r ∈ R , m2 ∈ M 2, t ∈ T (28)

anis Similarly, for the storage of animal products (Cpa,m2,t ):

anis aniS anis Cpa, m2, t = Spa, m2, t σpa, m2, t ,

∑∑

pa

−

m1

ra ani Pr C pa , m1, t

t

pa m2

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. First, the vegetable storage cost (Cvegs r,m2,t) considers the stored vegetables in a hub (SvegS r,m2,t) multiplied by the unit factor (σvegs r,m2,t): vegS vegs Crvegs , m2, t = Sr , m2, t σr , m2, t ,

m1

+

t

pa m2 m3

m1 m3

∀ pa ∈ PA , t ∈ T

m1

CraanifCU , m1, t

∑ ∑ Cr,vegTrM + ∑ ∑ Cr,vegTrHsTM t t pa

aniHStM aniTrHstM F pa , m1, m3, t σpa , m1, m3, t ,

ra

∑∑∑ r

Finally, the transportation cost for the animal products from the production site to the final markets (CaniTrHstM ) is stated as pa,t follows:

t

∑∑∑ pa

m 2 m3

aniTrHstM C pa ,t

m1

ra

aniHtM aniTrM F pa , m2, m3, t σpa , m2, m3, t ,

∀ pa ∈ PA , t ∈ T

∀ pa ∈ PA , m2 ∈ M 2, t ∈ T

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.

aniTrH ∑ ∑ F paaniHstH , m1, m2, t σpa , m1, m2, t ,

∀ pa ∈ PA , t ∈ T

∀ r ∈ R , m2 ∈ M 2, t ∈ T

aniSA Similarly, the profit for the sale of animal products (Cpa,m2,t ) aniHSA depends on the amount of sold animals (Fpa,m2,t ) and the unit aniSA sale price (σpa,m2,t ):

m 2 m3

aniTrH C pa = ,t

∀ pa ∈ PA , m3 ∈ M 3, t ∈ T (31)

∀ r ∈ R, t ∈ T

m1 m3

Cr,vegTrHtM t

∀ r ∈ R , m3 ∈ M 3, t ∈ T

∀ r ∈ R, t ∈ T

∀ pa ∈ PA , m2 ∈ M 2, t ∈ T (29) 8900


Research Article

ACS Sustainable Chemistry & Engineering 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 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 zones.44 Moreover, 85% of the municipalities in Mexico are rural zones.42 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 a 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

Figure 6. HDI dimensions.

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

municipalities with a great percentage of people living under poverty and the lowest HDI scores. Data for the Case Study. The municipalities with the lowest HDI were selected; afterward, for each considered municipality a distribution for the population based on age groups was performed, taken into account the report by INEGI.42 Table 1 shows the considered age groups; Table 2 Table 1. Population Range in Each Municipality Age (years)

Group

Age (years)

2 to 3

Scholars

4 to 8

Girls

9 to 13

31 to 50

Boys

9 to 13

More than 51 19 to 30

Teens

Figure 5. Location for the addressed case study.

under poverty conditions.45 Fourteen 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

Group

Preschool

Adults Women

Men

Group

Period

Pregnancy

1° Quarter 2° Quarter 3° Quarter 1° Quarter 2° Quarter 3° Quarter

19 to 30

Girls

14 to 18

31 to 50

Boys

14 to 18

More than 51

Nursling

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 8901


Research Article

ACS Sustainable Chemistry & Engineering Table 2. Population Distribution in the Selected Municipalities (%) Children

Girls

Municipalities

0−1

2 to 3

4 to 8

Charapan Churintzio Churumuco Huaniqueo Nahuatzen Nocupétaro Susupuato Tacámbaro Tangamandapio Tiquicheo Tumbiscatió

0.93 1.74 0.99 1.40 0.91 1.06 0.93 1.00 2.74 0.80 1.03 2.91 2.98 0.91

1.87 3.49 2.00 2.81 1.83 2.14 1.89 2.01 5.49 1.61 2.05 5.83 5.96 1.84

11.21 8.72 11.97 7.02 10.95 12.79 11.31 12.06 13.71 9.66 12.31 14.57 14.90 10.98

Turicato Tuzantla Tzitzio

Boys

Girls

Boys

Women

Men

Women

Men

Women

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 5.99 5.90 5.93 4.87 5.40 7.23 6.00 6.00 8.97 4.85 5.42 9.35 9.21 5.80

5.29 4.55 6.04 3.53 5.55 5.56 5.31 6.06 7.49 4.81 6.89 8.13 8.67 5.19

2.52 4.92 2.22 4.06 4.27 2.18 2.34 4.20 7.47 2.21 2.26 7.80 7.67 2.04

2.41 3.79 2.24 2.94 3.80 2.18 2.10 3.90 6.24 2.13 2.13 6.75 7.23 2.10

6.31 11.92 5.57 11.60 10.66 5.44 5.81 10.50 14.99 5.52 5.64 13.86 13.80 5.09

6.05 9.17 5.60 8.41 9.50 5.46 5.24 9.76 12.51 5.34 5.33 12.04 13.00 5.23

19.84 13.57 17.75 17.95 6.15 17.40 18.45 5.80 6.15 19.11 17.19 3.72 1.38 17.94

15.18 10.44 17.60 13.00 5.34 16.30 17.76 5.20 5.14 19.17 17.67 3.23 1.29 18.75

12.51 12.31 11.12 12.99 18.74 11.43 11.55 17.61 4.96 12.37 10.86 6.31 7.16 11.88

Men more than 51 9.88 9.49 10.97 9.41 16.92 10.84 11.32 15.89 4.14 12.41 11.23 5.49 6.74 12.26

Table 3. Nutritional Needs (tonnes/person × y) Sex

Age range

Carbohydrates

Fiber

Fats

Fatty acids polyunsaturated (n-3)

Fatty acids polyunsaturated (n-6)

Any Any Any Girls Boys Girls Boys Women Men Women Men Women Men

0 to 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

0.000539 0.00091 0.00091 0.00091 0.00091 0.00091 0.00091 0.00091 0.00091 0.00091 0.00091 0.00091 0.00091

0.000133 0.000133 0.000175 0.000182 0.000217 0.000182 0.000266 0.000175 0.000266 0.000175 0.000266 0.00021 0.00021

0.000217 0.00021 0.000245 0.000245 0.000245 0.000245 0.000245 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021

0.0000308 0.0000322 0.000049 0.00007 0.000084 0.00007 0.000077 0.000084 0.000119 0.000084 0.000119 0.000077 0.000098

0.0000035 0.0000322 0.000049 0.00007 0.000084 0.00007 0.000077 0.000084 0.000119 0.000084 0.000119 0.000077 0.000098

■

Table 4. Agricultural Land in Each Municipality (km2) Municipality

Current area

Available area

Maximum area

Charapan Churintzio Churumuco Huaniqueo Nahuatzen Nocupétaro Susupuato Tacámbaro Tangamandapio Tiquicheo Tumbiscatió

117 74.06 186.71 74.25 138.11 38.32 91.03 341.35 138.26 120.81 63.48 314.91 138.46 21.32

77.33 54.63 223 70.91 29.71 266.07 75.69 72.08 61.98 365.54 1252.44 630.61 363.4 402.79

194.33 128.69 409.71 145.16 167.82 304.39 166.72 413.43 200.24 486.35 1315.92 945.52 501.86 424.11

Turicato Tuzantla Tzitzio

Cholesterol 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75

× × × × × × × × × × × × ×

10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07 10−07

Proteins 0.00007 0.0000091 0.000133 0.000238 0.000238 0.000322 0.000364 0.000322 0.000392 0.000322 0.000392 0.000322 0.000392

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 s of CPU time using the solver CPLEX.43 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

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 databases.

Figure 8. Effect of animal food consumption increase on cost. 8902


Research Article

ACS Sustainable Chemistry & Engineering Table 5. Nutritional Demand and Input from Animal and Vegetable Products in Scenario A (tonnes/y) Polyunsaturated fatty acids Concept Demand Vegetal input Animal input Global balance

Carbohydrates

Fiber

Vegetal fat

(n-6)

(n-8)

Cholesterol

Vegetal protein

Animal protein

Calcium

Animal fat

Iron

Magnesium −1

12049 2293853

2729 127257

2368 69427

1097 29869

113 29869

12 8

3159 152408

788 0

12 1538

572 0

2 × 10 75

4 2108

0

0

0

0

0

0

0

0

0

0

0

0

−2281804

−124529

−67059

−28772

−29756

4

−149249

788

−1526

592

−74

−2104

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. The solution of Scenario A generates a TAC of USD$−224,475, the negative value is given by Equation 34, 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. Afterward, 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

Figure 9. Distribution of vegetable products.

supply shown by Figure 10, while the total cost of each type of animal product is shown in Table 6.

Figure 10. Animal products supply for different scenarios.

Table 6. Cost of Animal Products for Different Scenarios (USD/y) Product

A

B

C

D

Chicken Caw Pig

0 0 0

2,511,600 1,092,000 1,310,400

5,023,200 2,184,000 2,620,800

6,362,720 2,766,400 3,319,680

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 8903


Research Article

ACS Sustainable Chemistry & Engineering Table 7. Satisfied Nutrient Demand in Scenarios B, C and D (tonnes/y) Polyunsaturated fatty acids

Type of nutrient

Demand Global Scenario B Balance Scenario C (Ton/y) Scenario D

Carbohydrates

Fiber

Vegetal fat

(n-6)

(n-8)

Cholesterol

Vegetal protein

Animal protein

Calcium

Animal fat

Iron

Magnesi um

12049 −2281870 −2281937 −2281972

2729 −124529 −124529 −124529

2368 −67059 −67059 −67059

1097 −28772 −28772 −28772

113 −29756 −29756 −29756

12 −1 −6 −9

3159 −149249 −149249 −149249

788 325 −138 −385

12 −1528 −1530 −1531

572 423 −8 −57

2 × 10−1 −74 −75 −75

4 −2104 −2105 −2105

13 show the configuration of the food supply chain, where the veg animal and vegetable productions are identified as (RMr,m1,t ) and (NAra,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. 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

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

vegetable production remains constant, however it represents 97% of production cost in Scenario B, whereas 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

Figure 12. Diagram configuration of food supply chain for Scenarios A (above) and B (below). 8904


Research Article


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

R

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.

■

Ra T

AUTHOR INFORMATION

Variables

Corresponding Author

Aused r,m1,t Anew r,m1,t anif U Ara,m1,t Af UAF ra,m1,t Af CAF ra,m1,t

*José M. Ponce-Ortega. Tel.: +52 443 3223500. Ext. 1277. Fax: +52 443 3273584. E-mail: [email protected]. ORCID

José María Ponce-Ortega: 0000-0002-3375-0284 Notes

Af PAF ra,m1,t

The authors declare no competing financial interest.

■

CAF AFra,m1,t PAF AFra,m1,t aniPU Cra,m1,t Cveg r,m1,t

ACKNOWLEDGMENTS

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

■

PU Canif ra,m1,t anif CU Cra,m1,t CaniPr pa,m1,t CaniTrH pa,t

NOMENCLATURE

Index

L m1 m2 m3 Np

Nut Pa

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) Type of animal (1 = chicken, 2 = caw, 3 = pig) Period of time considered, one period takes 1 week (Periods 1−52)

Type of processed food (1 = cheese, 2 = bread, 3 = chicken meat, 4 = beef, 5 = pork meat, 6= ham, 7 = milk, 8 = protein, 9 = tortillas, 10 = sugar) Harvesting sites (municipalities) included in the analysis (Municipalities selected 1−14) Hub located in each municipality (1−14) Population to feed in each municipality (1−14) 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) Nutrient package (oils, fruits, vegetables, dairy products, beans and meat) Type of animal product (1 = meat, 2 = milk, 3 = eggs)

CaniTrM pa,t CaniTrHstM pa,t CvegTr r,t CvegTrM r,t CvegTrHTM r,t Canis pa,m2,t Cvegs r,m2,t CaniSA pa,m2,t CvegSA r,m2,t Dnut,m3,t 8905

Land used for agriculture (km2) New area designated to cultivation (km2) Area used for animal feed (km2) Tonnes of animal food used to feed (tonnes) Tonnes of animal food cultivated, residues from the crops (tonnes) Tonnes of animal food purchased from other sites (tonnes) Amount of cultivated animal food (tonnes) Amount of purchased animal food (tonnes) Generated cost by the animal purchase (USD$) Total production cost of the vegetal raw material (USD$) Purchased animal food cost (USD$) Production animal food cost (USD$) Production cost of animal food (USD$) Cost by the animal product transportation to the hub (USD$) Cost by the animal product transportation to the market from hub (USD$) Cost by the animal product transportation to the market from harvesting sites (USD$) Cost by vegetable transportation to the hub (USD$) Cost by vegetable transportation to the market (USD$) Cost by vegetable transportation from the hub to the market (USD$) Cost by the animal product storage (USD$) Cost by the vegetable product storage (USD$) Earnings by the animal product sales (USD$) Earnings by the vegetable product sales (USD$) Nutritional demand (tonne of each food group) DOI: 10.1021/acssuschemeng.7b01703 ACS Sustainable Chem. Eng. 2017, 5, 8895−8907

Research Article

ACS Sustainable Chemistry & Engineering P Fani pa,m1,t aniM Fpa,m3,t FaniHStH pa,m1,m2,t FaniHtM pa,m2,m3,t FaniHStM pa,m1,m3,t aniHSA Fpa,m2,t aniPU Fpa,m3,t Fveg r,m1,t FvegH r,m1,m2,t FvegMar r,m1,m3,t

FvegPU r,m3,t FvegHtm r,m2,m3,t FvegHStM r,m1,m3,t FvegHSA r,m2,t NAra,m1,t NaAP ra,m1,t Nasale ra,m1,t RMveg r,m1,t aniS Spa,m2,t SaniSD pa,m2,t−1 SvegD r,m2,t SvegSD r,m2,t−1 TAC

σvegs r,m2,t

Animal food produced (tonnes) Animal product sent to the markets (tonnes) Animals sent to the hub (tonnes) Animals sent to the market from the hub (tonnes) Animals sent directly to the market (tonnes) Animals sold (tonnes) Animal products purchased (tonnes) Total tonnes of vegetables produced (tonnes) Vegetables sent to the hubs (tonnes) Vegetables distributed directly to the population (tonnes) Vegetable products purchased from other producers (tonnes) Vegetables sent from the hub to the market (tonnes) Vegetable products sent from the harvesting site to the market (tonnes) Vegetables sold in the market (tonnes) Number of animals produced in each site (number) Number of bought animals from other municipality (animals) Number of sold animals to other municipalities (animals) Tonnes of vegetable raw material (fresh food) Animal product stored in the hub (tonnes) Animal product stored in the hub in the previous time period (tonnes) Vegetables stored (tonnes) Vegetables stored in previous period of time (tonnes) Total annual cost (USD$)

σaniSA pa,m2,t σvegSA r,m2,t

■

Tot−Ve Ar,m1,t TAF Ara,m1,t GEnut Pem3,t βHS r,m1,t YPA θra,m1,t

ξanin nut,pa ξvegn nut,r ϕRPA ra,r,m1,t λpa,ra,m1,t aniPU σra,m1,t aniPr σpa,m1,t σvegPr r,m1,t aniTrH σpa,m1,m2,t aniTrM σpa,m2,m3,t aniTrHstM σpa,m1,m3,t vegTrH σr,m1,m2,t vegTrM σr,m1,m3,t anif CU σra,m1,t anif PU σra,m1,t anis σpa,m2,t

REFERENCES

(1) FAO (Food and Agriculture Organization of the United Nations) (2016) FAO calls on governments to take concrete action on malnutrition, in all its forms. Available on: .http://www.fao.org/news/ story/en/item/434440/icode/ (accessed May, 2017). (2) Bortolini, M.; Faccio, M.; Ferrari, E.; Gamberi, M.; Pilati, F. Fresh food sustainable distribution: cost, delivery, time and carbon footprint three-objective optimization. J. Food Eng. 2016, 174 (1), 56−67. (3) Rutten, M.; Achterbosch, T. J.; De Boer, I. J. M.; CrespoCuaresma, J. M.; Geleijnse, J.; Havlík, P.; Heckelei, T.; Ingram, J.; Leip, A.; Marette, S.; Van Meijl, H.; Soler, L.-G.; Swinnen, J.; Van't Veer, P.; Vervoort, J.; Zimmermann, A.; Zimmermann, K. L.; Zurek, M. Metrics, models and foresight for European Sustainable food and nutrition security: The vision of the SUSFANS project. Agr. Syst. 2016, DOI: 10.1016/j.agsy.2016.10.014. (4) Nuhoff-Isakhanyan, G.; Wubben, E. F. M.; Omta, O. S. W. F.; Pascucci, S. Network structure in sustainable agro-industrial parks. J. Cleaner Prod. 2017, 141 (1), 1209−1220. (5) Guillén-Gosálbez, G.; Grossmann, I. A global optimization strategy for the environmentally conscious design of chemical supply chains under uncertainty in the damage assessment model. Comput. Chem. Eng. 2010, 34 (1), 42−58. (6) El-Halwagi, M. M. A return on investment metric for incorporating sustainability in process integration and improvement projects. Clean Technol. Environ. Policy 2017, 19, 611−617. (7) Bowling, I. M.; Ponce-Ortega, J. M.; El-Halwagi, M. M. Facility location and supply chain optimization for a biorefinery. Ind. Eng. Chem. Res. 2011, 50 (10), 6276−6286. (8) Santibañez-Aguilar, J. E.; Ponce-Ortega, J. M.; González-Campos, J. B.; Serna-González, M. M.; El-Halwagi, M. Optimal planning for the sustainable utilization of municipal solid waste. Waste Manage. 2013, 33 (12), 2607−2622. (9) Arredondo-Ramírez, K.; Ponce-Ortega, J. M.; El-Halwagi, M. M. Optimal planning and infrastructure development for shale gas production. Energy Convers. Manage. 2016, 119 (1), 91−100. (10) Yue, D.; Pandya, S.; You, F. Integrating hybrid life cycle assessment with multiobjective optimization: A modeling framework. Environ. Sci. Technol. 2016, 50 (3), 1501−1509. (11) El-Halwagi, A. M.; Rosas, C.; Ponce-Ortega, J. M.; JiménezGutiérrez, A.; Mannan, M. S.; El-Halwagi, M. M. Multi-objective optimization of biorefineries with economic and safety objectives. AIChE J. 2013, 59 (7), 2427−2434. (12) López-Díaz, D. C.; Lira-Barragán, L. F.; Rubio-Castro, E.; Ponce-Ortega, J. M.; El-Halwagi, M. M. Optimal location of biorefineries considering sustainable integration with the environment. Renewable Energy 2017, 100 (1), 65−77. (13) Martínez-Guido, S. I.; González-Campos, J. B.; Ponce-Ortega, J. M.; Nápoles-Rivera, F.; El-Halwagi, M. M. Optimal reconfiguration of a sugar cane industry to yield an integrated biorefinery. Clean Technol. Environ. Policy 2016, 18 (2), 553−562. (14) Noureldin, M. M. B.; El-Halwagi, M. M. Synthesis of C-H-O symbiosis networks. AIChE J. 2015, 61 (4), 1242−1262. (15) El-Halwagi, M. M. A shortcut approach to the multi-scale atomic targeting and design of C-H-O symbiosis networks. Process Int. Opt. Sust. 2017, 1, 3. (16) Garcia, D. J.; You, F. The water-energy-food nexus and process systems engineering: a new focus. Comput. Chem. Eng. 2016, 91 (1), 49−67. (17) Galán-Martín, A.; Vaskan, P.; Anton, A.; Jiménez-Esteller, L.; Guillén-Gosálbez, 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.

Parameters UAF Ara,m1,t Current Ar,m1,t

Price for the vegetable products storage (USD $/tonnes) Unit price for animal product sales (USD$/tonnes) Unit price for vegetable sales (USD$/tonnes)

Area used to feed the animals (km2) Current area designated to the harvesting of each crop (km2) Limit for the used area in each municipality (km2) Available area for the animal feed (km2) Nutrient group (type) Inhabitants (number) Yield factor of each cultivated crop (tonnes/km) Yield factor of produced animals (animals/tonnes food) Amount of needed animal nutrients (tonnes) Amount of needed vegetable nutrients (tonnes) Yield of raw material residues (tonnes/tonnes) Yield factor of produced animals (tonnes/amount of animal) Unit animal purchased cost (USD$/animal) Price of animal production (USD$/animal) Unit vegetable production cost (USD$/tonnes) Animal product price transportation from the harvesting sites to the hub (USD$/tonnes) Animal product price transportation from the hub to the market (USD$/tonnes) Animal product price transportation from the harvesting site to the market (USD$/tonnes) Vegetable price transportation from the harvesting sites to the hub (USD$/tonnes) Vegetable price transportation from the harvesting sites to the market (USD$/tonnes) Unit animal food cost (USD$/tonnes) Unit animal purchased food cost (USD$/tonnes) Price for the animal products storage (USD $/tonnes) 8906


Research Article

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Sustainable Optimization of Food Networks in Disenfranchised

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