Introduction

A supply chain (SC) is a sequence of processes and flows which take place within and between different players. It consists of all parties involved, directly or indirectly, in fulfilling a customers’ request (Chopra and Meindl 2007). An agro-fresh food supply chain (AFSC) includes all the processes from production (farmer) to delivery (customer) of short shelf life items (Shukla and Jharkharia 2013). A successful AFSC delivers the daily demanded fresh items at the lowest possible cost. It not only ensures the profitability of stakeholders but also focuses on less wastage by fast delivering fresh items to the customers. The structure of the supply chain network (SCN) plays a vital role in achieving the above objectives. AFSC in India lacks these objectives due to various unfathomable problems in the chain. Therefore, it is unsustainable for the farmers and is required to be reformed by solving real-life problems.

Structure of traditional Indian AFSC is shown in Fig. 1. The working of this SC is explained as follows: farmers grow crops based on their perception about future demand. After harvesting, they bring their products individually by using owned or hired vehicle(s) into the agricultural market to sell. The agriculture market (mandi) is a regulated market that is ruled by the Agriculture Produce Marketing Committee (APMC) under the state government regulation. In this market yard, a commission agent does an open auctioning, and the wholesaler buys these items through bidding the highest price in the auctioning. Subsequently, the retailers purchase these items from the wholesaler in small quantities. Finally, retailers sell the items to the customers by opening a temporary shop on the street or visiting the proximity locations of customers (Panda and Sreekumar 2012; Hegde and Madhuri 2013; Patidar et al. 2018a). The players between farmers and customers, i.e., agents, wholesalers, and retailers, are known as intermediaries in the chain.

Fig. 1
figure 1

Structure of traditional Indian AFSC

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The motivation behind the organizing and restructuring of SCN comes from the key shortcomings of traditional Indian AFSC, and these are as follows: (1) unorganized SC structure; (2) low profitability of farmers; (3) high wastage of agricultural products; and (4) a large number of small-farm-holding farmers. The description of these shortcomings is discussed in the below sections.

Unorganized SC structure

A comparative study of AFSCs across the world (developed versus developing countries) with special reference to India is presented by Samuel et al. (2012). The study discussed an insight into evolution, procurement, marketing strategies, and business models to provide an overview of varied existing AFSCs and compare SC structures across the world. Organized retailing has evolved in the UK, USA, Australia, New Zealand, and China. AFSC in Indian context is unstructured and mainly dominated by a large number of unorganized intermediaries. Thereby, the traditional Indian AFSC is unorganized and mainly governed and controlled by a large number of unorganized intermediaries. The pricing of products is decided by the unorganized intermediaries who play their monopoly in auctioning (Viswanadham et al. 2012). These intermediaries add service charges and profit margins into the price of the products. There is a lack of competitive environment in the chain that results in a higher price of the product. There is no direct communication between the farmers and the customer. However, in recent times, several information and communication technology (ICT) initiatives are implemented to improve communications amongst the different SC actors (Dandage et al. 2017). Further, the unorganized SC structure causes a longer delivery lead time and results in degradation of product quality in terms of its freshness with a large amount of wastage (Rajkumar 2010).

Low profitability of farmers

The unorganized SC structure and presence of a large number of intermediaries result in low profitability of farmers. Another reason for the low profitability of farmers can be understood through a set of studies (Raghunath and Ashok 2009; Panda and Sreekumar 2012; Hegde and Madhuri 2013; Kundu 2013). These authors examined the traditional AFSC and reported that individually farmers transport their products into market premises to sell. In this process, farmers manage and pay the cost of transportation facilities. Farmers feel this as a hurdle in every visit to the market. Due to this, they are forced to sell their products to local intermediaries rather than selling into the regulated market or mandi. Finally, farmers are deprived of higher prices of products and the profit margins are taken by intermediaries. This results in customers paying the higher prices of products and farmers receiving the only one-third prices paid by the customers. The third reason for the low profitability of farmers is continuously rising prices of input resources like fuel, fertilizers, pesticides, farm equipment, labor, whereas average prices of agricultural products are not increased in the proportional increase in the prices of the input resources. Thus, farming is not a profitable business for the farmers’ community. Therefore, farmers are continuously demanding profitable (or at least better) prices of the crops and many times they agitate against the government to raise the issue of poor pricing of products (Hindustan Times 2017).

High wastage of agricultural products

The third main problem in Indian AFSC is the high wastage of agricultural products as identified in a set of papers (Balaji and Arshinder 2016; Gardas et al. 2017, 2018; Gokarn and Kuthambalayan 2017). According to these papers, 15–25% of fresh items are lost due to improper storage and handling, poor SCN design, presence of a large number of intermediaries, and lack of demand–supply integration. Further, this wastage results in low profitability of farmers, decrease in nutrition level, increase in the prices of products, and non-productive use of natural resources. Another cause of food wastage is the inherent characteristic of fresh items, i.e., perishable nature of products.

A large number of small-farm-holding farmers

The continuous population growth leads to family expansion and other infrastructural development. Due to these, the average agricultural landholding per family has been reduced from 2.28 hectares in 1970–71 to 1.16 hectares in 2010–11. Hence, the small farmers—having farming land less than 2 hectares—have been increased from 70% to 85% from the years 1970–71 to 2010–11 (NABARD 2014). The small farmers are the residence of geographically scattered rural areas. In the scattered production scenario, most of the farmers bring their product individually in the agriculture market by traveling long distances, as discussed in  "Low profitability of farmers" section. This increases the overall transportation cost in the SC, which is in the range of 30–40% of total transaction costs (Panda and Sreekumar 2012; Hegde and Madhuri 2013).

Research gap

A set of review papers (Rajurkar and Jain 2011; Samuel et al. 2012; Dandage et al. 2017; Gardas et al. 2017; Negi and Anand 2017; Siddh et al. 2017) identified operational issues like lack of loading–unloading facilities, appropriate packing methods, tracking, and traceability facilities due to improper SCN. These articles revealed that although a lot of research work in the field of AFSC had been done in the past, yet the organizing and restructuring of the chain for perishable products in the Indian context was overlooked by the researchers. Unanimously, the authors recommended designing an appropriate SCN model for Indian AFSC. However, few researchers (Anjaly and Bhamoriya 2011; Kundu 2013; Sihariya et al. 2013; Sohoni and Joshi 2015) discussed the case study-based conceptual model for the distribution of fresh produce. Recently, Patidar et al. (2018a) analyzed the Indian AFSC and reported that the improper SCN model is responsible for high wastage of produce and low profitability of farmers. The authors suggested developing a suitable model for the integration of small farmers and aggregate product transportation from farmers to market. Additionally, the perishability of items was identified as the main challenge in SCN modeling to reduce food waste in Indian AFSC (Gokarn and Kuthambalayan 2017). Hence, the designing of the SCN model for the Indian scenario is a crucial requirement in order to solve identified shortcomings (sections "Unorganized SC structure" to "A large number of small-farm-holding farmers").

The efficient transportation of products from small scattered farmers to market can mitigate the identified shortcomings. However, it is not feasible for retailers or wholesalers to collect the products directly from geographically scattered small farmers (Trebbin 2014). A possible solution to the above shortcomings is proposed in this paper by considering aggregate product transportation from cluster centers to market. Defining the clustering of farmers is the first and foremost task for aggregate product transportation. It also enables the farmers to participate in competitive SC in a consolidated form. The aggregate product transportation and perishability consideration in the proposed model have capabilities to address the following three aspects of sustainability: first, the aggregate product transportation by clustering of farmers is capable to reduce the transportation cost (economic aspect). Second, the reduced transportation cost can be realized by farmers, which increases the farmers’ profitability (social aspect). Third, the perishability consideration in the proposed model will determine to be expired products in advance. These excess products can be supplied to other institutional demand nodes (like hospitals, hostels, and restaurants) in less price; thus, it will reduce the wastage of agricultural products (environment aspect). The idea of aggregate product transportation in the proposed model also supports easy product handling and reduction in carbon emissions. Hence, this novel concept may reform traditional Indian AFSC by distributing fresh items in efficient and effective ways as well as reducing the actual shortcomings of the system. Therefore, the purpose of this work is to propose an environmentally sustainable SCN for Indian AFSC with considering the aggregate product transportation and perishability of products into the model.

Literature review

The SCN design is a strategic decision that identifies SC structure and configuration over the next several years by developing an appropriate mathematical model (Chopra 2003). The developed mathematical model determines the locations and allocations of facilities to serve customers’ demand efficiently and effectively. Therefore, this type of model is also known as the location–allocation problem (Daskin et al. 2005; Amiri 2006). The problem can be formulated as discrete or continuous, single objective or multi-objective, single period or multi-period, with or without the restriction of capacitated facilities (Melo et al. 2009).

To investigate the state-of-the-art in the field of the SCN models, the literature review is divided into three sections as follows: the first section discusses the papers related to the models of SC structure. The recent papers that considered perishability into the SCN models are described in the second section. The third section explains some relevant papers on aggregate product transportation and distribution in the SC models.

Single versus multi-period SCN model

Jayaraman and Ross (2003) formulated a single period, three-echelon SCN model for multi-product in two stages. The first stage determined decisions about locating facilities among the available potential locations and accordingly, assignments between these facilities were made into the second stage. Another single period, four-echelon SC model by considering hybrid and flexible multi-objective outbound logistics network for different variants of items (i.e., fast, slow, and very slow-moving items) was formulated by Hiremath et al. (2013). The proposed network was defined as hybrid and flexible by considering varying delivery lead time and possible roll-back strategy in the model. In recent years, researchers have started the designing of agriculture SCN in order to solve real-life problems by adopting the idea of SC modeling from the available literature. The integrated SCN of production and distribution for fresh items were formulated as a mixed-integer linear programming model in the set of articles (Ahumada and Villalobos 2011; Farahani et al. 2012). Etemadnia et al. (2015) designed a three-echelon wholesale hub location model for efficient distribution of locally grown fruits and vegetables in the USA.

The multi-period model helps in determining the impact of supply and demand variability with respect to time on the SC structure, and it ascertains whether it is worth to use a more complex multi-period model for designing SCN (Melo et al. 2009). Khamjan et al. (2013) developed a mathematical model to determine the location–allocation and capacity of the existing and new sugar cane loading stations for Thailand. Gelareh et al. (2015) developed a multi-period hub location model for hub-and-spoke network structure by considering installation, maintenance, and closing costs associated with each hub. Gholamian and Taghanzadeh (2017) formulated a five-echelon wheat SCN model of Iran to determine the location–allocation decisions of various facilities with considering multi-mode transportation. In the model, the authors considered the blending of different types of wheat to produce different products with quality variations.

Perishability consideration in SCN model

After harvesting, the perishable products deteriorated with elapsed time. Over the succeeding useful shelf life, such products became expired items—that need to be disposed of—which requires an additional cost. In the literature, researchers have accounted for perishability in the following two ways: (1) continuous function of deterioration and (2) step function of deterioration. Therefore, the available literature on perishable food SC has been summarized in these two groups. Rong et al. (2011) developed a production and distribution planning model for a single product with considering continuous food quality deterioration in storage and transportation activities. The model determined the duration of storage and transportation activities together with the appropriate temperature for the different locations and transportation equipment in order to minimize the overall cost of logistics and preservation. Nourbakhsh et al. (2016) developed a mathematical model by considering quantitative and qualitative post-harvest losses in the SCN model. The model determined optimal locations of pre-processing facilities and plans for transportation and infrastructure investment by identifying roadway/railway capacity expansion. Dolgui et al. (2018) developed a mathematical model to optimize integrated production, inventory, and distribution decisions for perishable items in a multi-stage SC.

A few articles considered perishability as a step function of deterioration, which means that during the shelf life of the product, there is no deterioration, and the product can be used with the original value. After crossing the shelf life, its salvage value is zero, and the product cannot be used (a binary decision). Rahimi et al. (2017) developed a single-stage inventory-routing model for the distribution of fresh products in urban areas by considering the perishability as a step function. Recently, Savadkoohi et al. (2018) developed a three-echelon location-inventory model for the perishable pharmaceutical SC. The model determined manufacturing and distribution centers’ locations, material flow in the network, and the optimal inventory policy considering the step function of perishability to minimize the total SC cost.

Ahumada and Villalobos (2009); Shukla and Jharkharia (2013); Tsolakis et al. (2014); Soto-Silva et al. (2016) reviewed agriculture SC planning models and suggested to develop appropriate SCN models by dealing with particular region-specific problems. The papers (Routroy and Behera 2017; Siddh et al. 2017) provided a structural literature review on perishable food SC and reported that the designing of SCN model for the developing countries had been given less attention in comparison with the developed countries.

Aggregate product transportation/distribution in the SCN model

The aggregate product transportation results in efficient flow of products of an SC by reducing overall transportation cost in comparison with the point to point transportation. The product aggregation can be done by forming the groups of farmers of the nearby locations. Bosona and Gebresenbet (2011) considered clustering of farmers and optimized the location of clusters to integrate the logistics activities in the local food SC. On the other hand, Boudahri et al. (2011) developed a single period, three-echelon chicken meat SC for the single product with considering clustering of customers. The authors formulated the problem in two submodels. The first model determined the centroid of customers’ clusters to establish retail centers, and accordingly, the assignments were determined into the second model. Based on literature review, SC characteristics, and configuration variables, Dreyer et al. (2016) developed strategies to improve AFSC for Norwegian small-scale producers. The authors reported that farmers’ clustering would help in collaboration and consolidation of volume and products, which will increase service levels and fulfill requirements by prioritizing products to sell and to what customers. Most risks in perishable SC comes from internally, and it can be mitigated by horizontal and vertical integration and collaboration among players (Ali et al. 2017). In the literature of SC models, clustering of players has not been considered in single-step SCN modeling. However, in recent years, Rancourt et al. (2015) and Khalilpourazari and Khamseh (2017) used covering radius to identify the location (out of potential site) to establish food distribution centers and temporary/permanent blood transportation facilities in disaster relief SC, respectively.

Recently, Zhu et al. (2018) reviewed the food SC models and reported that the involvement of small farmers is neglected. The small farmers have weak participation power in competitive SC. Moreover, if we look from the application point of view, clustering of farmers is an essential requirement of the system as well as it has the potential to solve the identified problems of Indian AFSC (sections "Unorganized SC structure" to "A large number of small-farm-holding farmers"). It has been identified from the literature that the clustering of farmers (suppliers) is not yet considered in the designing of SCN as reported in the above section. Therefore, it is worthwhile to propose a restructured SCN by formulating a mathematical model with considering the clustering of farmers and perishability of products.

Proposed model description and formulation

As discussed in the introduction section, the traditional Indian AFSC has an unorganized SC structure, high wastage of agricultural products, and inefficient transportation of products from small farmers to market. To organize and restructure SCN, a discrete location–allocation problem is considered to formulate the chain for perishable products. The problem is to identify the optimal location and allocation of facilities among the set of available potential locations and movement of products between these facilities such that total SC cost is minimized. The complete description and formulation of the proposed restructured model for Indian AFSC are explained in the following sections.

Model description

The working of traditional Indian AFSC (Fig. 1) has been explained in the introduction section. The agents and wholesalers work at the same location inside the market premises to match demand and supply. So, authors assume both as a single SC entity as a hub to organize the SC structure. There can be multiple hubs, and the locations of these hubs can be multiple places in a region. Similarly, retailers sell products to customers by visiting customers’ proximity locations. Therefore, the retailers and customers are assumed at the same echelon in the SC and named as customer zone (CZ) in the formulation. The number of CZs depends on the population of a region like wards in a city.

In traditional Indian AFSC, the small farmers bring their products individually to markets (hubs) to sell. It is inefficient as well as an ineffective way of product transportation from farmers to hubs. Authors propose the idea of aggregate product transportation by identifying groups of farmers based on the location of neighborhood farmers. Farmers belonging to a group called as farmer cluster (FC), bring their products to the central location of that cluster which is named as farmers’ cluster center (FCC). The central location within a group is considered as any location of a farmer in the group. In this way, multiple FCs and the respective FCCs can be identified. Each farmer can be assigned to only one FCC in each period; therefore, a farmer’s supply cannot split into FCCs. On the other side, FCC can split their delivery to any hub. The aggregated products at these FCCs can now be shipped efficiently to the hubs. The lower bound on supply from an FCC to hubs are considered to ensure a minimum quantity of products transported to the lower echelon. It is assumed that FCCs and hubs do not store any items and are used to manage the transshipment of products in SCN to satisfy CZ demand economically. A CZ can receive a split supply from any hub. Similarly, the lower bound on supply from a hub to CZs is considered to ensure a minimum quantity of product movement from a hub.

The aggregate product transportation helps in hassle-free products movement as well as it reduces transportation cost in the delivery of fresh items. Further, it helps in handling various operational issues like easy material handling, proper utilization of facilities, integration of supply, and demand of products. Other issues like carbon emissions, traffic congestion, can be reduced by aggregate transportation. Hence, it is an eco-friendly way of product movement. Also, we consider the perishable nature of products in the modeling of SCN. The excess products are stored in CZs and are used in the next period. The workable inventory and to be expired products are calculated based on the fixed shelf of products; therefore, a suitable inventory flow equation is developed for each CZ. This helps in the reduction of food wastage by determining these excess (to be expired) products which can be supplied to nearby institutional demand nodes like hotel, restaurant, hospital, and hostel.

In traditional Indian AFSC, an agent auctions and matches supply and demand for a market and plays his monopoly in the pricing of products (Viswanadham et al. 2012). The role of this agent can be substituted with modern technology-enabled ‘FCC’ in the proposed SCN to make the sustainable SC. The modern technology includes the use of image processing to check quality of product, ICT to share information between the partners and radio-frequency identification (RFID) tag to recognize and track the products, etc. which make the whole system dynamic and adaptable for changing scenario (Rais and Sheoran 2015; Dandage et al. 2017; Gokarn and Kuthambalayan 2017; Patidar et al. 2018ba).

The four-echelon location–allocation model consists of farmers, FCCs, hubs, and CZs, as shown in Fig. 2. A mathematical model is formulated by considering single-mode transportation, multi-period, multi-product, and perishability of products in this section. In the model, we first define FCs and the locations of the respective FCCs based on the distance between farmers. All assigned farmers in each FC bring their products to the common collection points, i.e., FCCs. Further, these aggregated products are shipped from FCCs to hubs and hubs to CZs to satisfy demand at CZs such that total SC cost is minimized.

Fig. 2
figure 2

The proposed SCN model for Indian AFSC

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The proposed mixed-integer nonlinear programming (MINLP) formulation of restructured SCN determines the following decisions in each period:

  • The appropriate number of FCCs and their locations for the aggregation of products.

  • The location and allocation of each hub from the available potential locations to satisfy demand at CZs.

  • The quantity of each type of product flow between any two nodes at different echelons.

  • The inventory of products at each CZ.

  • The to be expired products in each period at each CZ.

Assumptions

The SCN model is formulated using the following assumptions:

  1. 1.

    The model parameters are fixed, and thus, the model is deterministic.

  2. 2.

    The model is multi-period; therefore, excess items in the previous period are used in future periods.

  3. 3.

    Inventory at any echelon arrives at the beginning of a period.

  4. 4.

    The length of a period is one day.

  5. 5.

    Product flow between hubs is not considered in the model.

Proposed formulation

The proposed SCN model is formulated as follows:

$$Minimize\;{\text{Z }} = {\text{Z1 }} + {\text{ Z2 }} + {\text{ Z3 }} + {\text{ Z4 }} + {\text{ Z5 }} + {\text{ Z6 }} + {\text{ Z7}}$$
(1)
$${\text{Z1 }} = \sum\limits_{t = 1}^{T} {\sum\limits_{i = 1}^{I} {FC1_{i}^{{}} F_{i}^{t} } }$$
(1a)
$${\text{Z2 }} = \sum\limits_{t = 1}^{T} {\sum\limits_{i = 1}^{I} {\sum\limits_{f = 1}^{F} {\sum\limits_{p = 1}^{P} {D1_{fi}^{{}} TC_{1}^{{}} H_{fp}^{t} Y_{fi}^{t} } } } }$$
(1b)
$${\text{Z3 }} = \sum\limits_{t = 1}^{T} {\sum\limits_{j = 1}^{J} {FC2_{j}^{{}} Z_{j}^{t} } }$$
(1c)
$${\text{Z4 }} = \sum\limits_{t = 1}^{T} {\sum\limits_{i = 1}^{I} {\sum\limits_{j = 1}^{J} {\sum\limits_{p = 1}^{P} {D2_{ij}^{{}} TC_{2}^{{}} Q_{ijp}^{t} } } } }$$
(1d)
$${\text{Z5 }} = \sum\limits_{t = 1}^{T} {\sum\limits_{j = 1}^{J} {\sum\limits_{k = 1}^{K} {\sum\limits_{p = 1}^{P} {\sum\limits_{\tau \ge t}^{T} {D3_{jk}^{{}} TC_{3}^{{}} Q_{jkp}^{t\tau } } } } } }$$
(1e)
$${\text{Z6 }} = \sum\limits_{t = 1}^{T} {\sum\limits_{k = 1}^{K} {\sum\limits_{p = 1}^{P} {HC_{kp}^{{}} I_{kp}^{t} } } }$$
(1f)
$${\text{Z7}} = \sum\limits_{t = 1}^{T} {\sum\limits_{k = 1}^{K} {\sum\limits_{p = 1}^{P} {DC_{p}^{{}} Ex_{kp}^{t} } } }.$$
(1 g)

The objective function (1) minimizes the total cost (TC) occurring at various stages of the SC. TC includes four types of costs, i.e., fixed costs, transportation costs, inventory holding cost, and disposal cost of expired products at CZs. The explanation of these costs is as follows. Equations (1a) and (1c) denote fixed costs of forming FCCs and opening hubs, respectively. Equations (1b), (1d), and (1e) describe transportation costs from farmers to FCCs, FCCs to hubs, and hubs to CZs, respectively. Lastly, Eqs. (1f) and (1g) represent total inventory holding cost and disposal cost for the expired products at CZs, respectively.

Subject to:

$$D1_{fi}^{{}} Y_{fi}^{t} \le D1_{m}^{{}} ,\quad \forall f,\forall i,\forall t$$
(2)
$$\sum\limits_{i = 1}^{I} {Y_{fi}^{t} F_{i}^{t} = 1} ,\quad \forall f,\forall t.$$
(3)

Equations (2) and (3) define the FCs by identifying the associated farmers, and the respective FCCs based on allowed maximum distance traveled by a farmer.

$$\sum\limits_{f = 1}^{F} {H_{fp}^{t} Y_{fi}^{t} \le M \times F_{i}^{t} } ,\quad \forall i,\forall p,\forall t$$
(4)
$$\sum\limits_{j = 1}^{J} {Q_{ijp}^{t} = } \sum\limits_{f = 1}^{F} {H_{fp}^{t} Y_{fi}^{t} } ,\quad \forall i,\forall p,\forall t.$$
(5)

Equation (4) ensures the movement of products from farmers to the established FCCs only. Equation (5) ensures the sum of products shipped from each FCC to any hub is equal to the available aggregate product of each type during each period.

$$\sum\limits_{j = 1}^{J} {Q_{ijp}^{t} } \ge LB_{ip}^{{}} F_{i}^{t} ,\quad \forall i,\forall p,\forall t$$
(6)
$$\sum\limits_{i = 1}^{I} {Q_{ijp}^{t} } \le M \times Z_{j}^{t} ,\quad \forall j,\forall p,\forall t.$$
(7)

The lower bound on supply from each FCC to any hub is ensured by Eq. (6). Equation (7) ensures shipment of product from FCCs to the opened hubs only.

$$\sum\limits_{k = 1}^{K} {\sum\limits_{\tau \ge t}^{T} {Q_{jkp}^{'t\tau } = \sum\limits_{i = 1}^{I} {Q_{ijp}^{t} } } } ,\quad \forall j,\forall p,\forall t$$
(8)
$$\sum\limits_{j = 1}^{J} {\sum\limits_{t - lp \le \tau \le t}^{T} {Q_{jkp}^{'\tau t} } } \ge D_{kp}^{t} ,\quad \forall k,\forall p,\forall t.$$
(9)

Conservation of products’ flow at each hub for each period is governed by Eq. (8). Equation (9) guarantees that the quantity of delivered products to each CZ is greater than or equal to the demand during each period.

$$I_{kp}^{t - 1} + \sum\limits_{j = 1}^{J} {\sum\limits_{\tau \ge t}^{T} {Q_{jkp}^{'t\tau } } } - D_{kp}^{t} - Ex_{kp}^{t} = I_{kp}^{t} ,\quad \forall k,\forall p,\forall t$$
(10)
$$\sum\limits_{j = 1}^{J} {\sum\limits_{{\tau > t + l_{p}^{{}} }}^{T} {Q_{jkp}^{'t\tau } } } = Ex_{kp}^{t} ,\quad \forall k,\forall p,\forall t.$$
(11)

Inventory flow balance is governed by Eq. (10) for two consecutive periods at each CZ. Equation (11) determines the to be expired products for each product type in every period at each CZ based on the pre-defined shelf life of each product type.

$$\sum\limits_{k = 1}^{K} {\sum\limits_{\tau \ge t}^{T} {Q_{jkp}^{'t\tau } } } \ge LB_{jp}^{{}} Z_{j}^{t} ,\quad \forall j,\forall p,\forall t.$$
(12)

The lower bound on supply from each opened hub to any CZ is warranted by Eq. (12).

$$\sum\limits_{j = 1}^{J} {Z_{j}^{t} } = NH,\quad \forall t.$$
(13)

Equation (13) ensures the total number of hubs to be opened in each period.

$$F_{i}^{t} , \, Z_{j}^{t} , \, Y_{fi}^{t} = \left\{ {0, \, 1} \right\}.$$
(14)

The binary variables are ensured by Eq. (14).

Model implementation and numerical results

In this section, a case study of AFSC of Madhya Pradesh (a central province of India) has been considered to implement the proposed model. Madhya Pradesh is agriculturally productive and has won five successive the ‘Krishi Karman Award’ for the huge agriculture production in the financial year 2012–13 to 2016–17 (The Times of India 2018). As reported in "High wastage of agricultural products" section, a large amount of agricultural products is being wasted due to poor logistics management. This wastage leads to environmental pollution in terms of both bad air quality and development of bacteria, especially near the Mandis and warehouses. Additionally, the unorganized SC structure and inefficient transportation of products leads to the low profitability of farmers. The proposed model has been framed to organize and mitigate the actual shortcomings by incorporating the perishability of products and clustering of farmers. Further, the case study problem aims to implement our proposed model by dealing with actual circumstances. The complete illustration of data collection, optimal results, SC dynamics, and sensitivity analysis for the case study problem are explained in "Data collection" to "Sensitivity analysis" section, respectively.

Data collection

The farmers (supply nodes) and customers (demand nodes) in Mandsaur District of Madhya Pradesh province are chosen as candidate locations for the vegetable SC. The common vegetables which are generally produced by farmers (MoAFW 2017) and consumed by customers (NSSO 2014) for the district are identified. These common vegetables are assumed and classified into four groups based on the shelf life of products. These groups of vegetables are mentioned as product types in the model and are described in Table 1.

Table 1 Group of vegetables
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Farmers from the villages and customers from highly populated zones (in a city) supply and demand the vegetables, respectively. In this work, it is assumed that each village as a farmer unit and its location as a farmer’s location. The case study assumes fifty available farmers’ locations (F1–F50), which supply four types of vegetables (P1–P4). A total of twenty wards of Mandsaur City are considered as CZs’ locations (C1–C20). A set of seven locations (H1–H7) in the city area is defined as hubs’ locations for the re-distribution of products from farmers/FCCs to CZs. Farmer’s vegetable production is estimated using the data of per hectare vegetable yield (MoAFW 2017) and average landholding of each farmer (Census of India 2011). Similarly, consumption in each CZ is estimated using the data of consumption of vegetables per person/day (NSSO 2014) and the population of each CZ (Census of India 2011). Based on these data, the average supply and demand of vegetables are calculated for all farmer units and CZs. The minimum and maximum farmers’ supply capacities, as well as minimum and maximum CZs’ demand quantities for a single period, are presented in Table 2. Further, these single period estimates of supply and demand are used to generate supply and demand for ten periods (T1–T10) with the help of probabilistic uniform distribution function. The values of lower bound on supply from an FCC and a hub for the estimated data for different product types are shown in Table 2. The fixed cost, transportation cost, holding cost, and disposal cost for the problem are assumed based on our experience and prevailing conditions of Mandsaur District as presented in Table 3. Further, the distance between farmers, farmers/FCCs to hubs, and hubs to CZs are obtained from google maps (Google Maps 2018). Figure 3 shows the locations of farmers, hubs, and CZs for the case study problem.

Table 2 Estimated value of parameters in kg
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Table 3 Value of various cost parameters
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Fig. 3
figure 3

a Locations of farmers, hubs, and CZs of Mandsaur region for case study problem; b locations of hubs and CZs in the zoomed figure

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Optimal results

The proposed MINLP model is coded and solved using LINGO 17.0 optimization package with a PC having Windows 10 operating system, Intel Core i5 processor, and 8 GB of RAM configuration. The MINLP model is solved for the case study problem by referring the data from Tables 1, 2, and 3. The problem has a total 34,519 constraints, 500 nonlinear constraints, 97,438 variables, and 25,500 integer variables.

The formation of FCs is based on quantities supply by farmers and allowed maximum distance traveled by a farmer for belonging to an FCC. Similarly, decisions regarding the opening of hubs depend on supply and demand, and the distances between any two nodes of consecutive echelons. To find the best result, 16 experiments by changing the number of hubs to be opened and the maximum distance traveled by a farmer are conducted. The results of these experiments are shown in Table 4. It is reported that the experiment (A4), which has 4 number of hubs and 18 km distance traveled by a farmer, gives the best result (minimum TC). The solver reports an optimal cost of INR 2.794 × 106 by solving the proposed MINLP model in 17 min and 29 s. The best result reports that in order to meet the supply and demand of the defined problem, FCCs between 15 and 18 are formed in different periods for the aggregation of the products out of 50 farmers. All costs incurred in the proposed SCN model are shown in Table 4. Figure 4 shows the locations of farmers, FCCs, CZs, and hubs for period 1.

Table 4 Computational results for the case study problem
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Fig. 4
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a Locations of farmers, FCCs, hubs, and CZs of Mandsaur region based on the proposed SCN model for T1; b locations of hubs and CZs in the zoomed figure for T1; (c) locations of farmers and FCCs of the dotted rectangle for T2

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The percentage of various costs incurred for the experiment A4 (best result) is shown in Fig. 5. One important observation that can be noted from the figure is that the sum of the percentage contribution of costs Z2 and Z4 is 85% of the total SC cost. This suggests to reduce these two costs. The cost Z2 can be reduced by decreasing the distance traveled by farmers to FCCs. This, in turn, increases the number of FCs/FCCs, which will increase the cost of product transportation from FCCs to hubs. Hence, the major focus should be to design a transportation model for the transportation of agriculture products from FCCs to hubs in an efficient manner for minimization of Z4.

Fig. 5
figure 5

The percentage of costs incurred in the proposed SCN model

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SC dynamics

As discussed in  "Model description" section, the proposed model has been developed to address the realistic problems of the Indian AFSC. The dynamics of the SC for the case study problem has been presented to show the model capabilities for the best scenario (experiment A4, Table 4). The inputs (supply and demand data) and outputs (quantities of product shipped and inventory) for this experiment are presented for time periods T1 and T2 in ‘Appendix’ (Tables 8–12). The quantities of products P1 and P3 shipped in periods T1 and T2 from farmers to CZs through FCCs and hubs are presented in Table 5 (cases I–IV) and Tables 6 and 7 (cases V–VIII) for H4 and H3, respectively. The dynamics of the SC is analyzed by mainly emphasizing on the formation of the cluster, allocation of FCCs to hubs, inventory dynamics in terms of quantities held and to be expired products. Various observations and corresponding explanations in terms of the formation of FCCs, and distribution of products (based on the supply/demand in a period) with the main objective of distance minimization are given as follows.

Table 5 Supply chain dynamics in periods T1 and T2 for products P1 and P3 at hub H4
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Table 6 Supply chain dynamics in period T1 for product P1 and P3 at hub H3
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Table 7 Supply chain dynamics in period T2 for product P1 and P3 at hub H3
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  1. (1)

    It is observed that many times an FCC is supplying to the multiple hubs, for example, cases II and III for products P3 and P1, respectively. In case II, FCC F3 supplies 16 units of product to hub H4 to satisfy its demand, and the remaining 117 units are supplied to hub H3 because H3 is near with respect to H4 (Fig. 3). Similarly, FCC F37 for cases II and III supplies the needed quantities of the product at hub H5 and the remaining units of product are supplied to hub H4 because H4 is near concerning H5.

  2. (2)

    Another observation is that the formation of clusters in a time period is the same for all products. For example, compare cases I and II for FCC at F33. When we look for product P1 (case I) and P3 (case II) in period T1, FCC 33 has been re-allocated from H3 to H4 to fulfill the higher demand of product P3 at H4. In the proposed model, the formation of FCs and respective FCCs in a period for different products remains the same, which allows the farmers to transport all the products to the single FCC. It means there is no split supply from farmers to FCC. Although the supply from FCC to the hub(s) can be split based on the demand at CZs. A similar observation can be noted in period T2.

  3. (3)

    Another observation is that the model tries to modify an FC—formed in the previous period —by merging with or breaking existing cluster(s) to satisfy the demand at CZs based on available supply in a period. For example, the demand for product P1 at H1 (Table 11) has increased by 24 units from period T1 to T2. In order to satisfy the increased demand in T2, the FCCs F2, F7, and F25 supply to H1 as well as farmer F50 merge in FCC at F25 (case VII). On the side, FCC F11 enlarges by merging farmer F26, F38, and F41 which supply to H3. The merging of FCC F26 and F41 in F11 reduces the formation cost of FCCs.

  4. (4)

    Further, the results of the model maintain cluster formation nearly the same in different periods (compare case I/II with case III/IV). The model tries to maintain consistency in the assignment of farmers to an FCC and an FCC to the hub(s) for the distribution of products in different periods.

  5. (5)

    The model determines the excess inventory at the end of a period, which is to be used in the next period(s), and to be expired inventory based on supply/demand, planning horizon, and shelf life of products. In case II, the total demand at CZs C1, C8, and C10 is 261 units, whereas 274 units are shipped from hub H4 to CZs. The excess 13 units at C1 will be used in the next period(s) (Table 12). On the other hand, in case V, the total demand at CZs C16, C17, C19, and C20 is 87 units only, whereas 293 units are supplied from hub H3 to these CZs. The excess 206 units supplied at C20 are the to be expired inventory at the end of the period (since the shelf life of P1 is one period). Hence, the model is capable of determining the to be expired products in advance, which can be supplied to other institutional demand locations/nodes.

  6. (6)

    It is observed that a greater number of farmers and FCCs are allocated to hub H3 because H3 is near the most of farmers in comparison with H4 (refer Fig. 3 and Tables 5, 6, 7). Also, the excess products from hub H3 are supplied to CZ C20, which is closest in comparison with other CZs. For example, the difference between the total supply and demand of product P1 in period T1 through all hubs (Tables 10 and 11) is higher in comparison with P3; therefore, the excess production of P1 is supplied to H3 (case V).

Sensitivity analysis

Sensitivity Analysis is a tool used in mathematical modeling to analyze how the different values of an independent variable affect dependent variables. The analysis is performed to check the effects of the maximum distance traveled by a farmer (D1m) to reach an FCC and number of hubs to be opened (NH) on the various costs. The following observations are reported in Table 4. The first outcome is reported by viewing the results of the experiments from A1 to A4. Increasing maximum distance traveled by a farmer (with a fixed value of number of hubs) increases the size of an FC (a greater number of farmers can access an FCC) and reduces the number of FCCs which in turn minimizes cost Z1. Further, reducing the number of FCCs results in decreased transportation cost from FCCs to hubs (Z4) since the total distance traveled from all FCCs to hubs is decreased. On the other side, transportation cost from farmers to FCCs (Z2) is increased due to increasing distance traveled by farmers. However, the cost Z3 observes no effect, and Z5 reports insignificant variation within the same set of experiments. Finally, the overall effect of changing maximum distance traveled by a farmer on the TC is very small. Similar patterns in costs variations are also reported in the sets of experiments B1–B4, C1–C4, and D1–D4.

The second outcome is reported by analyzing experiments A1, B1, C1, and D1. By increasing the value of the number of hubs to be opened (with a constant value of maximum distance traveled by a farmer), the cost required of opening hubs (Z3) increases because each hub is associated with some fixed opening cost. On the other side, transportation cost from FCCs to hubs (Z4) is observed with no trivial variations because of the potential locations of all hubs are nearer with respect to the distances from farmers, whereas transportation cost from hubs to CZs (Z5) is reduced due to the locations of new opening hubs dispersed in the city area which minimizes the total distance traveled from hubs to CZs (Fig. 3b). There is no effect of changing the value of number of hubs on the fixed cost of forming FCCs (Z1). In this way, the TC increases with respect to increasing the value of number of hubs. Similar patterns in the results are also found for the experiments A2, B2, C2, D2 and A3, B3, C3, D3 and A4, B4, C4, D4 in Table 4.

The third observation is that there is no effect of changing maximum distance traveled by a farmer and number of hubs to be opened on the inventory costs Z6 and Z7 (almost constant) in all the experiments (A1–D4), because these costs mainly depend on supply and demand, which are considered the same for all the experiments. Hence, it is concluded that our model is robust with respect to changes in the maximum distance traveled by a farmer to reach a farmer cluster center. On the other hand, the model is sensitive with respect to changes in the number of hubs to be opened.

Concluding remarks and future work

Out of the four major problems which are identified in this research work, one of the shortcomings improper structure of traditional Indian AFSC results in the other two shortcomings—low profitability of farmers and high wastage of agriculture products. From small-farm-holding farmers (which is a shortcoming), the inefficient transportation of products to market is the another (major) cause of the farmers’ low profitability. In this work, authors suggest the clustering of farmers for the integration of small farmers’ supply at the cluster centers and transportation of these aggregated products to the hubs. The idea of aggregate product shipment reduces the transportation cost from farmers to hubs. Further, the perishable nature of products in the modeling of the distribution network is considered to reduce food wastage in the chain.

A four-echelon, multi-period, multi-product SCN model for Indian AFSC is developed by considering the clustering of farmers and perishability of products. The model aims to minimize the total distribution cost which comprises the fixed cost of opening facilities, transportation costs from farmers to CZs, inventory holding cost and disposal cost of expired products at CZs. The developed model determines the required number of FCCs for aggregation of products, allocation of facilities (FCCs and hubs), quantities of products flow between the facilities as well as inventory and the to be expired products at each CZ. To implement the model, a case study problem of Mandsaur District (India) is considered for the distribution of vegetables. Sensitivity analysis shows that the proposed model is robust and sensitive with respect to changes in the maximum distance traveled by a farmer to reach a cluster center and the number of hubs to be opened, respectively.

The model has been proposed in order to solve the identified shortcomings in the following ways: The organized SC is well planned to reach the consumers. It governs and controls all the activities of the SC. Hence, we have developed an SC model to organize the Indian AFSC. The effects of small-farm-holding farmers are mitigated by considering aggregation of products using clustering of farmers. The transportation of aggregate products reduces transportation cost from farmers to hubs which will be benefited to the farmers. The proposed formulation also includes the perishable nature of products which determines excess products in advance. These excess products can be supplied to other institutional demand nodes (like hospitals, hostels, and restaurants); thus, it will reduce the wastage of agricultural products.

In the article, authors addressed three dimensions of sustainability: economical (minimization of transportation cost), social (enhancement of farmers’ profitability), and environmental dimension (reduction of agricultural wastage and carbon emissions). The SC dynamics shows that the proposed model is capable to include the supply and demand variability in determining the optimal location–allocation of FCCs and hubs. The proposed SCN model may help the existing agricultural retail chains (like Reliance Fresh, Big Bazar, Big-basket) in the collection of items from the small farmers.

Managerial insights

Based on the results of the study, the following managerial insights can be noted. In traditional SC, farmers individually bring their products from the farming locations to the hubs. The TC of product movement is borne by the farmers, and it is mainly responsible for the low profitability of the farmers, as reported in "Low profitability of farmers" section. In this work, authors recommend that farmers should aggregate their products at an optimal cluster center then, transport these products from an FCC to the hub by incorporating an appropriate transportation plan to minimize transportation cost. The outcome of the model further confirms the same which shows that the transportation costs from farmers to FCCs (Z2) and FCCs to hubs (Z4) have 85% contribution to the total SC cost (Fig. 5). The results of the sensitivity analysis report that the minimum number of hubs to be opened (transshipment nodes) gives the best result of the model. The developed model guides managers and policymakers to identify the optimal location of facilities (FCCs and hubs) where suitable infrastructure can be developed. The aggregate transportation of products will reduce carbon emissions and traffic congestion; hence, it is an eco-friendly strategy for product transportation. Further, the proposed formulation can be applied for other products’ SC with considering shelf life of the products (Gholamian and Taghanzadeh 2017).

Future work

This paper has proposed a mathematical model to redesign the traditional Indian AFSC. It is obvious that the formulated mathematical model is not applicable without addressing other aspects of the SC. Although the proposed model is practical, there are two main limitations that need to be improved in future studies: first, the conceptual framework and policies to handle various operational issues like pricing, packaging and coordination and cooperation amongst the SC actors, and Second, the information technology model (app/website) to maintain the dynamic relationship between players for the proposed SCN model. Additionally, a suitable vehicle routing model can be included to reduce further the transportation cost from FCCs to the hub(s). Also, meta-heuristic solution approaches can be used to study computational complexity for large data set problems. The concept of reverse logistics, as suggested by Bottani et al. (2019), can be incorporated to move the waste products and packaging materials from hubs to farmers/FCC locations, where it can be recycled (to make compost) (Waqas et al. 2018) and reused, respectively.