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Restructuring the Indian agro-fresh food supply chain network: a mathematical model formulation

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Abstract

In traditional Indian agro-fresh food supply chain (AFSC), authors identify the following four shortcomings through the literature survey: (1) unorganized supply chain structure; (2) low profitability of farmers; (3) high wastage of agricultural products; and (4) a large number of small-farm-holding farmers. According to the fourth shortcoming, 85% of farmers have less than 2 hectares of farming land, and these farmers transport their products independently into the market to sell. Owing to this, a higher transportation cost is incurred in traditional AFSC, which leads to low profit for farmers. To overcome these shortcomings, authors propose aggregation of products by forming clusters of farmers and its transportation from these cluster centers to market. This paper formulates multi-period, multi-product, mixed-integer nonlinear programming model to design a four-echelon supply chain with considering the clustering of farmers and perishability of products. A real case study problem of Mandsaur District (India) of vegetable distribution is solved in LINGO 17.0 to check the validity of the formulated model. The results revealed that 85% of the total distribution cost incurred in the transportation of products from farmers to the market. Hence, the major focus should be to design an efficient transportation plan for the minimization of transportation cost from farmers to the market. Further, sensitivity analysis shows that the proposed model is robust and sensitive to changes in maximum distance traveled by a farmer to reach a cluster center and number of hubs to be opened, respectively.

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Abbreviations

f :

Index of farmers (suppliers), \(f \in \left\{ {1,..,F} \right\}\)

i :

Index of FCCs, \(i \in \left\{ {1,..,I} \right\} \in F\)

j :

Index of hubs, \(j \in \left\{ {1,..,J} \right\}\)

k :

Index of CZs (retailers), \(k \in \left\{ {1,..,K} \right\}\)

p :

Index of product types, \(p \in \left\{ {1,..,P} \right\}\)

t, τ :

Index of periods, \(t \in \left\{ {1,..,T} \right\}\)

\(H_{fp}^{t}\) :

The harvested quantity of product type p available to supply from fth farmer (kg)

\(l_{p}^{{}}\) :

The shelf life of product type p (period)

\(D_{kp}^{t}\) :

The quantity demanded at kth CZ for product type p (kg)

\(D1_{fi}^{{}}\) :

Distance from farmer fth to ith FCC (km)

\(D1_{\text{m}}^{{}}\) :

Maximum distance to be traveled by a farmer to belong to any FCC (km)

\(D2_{ij}^{{}}\) :

Distance from ith FCC to jth hub (km)

\(D3_{jk}^{{}}\) :

Distance from jth hub to kth CZ (km)

\({\text{TC}}_{ 1}\) :

Unit transportation cost from a farmer to an FCC [INR (The current value of 1 INR is equal to 0.014 USD as on September 10, 2020)/km/kg]

\({\text{TC}}_{ 2}^{{}}\) :

Unit transportation cost from an FCC to a hub (INR/km/kg)

\({\text{TC}}_{ 3}^{{}}\) :

Unit transportation cost from a hub to a CZ (INR/km/kg)

\({\text{HC}}_{kp}^{{}}\) :

Per period inventory holding cost of product type p at kth CZ (INR/kg/period)

\({\text{LB}}_{ip}^{{}}\) :

Lower bound on supply from ith FCC to hub(s) for product type p (kg)

\({\text{LB}}_{jp}^{{}}\) :

Lower bound on supply from jth hub to CZ(s) for product type p (kg)

\({\text{NH}}\) :

Number of hubs to be opened

\({\text{FC}}1_{i}^{{}}\) :

Fixed cost of forming ith FCC (INR)

\({\text{FC}}2_{j}^{{}}\) :

Fixed cost for opening jth hub (INR)

\({\text{DC}}_{p}^{{}}\) :

Disposal cost of expired product type p (INR)

\(M\) :

Big number

\(F_{i}^{t}\) :

\(\left\{ {\begin{array}{*{20}l} 1 \hfill & {{\text{if }}i{\text{th FCC is formed in period }}t{\text{;}}} \hfill \\ 0 \hfill & {{\text{otherwise}}}. \hfill \\ \end{array} } \right.\)

\(Y_{fi}^{t}\) :

\(\left\{ {\begin{array}{*{20}l} 1 \hfill & {{\text{if }}f{\text{th farmer is assigned to }}i{\text{th FCC in period }}t{\text{;}}} \hfill \\ 0 \hfill & {{\text{otherwise}}{\text{.}}} \hfill \\ \end{array} } \right.\)

\(Z_{j}^{t}\) :

\(\left\{ {\begin{array}{*{20}l} 1 \hfill & {{\text{if }}j{\text{th hub is opened in period }}t{\text{;}}} \hfill \\ 0 \hfill & {{\text{otherwise}}}. \hfill \\ \end{array} } \right.\)

\(Q_{ijp}^{t}\) :

Quantity of product type p shipped from ith FCC to jth hub in period t (kg)

\(Q_{jkp}^{'t\tau }\) :

Quantity of product type p shipped from jth hub to kth CZ in period t for use in period τ \((\tau \ge t)\) (kg)

\(I_{kp}^{t}\) :

Inventory of product type p at kth CZ in period t (kg)

\({\rm Ex}_{kp}^{t}\) :

Quantity of the to be expired product type p supplied in period t by any hub to kth CZ (kg)

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Authors and Affiliations

  1. Department of Mechanical Engineering, PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur, India

    Rakesh Patidar & Sunil Agrawal

Authors
  1. Rakesh Patidar
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  2. Sunil Agrawal
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Correspondence to Rakesh Patidar.

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Appendix

Appendix

See Tables 8, 9, 10, 11, and 12.

Table 8 Farmer supply availability for periods T1 and T2
Full size table
Table 9 Customer zone demand for periods T1 and T2
Full size table
Table 10 Quantity of product shipped from FCC to the hub in periods T1 and T2
Full size table
Table 11 Quantity of product shipped from hub to CZ in periods T1 and T2
Full size table
Table 12 Status of inventory based on supply/demand of planning horizon T1–T10
Full size table

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Patidar, R., Agrawal, S. Restructuring the Indian agro-fresh food supply chain network: a mathematical model formulation. Clean Techn Environ Policy 22, 2053–2077 (2020). https://doi.org/10.1007/s10098-020-01955-3

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  • DOI: https://doi.org/10.1007/s10098-020-01955-3

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