Green food supply chain design considering risk and post-harvest losses: a case study

Abstract

The global food insecurity, malnourishment and rising world hunger are the major hindrances in accomplishing the zero hunger sustainable development goal by 2030. Due to the continuous increment of wheat production in the past few decades, India received the second rank in the global wheat production after China. However, storage capacity has not been expanded with similar extent. The administrative bodies in India are constructing several capacitated silos in major geographically widespread producing and consuming states to curtail this gap. This paper presents a multi-period single objective mathematical model to support their decision-making process. The model minimizes the silo establishment, transportation, food grain loss, inventory holding, carbon emission, and risk penalty costs. The proposed model is solved using the variant of the particle swarm optimization combined with global, local and near neighbor social structures along with traditional PSO. The solutions obtained through two metaheuristic algorithms are compared with the optimal solutions. The impact of supply, demand and capacity of silos on the model solution is investigated through sensitivity analysis. Finally, some actionable theoretical and managerial implications are discussed after analysing the obtained results.

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Appendix 1

Appendix 1

Indices

\( p \) :

Index for procurement centres, p = 1,2,…, P

\( b \) :

Index for a potential location of base silos, b = 1,2,…, B

\( f \) :

Index for a potential location of field silos, f = 1,2,…, F

\( r \) :

Index for regional warehouse, r = 1,2,…, R

\( d \) :

Index for destination warehouse, d = 1,2,…, D

\( t \) :

Index for time period t = 1,2,…, T

h :

Index for capacity of base silo, h = 1,2,…, H

j :

Index for capacity of field silo, j = 1,2,…, J

\( n_{1} \) :

Index for truck type present at procurement centre, \( n_{1} \)= 1,2,…, \( N_{1} \)

\( n_{2} \) :

Index for rake type present at base silo, \( n_{2} \)= 1,2,…, \( N_{2} \)

\( n_{3} \) :

Index for truck type present at field silo, \( n_{3} \)= 1,2,…, \( N_{3} \)

\( n_{4} \) :

Index for truck type present at regional warehouse, \( n_{4} \)= 1,2,…, \( N_{4} \)

Model parameters

Cost parameters

\( F_{b}^{h} \) :

Fixed cost of establishing the base silo with capacity h at location b

\( F_{f}^{j} \) :

Fixed cost of establishing the field silo with capacity j at location f

\( tc_{pb} \) :

Transportation cost from procurement centre p to base silo b (per MT per km)

\( tc_{bf} \) :

Transportation cost from base silo b to field silo f (per MT per km)

\( tc_{fr} \) :

Transportation cost from field silo f to regional warehouse r (per MT per km)

\( tc_{rd} \) :

Transportation cost from regional warehouse r to destination warehouse d (per MT km)

\( ih_{b} \) :

Inventory holding cost at base silo b (per MT per period)

\( ih_{f} \) :

Inventory holding cost at field silo f (per MT per period)

\( ih_{r} \) :

Inventory holding cost at regional warehouse r (per MT per period)

\( lc \) :

Food grain lost cost (per MT)

\( ce \) :

Cost of ton of carbon dioxide emission

\( rc \) :

Risk penalty cost

Distance parameters

\( dis_{pb} \) :

Distance between procurement centre p to base silo b

\( dis_{bf} \) :

Distance between base silo b to field silo f

\( dis_{fr} \) :

Distance between field silo f to regional warehouse r

\( dis_{rd} \) :

Distance between regional warehouse r to destination warehouse d

Vehicle related parameters

\( cv_{{n_{1} }} \) :

Capacity of truck type \( n_{1} \)

\( cv_{{n_{2} }} \) :

Capacity of rake type \( n_{2} \)

\( cv_{{n_{3} }} \) :

Capacity of truck type \( n_{3} \)

\( cv_{{n_{4} }} \) :

Capacity of truck type \( n_{4} \)

\( nv_{{n_{1} p}}^{t} \) :

Total number of \( n_{1} \) type trucks available at procurement centre p in period t

\( nv_{{n_{2} b}}^{t} \) :

Total number of \( n_{2} \) type rakes available at base silo b in period t

\( nv_{{n_{3} f}}^{t} \) :

Total number of \( n_{3} \) type trucks available at field silo f in period t

\( nv_{{n_{4} r}}^{t} \) :

Total number of \( n_{4} \) type trucks available at regional warehouse r in period t

Procurement, demand, capacity and percentage of loss parameters

\( A_{p}^{t} \) :

Amount of food grain quantity available at procurement centre p in period t

\( L_{d}^{t} \) :

Demand of food grain of destination warehouse d in period t

\( cb_{h} \) :

Capacity of base silo type h

\( cf_{j} \) :

Capacity of field silo type j

\( cr_{r} \) :

Capacity of regional warehouse r

\( lb \) :

Transit loss of food grain if transported in bulk form

\( lj \) :

Transit loss of food grain if transported using conventional way of jute bags

\( ls \) :

Storage loss of food grain if stored in silos

\( lw \) :

Storage loss of food grain if stored in conventional warehouses

Emission parameters

\( e_{pb}^{{n_{1} }} \) :

Amount of CO2 released per unit distance for each \( n_{1} \) type of truck travelling from procurement centre p to base silo b

\( e_{bf}^{{n_{2} }} \) :

Amount of CO2 released per unit distance for each \( n_{2} \) type of rake travelling from base silo b to field silo f

\( e_{fr}^{{n_{3} }} \) :

Amount of CO2 released per unit distance for each \( n_{3} \) type of truck travelling from field silo f to regional warehouse r

\( e_{rd}^{{n_{4} }} \) :

Amount of CO2 released per unit distance for each \( n_{4} \) type of truck travelling from regional warehouse r to destination warehouse d

Risk related parameters

\( \varepsilon_{b}^{h} \) :

Establishment risk of locating base silo with size h at potential location b

\( \varepsilon_{f}^{j} \) :

Establishment risk of locating field silo with size j at potential location f

\( g_{pb} \) :

Risk of transportation between procurement centre p to base silo b

\( g_{bf} \) :

Risk of transportation between base silo b to field silo f

\( g_{fr} \) :

Risk of transportation between field silo f to regional warehouse r

\( g_{rd} \) :

Risk of transportation between regional warehouse r to destination warehouse d

Decision variables

Binary variables

\( X_{b}^{h} \) :

1, if base silo type h is selected to be established at location b

0 Otherwise

\( X_{f}^{j} \) :

1, if field silo type j is selected to be established at location f

0 Otherwise

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

1, if procurement centre p is assigned to base silo b in time period t

0, Otherwise

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

1, if base silo b is assigned to field silo f in time period t

0, Otherwise

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

1, if field silo f is assigned to regional warehouse r in time period t

0, Otherwise

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

1, if regional warehouse r is assigned to destination warehouse d in time period t

0, Otherwise

Continuous variables

\( U_{pb}^{t} \) :

Shipment quantity from procurement p to base silo b in period t

\( U_{bf}^{t} \) :

Shipment quantity from base silo b to field silo f in period t

\( U_{fr}^{t} \) :

Shipment quantity from field silo f to regional warehouse r in period t

\( U_{rd}^{t} \) :

Shipment quantity from regional warehouse r to destination warehouse d in period t

\( Tl_{pb}^{t} \) :

Fraction of shipment quantity that loss from procurement p to base silo b in period t

\( Tl_{bf}^{t} \) :

Fraction of shipment quantity that loss from base silo b to field silo f in period t

\( Tl_{fr}^{t} \) :

Fraction of shipment quantity that loss from field silo f to regional warehouse r in period t

\( Tl_{rd}^{t} \) :

Fraction of shipment quantity that loss from regional warehouse r to destination warehouse d in period t

\( IN_{b}^{t} \) :

Inventory in base silo b at the end of period t

\( IN_{f}^{t} \) :

Inventory in field silo f at the end of period t

\( IN_{r}^{t} \) :

Inventory in regional warehouse r at the end of period t

\( Sl_{b}^{t} \) :

Fraction of inventory stock that loss in period t at base silo b

\( Sl_{f}^{t} \) :

Fraction of inventory stock that loss in period t at field silo f

\( Sl_{r}^{t} \) :

Fraction of inventory stock that loss in period t at regional warehouse r

Integer variables

\( V_{pb}^{{n_{1} t}} \) :

Number of \( n_{1} \) type of vehicles used from procurement centre p to base silo b in time period t

\( V_{bf}^{{n_{2} t}} \) :

Number of \( n_{2} \) type of rakes used from base silo b to field silo f in time period t

\( V_{fr}^{{n_{3} t}} \) :

Number of \( n_{3} \) type of vehicles used from field silo f to regional warehouse r in time period t

\( V_{rd}^{{n_{4} t}} \) :

Number of \( n_{4} \) type of vehicles used from regional warehouse r to destination warehouse d in time period t

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Mogale, D.G., Kumar, S.K. & Tiwari, M.K. Green food supply chain design considering risk and post-harvest losses: a case study. Ann Oper Res (2020). https://doi.org/10.1007/s10479-020-03664-y

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Keywords

  • Food grain supply chain
  • Food security
  • Transportation
  • Inventory
  • Particle swarm optimization