A mathematical model for multi-period multi-stage multi-mode multi-product capacitated wheat supply network design problem and a case study

Purpose: The purpose of this paper is to develop a cost-effective network design model, including transport and storage that will enable a decision at a tactical and strategic level to be taken to optimize the structure of the Turkey wheat supply chain. Theory and Methods: The proposed model was developed using 0-1 mixed integer linear programming. First, the model was tested with the data obtained from the interviews with 103 farmers to investigate whether the model worked properly. Then, the case study method was used to test the model with the data obtained from a Flour Mill Company which is one of the first 500 industrial enterprises in Turkey. Results: The results were obtained by using IBM ILOG CPLEX Optimization Studio 12.6.2.0. Although farmers used eighteen different-capacity vehicles for transport, five different-capacity vehicles were used in the model. Smaller capacity vehicles were used by the farmers; however, the model proposed larger-capacity vehicles. Wheat was transported by farmers with 10-ton vehicles using 100 trips, 20-ton vehicles using 115 trips and 30-ton vehicles using 13 trips. However, the model proposed transportation using 10-ton vehicles and 13 trips, 20-ton vehicles and 22 trips and 30-ton vehicles and 151 trips. The proposed model reduced the number of smaller-capacity vehicle trips and increased the number of larger-capacity vehicle trips. As a result, the model has significantly reduced total transportation costs in wheat supply chain in Turkey. Conclusion: In this study, a mathematical model for multi-period multi-stage multi-mode multi-product capacitated was developed for wheat supply chain in Turkey. The developed supply network design model selected a vehicle of the appropriate capacity to suit the amount of load to be transported in the wheat supply chain and decrease the number of vehicle trips. This improvement gained by the model can be applied to other sectors. The model showed that supply warehouses, which have been considered for rental to the private sector, can be effectively used for cost-effectiveness. Additionally, the consolidation of the purchased wheat provides an alternative way for the wheat to be transported, in particular by rail.