Optimization of a coordinated sustainable multi-vendor multi-livestock multi-rancher supply chain for growing products

Abstract

Inventory management for growing items is crucial in many industries, including agriculture, aquaculture, and animal husbandry. This paper develops a new mathematical model for the inventory management of growing products in a multi-vendor, multi-livestock, multi-rancher supply chain. The possibility of partial backorder shortages is considered, and both backorder and lost sale shortages are possible. To address environmental concerns, the carbon emissions of the system are limited by a direct cap policy. The main objective is to determine the optimal ordering and shortage quantity for each livestock type for each rancher. We incorporate the Hill coordination strategy into our proposed model to provide a centralized decision-making framework. Given the nonlinearity and dimensionality of the model, we propose metaheuristic algorithms as the solution approach. To this end, genetic algorithms, differential evolution, and particle swarm optimization algorithms are designed and implemented for the problem. The input parameters of all algorithms are tuned using Taguchi's design of experiments. We evaluate the performance of these algorithms by solving several numerical instances in small, medium, and large size categories. The experimental results show that the genetic algorithm outperforms the other metaheuristics regarding the quality of solutions. Finally, some suggestions for extending the current study are discussed