Nowadays, environmental considerations and advancements in the field of logistics have extended successful management of supply chains to effectively combine forward and reverse distribution into one integrated bidirectional flow network. In this paper, we consider a closed loop multi-echelon inventory-location problem and we formulate it as a non-linear mixed integer program in which the objective function is neither concave nor convex. We model the forward distribution of a single type of product from a single plant to a set of retailers through a set of warehouses that can be located at various predetermined sites. In addition, our model also considers the reverse flows of returned products to be shipped back to the plant for undergoing recycling or disposal. In light of this, there are three types of warehouses considered in the network: forward warehouses, reverse warehouses, and joint warehouse which simultaneously deal with products from both directions. The objective aims to minimize the system-wide costs, including fixed location cost, fixed ordering cost, inventory holding cost, shipment cost, and the processing cost for returned products. Model properties are outlined and sensitivity analysis is conducted to study the effects of varying weighting values for different cost components under closed loop supply chain network design.
Nowadays, environmental considerations and advancements in the field of logistics have extended successful management of supply chains to effectively combine forward and reverse distribution into one integrated bidirectional flow network. In this paper, we consider a closed loop multi-echelon inventory-location problem and we formulate it as a non-linear mixed integer program in which the objective function is neither concave nor convex. We model the forward distribution of a single type of product from a single plant to a set of retailers through a set of warehouses that can be located at various predetermined sites. In addition, our model also considers the reverse flows of returned products to be shipped back to the plant for undergoing recycling or disposal. In light of this, there are three types of warehouses considered in the network: forward warehouses, reverse warehouses, and joint warehouse which simultaneously deal with products from both directions. The objective aims to minimize the system-wide costs, including fixed location cost, fixed ordering cost, inventory holding cost, shipment cost, and the processing cost for returned products. Model properties are outlined and sensitivity analysis is conducted to study the effects of varying weighting values for different cost components under closed loop supply chain network design.
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