Dynamic modelling of cold chain logistics services under budget constraints for the delivery of fresh products in an urban area

The quality of perishable products declines continuously during the transportation process, rendering the delivery of a product with good freshness a challenging task in urban areas. We investigate how to plan activities to preserve the freshness level of products within a specific distance range. To this end, we construct an analytical model consisting of an online retailer and a third-party logistics service provider that loads the product from the retailer's fulfillment center and delivers it to various destinations with cold-chain logistics operations. The retailer seeks an appropriate balance between the delivery of good freshness, the farthest distance of delivery, and a limited budget for cold-chain logistics. We derive the optimal size of the area in which the freshness of products is maintained to the maximum possible level and the farthest distance that the retailer should consider when fulfilling online orders. This study includes three scenarios: in-house operation, outsourcing, and a hybrid mode. In outsourcing, the retailer pays a service fee based on the number of orders fulfilled within a specific area. The primary finding is that the retailer can choose an appropriate combination of the service fee rate and budget to control the scale of the area that guarantees good freshness. This finding has managerial significance, in that the ability to accurately predict and control the freshness by the distance range can reduce the occurrence of customers complaining about the quality of the delivered products.