Modelling shipment consolidation and pricing decisions for a manufacturer-distributor

Consider a supply chain with one vendor and multiple buyers. That vendor not only manufactures the goods demanded, but also transports them by its own fleet of trucks to buyers that are densely dispersed in a distribution zone. The buyers are sensitive to both price and delivery-time guarantee. We model and maximise the vendors expected profit rate when the prices charged depend on the arrival times of orders. The optimal profit rate is found to be concave in the vehicle capacity. We illustrate our theoretical findings with numerical examples and sensitivity analyses to furnish managerial insights.