Fluid approximation to pricing batched products with no product type mixing within batches

We consider a vendor selling a combined offer of multiple product types plus delivery, where delivery capacity is limited. Delivery occurs in batches each containing only a single product type. This situation occurs for fuel wholesalers who deliver to customers in tanker trucks, which can carry only one fuel grade per trip. In certain fuel markets, customers are quoted individualised prices based on willingness‐to‐pay segmentation. Optimising such prices requires an estimate of the opportunity cost of the remaining delivery capacity. We adapt standard fluid approximation estimates of opportunity cost to accommodate discrete assignment of product type to delivery unit.