In vendor-to-retailer systems where retailers with limited inventory capacity place orders and vendors dispatch trucks within soft time windows, trucks may arrive before sufficient space is available, requiring them to wait on site resulting in inventory-driven delays. Since no existing formulation incorporates inventory-dependent service times, this study models the dispatch problem as a discrete-time Markov Decision Process (MDP) with inventory-dependent service times, solved using Approximate Dynamic Programming (ADP) with a Partial Value Function Approximation (PVFA) that ranks outstanding orders based on urgency. The model is implemented at an Ethiopian brewery and benchmarked against a First-In First-Out (FIFO) policy across three replenishment strategies: Retailer-Managed Inventory (RMI) with Poisson-generated orders, threshold-based replenishment with a fixed lead time, and Vendor-Managed Inventory (VMI) where order timing is optimized. Results show that, depending on the replenishment strategy, the PVFA reduces unmet demand by 53–98%, lowers extended service times by 65–93%, and frees 8–16% of fleet capacity to be repurposed, with the total number of orders served ranging from a 5% decrease to a 22% increase. These findings demonstrate that inventory-driven delays can be effectively incorporated into a dispatch model, enabling soft handling of inventory constraints. The PVFA consistently outperforms the FIFO benchmark across all scenarios, demonstrating its ability to anticipate even in reactive systems. It also exhibits lower variance on Key Performance Indicators (KPIs), indicating robustness under different replenishment settings. As such, the model is well suited for environments where order policies vary or inventory-driven delays are common. Future work may address dynamic order generation, parameter uncertainty, and extensions toward the general Inventory Routing Problem (IRP).