Dispatch optimization under inventory-driven delays

Abstract

Inventory capacity constraints represent real-world space scarcity in warehouses. When only full truckloads are permitted, these constraints are typically enforced by blocking deliveries that would violate the capacity. However, when the inventory is simultaneously too high to allow a delivery while also too low to serve all demand, this method leads to unmet demand. This study therefore introduces inventory-driven delays, where vehicles are held at the destination until enough inventory capacity is available, as a method to enforce capacity constraints. To capture these delays, the dispatch problem is formulated as a discrete-time Markov Decision Process (MDP) with inventory-dependent service times. The problem is solved using Approximate Dynamic Programming (ADP), which accounts for opportunity costs associated with waiting vehicles, allowing the policy to handle the state-dependent costs introduced by inventory-driven delays. A case study is developed based on data from an Ethiopian brewery. The proposed method is compared against multiple heuristics across four different replenishment strategies. Results show that one full truckload of unmet demand is recovered per ten cumulative days of inventory-driven delays, suggesting that allowing such delays can serve as a strategic buffer in inventory-capacitated, full-truckload systems. Future work may address dynamic order generation, parameter uncertainty, and extensions toward the general Inventory Routing Problem (IRP).