Inventory Routing Problem With Split Delivery and Variable Time Windows for Customers With Small Capacity and Large Sales

In push delivery mode, a supplier determines both delivery orders of customers and vehicle routes. Some customers have small inventory capacity and rapid sale speed (called small-C/S customers). Thus, each of them needs to receive multiple deliveries in a work shift (e.g., one day). The number of deliveries and quantity of each delivery for a customer are unknown. Each delivery has a pair of accommodation time and stockout time, both of which are variable and constitute the soft time window of the delivery. This work proposes a Single-period Inventory Routing problem with split delivery and variable time windows for Small-C/S customers (SIRSC). The number of deliveries for each customer, and the quantity, time window, and arrival time of each delivery are variable. Various products that cannot be mixed can be loaded on the same truck with multiple compartments and a truck can return several times to the depot to resupply in the period. A mathematical programming model is developed for SIRSC, to minimize the sum of transportation and stockout costs. A hybrid ant colony optimization with variable neighborhood search (ACO-VNS) is proposed to solve SIRSC. A distribution network model of ACO is developed and several problem-specific neighborhood structures are designed. ACO-VNS is applied to some problem instances and a real-world gasoline delivery case. Experimental results show that it can effectively solve SIRSC, and outperforms CPLEX and other meta-heuristics.