Solving the petroleum replenishment and routing problem with variable demands and time windows

In this paper we develop a methodological framework for designing the daily distribution and replenishment operations of petroleum products over a weekly planning horizon by taking into account the perspectives of both the transporter and its customers. The proposed approach considers the possibility of having late deliveries due to the variability of the customers’ demands and expected time windows. We first develop an inventory model for the customers to identify the optimal order quantities and time windows. Then, we solve a sequence of mixed-integer optimization models for designing distribution routes based on the order quantities and time windows selected by the inventory models. We design the optimization models so that late deliveries are balanced among the customers in order to mitigate the overall customer dissatisfaction. We test the proposed approach by solving a set of instances adapted from the literature. The empirical results show that the proposed approach can be used for designing the distribution plan for delivering petroleum products in conditions where the operational capabilities of the transporter are limited for generating optimal on-time plans.