Lagos, F., Boland, N., & Savelsbergh, M. (2022). Dynamic discretization discovery for solving the Continuous Time Inventory Routing Problem with OutandBack Routes. Comput. Oper. Res., 141, 105686.
Abstract: In time dependent models, the objective is to find the optimal times (continuous) at which activities occur and resources are utilized. These models arise whenever a schedule of activities needs to be constructed. A common approach consists of discretizing the planning time and then restricting the decisions to those time points. However, this approach leads to very large formulations that are intractable in practice. In this work, we study the Continuous Time Inventory Routing Problem with OutandBack Routes (CIRPOB). In this problem, a company manages the inventory of its customers, resupplying a single product from a single facility during a finite time horizon. The product is consumed at a constant rate (product per unit of time) by each customer. The customers have local storage capacity. The goal is to find the minimum cost delivery plan with outandback routes only that ensures that none of the customers run out of product during the planning period. We study the Dynamic Discovery Discretization algorithm (DDD) to solve the CIRPOB by using partially constructed timeexpanded networks. This method iteratively discovers time points needed in the network to find optimal continuous time solutions. We test this method by using randomly generated instances in which we find provable optimal solutions.
