Optimising transportation plans for multi-warehouse, multi-product systems: mitigating the impact of new purchase and sales orders

In the rapidly evolving landscape of supply chain management, the agility to adapt to changing demands while maintaining operational efficiency is paramount. This paper introduces a novel approach to managing transportation plans within a multi-warehouse, multi-product framework, focussing on minimising disruptions to existing schedules in response to new purchase and sales orders. Our research aims to redefine existing transportation plans, originally set before the arrival of additional orders, with the objective of implementing the least possible alterations while satisfying all customer requirements. The primary challenge addressed in this study is to maintain stock levels above a predefined minimum threshold in various warehouses without compromising the efficiency of the distribution network. Unlike traditional routing problems, the focus is not on selecting the routes for transportation, but on strategically deciding when to initiate a vehicle trip or adjusting the number of products in already scheduled trips. To address the problem, a mixed-integer linear programming model based on a flow network graph is proposed. To reduce the size of the network, exact and heuristic pre-processing procedures are developed. A first set of computational tests was conducted on data provided by a textile industry that needs to minimise changes in the transport plan to meet the variation in demand for different goods. A detailed analysis of the results of instances with up to 14,000 products and 23 million items is reported. Further computational tests were randomly generated to verify the efficiency of the proposed techniques in different scenarios. The promising results of the computational tests highlight the applicability of the proposed approach in the industrial scenario analysed.