Aggregating disjoint partial sub-orders – an internal logistics application

Abstract

The problematic addressed in this work concerns an internal logistics issue that arises in warehousing. It first concerns the aggregation of a several ordered flows of loads (cartons, totes, containers, etc.) into a single flow, called the load sequencing problem. Then, this flow should be injected into the system at a maximal throughput, which gives the load injection problem. From the theoretical perspective, the load sequencing problem belongs to the class of partial-order aggregation problems, known to be NP-Hard. We describe a use-case application in logistics and formulate it in mathematical terms as a specific partial-order aggregation problem, namely disjoint partial sub-orders aggregation. We then present two exact solution methods in detail, one based on integer linear programming and the other using dynamic programming combined with a Branch & Cut scheme. All methods perform very well for randomly generated industrial instances. At the end, we provide a heuristic based on the dynamic programming algorithm. This heuristic is implemented for industrial use and gives near-optimal solutions in a very short computation time. The load injection problem falls in the category of scheduling problem (Job shop problem). In practice, this comes to compute the injection dates of loads in the collector with goal of ensuring a maximal debit exit flow with respect to the capacity of the system. We provide the formula for the injection date which achieves maximal debit exit flow. With respect to the application in hand, the proposed method outperforms the existing used method in terms of flow management and brings in practice a significant increase (up to 20%) of a number of loads proceeded for the same amount of time. Our findings are supported by numerical results.