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Palletization, a core activity in warehousing and distribution, involves the solution of a three-dimensional bin packing problem with side constraints. This problem is known as the mixed-case palletization problem. Motivated by the fact that solving industry-size instances is still very challenging for existing methodology, we propose a data-driven solution approach that combines data analysis at the instance level and optimization. For each instance, box heights are analyzed to identify possible layer heights and to derive relative positions of boxes. Boxes are then grouped in pairs and trios and stacked in stable arrangements called super-boxes. Using stable super-boxes of uniform height, a two-dimensional bin packing problem is solved to create layers of even height. The layers are then stacked on top of one another to create stable pallets. The layering approach combined with a careful layer and pallet formation leads to fully supported boxes. Computational tests on industry data demonstrate the efficiency of the approach in producing high-quality solutions in quick computational times, consistently placing around 80% of boxes in layers, achieving an average pack density of 84%, and attaining full support for more than 99% of boxes.

This article presents an extended facility location model for multiproduct supply chain network design, that accounts for concave capacity, transportation, and inventory costs (induced by economies...

Pallet loading requires the solution of a three-dimensional bin packing problem (3DBPP) with additional requirements. In particular, vertical support and load bearing, which are not enforced in 3DBPP, are essential in practice. In this work, we provide a complete solution approach for pallet loading problems where practical constraints of vertical support, load bearing, planogram sequencing, and weight limits are fully accounted for. Using a layer based column generation approach, we tackle vertical support using second order cone programming, and satisfy load bearing through a graph representation to trace load distribution. Additionally, we use industry data to propose an instance generator that produces realistic items with practical attributes such as support surface, load capacity, weight, and planogram sequence number. Extensive numerical testing reveals the ability of the approach to find high quality solutions for industry size instances in fast computational times.

Motivated by the need to solve large hub location problems efficiently and accurately, we discover an important characteristic of optimal solutions to p-hub median problems that we call spatial separability. It refers to the partitioning of the network into allocation clusters with nonoverlapping convex hulls. We illustrate numerically that the property persists over a wide range of randomly generated instances and propose a data-driven approach based on an insight from the property to tackle very large problem sizes. Computational experiments corroborate the effectiveness of the proposed approach in generating high-quality solutions within reasonable computational times. We then explore a new application area of hub location problems in brain connectivity networks and introduce the largest and the first set of three-dimensional instances in the literature. Computational results demonstrate the capability of hub location models in successfully depicting the hub organization of the human brain, as validated by the medical literature, thus revealing that hub location models can play an important role in investigating the intricate connectivity of the human brain.

We analyze data emanating from a major e-commerce warehouse and provided by a third-party warehouse logistics management company to replicate flow diagrams, assess order fulfillment efficiency, identify bottlenecks, and suggest improvement strategies. Without access to actual layouts and process-flow diagrams and purely based on data, we are able to describe the processes in detail and prescribe changes. By investigating the characteristics of orders, the wave-sorting operation, and the order-preparation process, we find that products from different orders are picked in batches for efficiency. Similar products are picked in small containers called totes. Totes are then stored in a buffer area and routed to be emptied of their contents at induction lines. Orders are then consolidated at the put wall, where each order is accumulated in a cubby. This order consolidation process depends on the sequence in which totes are processed and has a huge impact on order-completion time. We, therefore, present a generalization of the parallel machine–scheduling problem that we call the order consolidation problem to determine the tote-processing sequence that minimizes total order completion time. We provide mathematical formulations and devise heuristic and exact solution methods. We propose a fast simulated annealing metaheuristic and a branch-and-price approach in which the subproblems are variants of the single machine-scheduling problem and are solved using dynamic programming. We also devise a new branching rule, compare it against the literature, and test it on randomly generated and industry data. Applied to the data and the warehouse under study, optimizing the order consolidation is found to decrease the completion time of 75.66% of orders and achieve average improvements of up to 28.77% in order consolidation time and 21.92% in cubby usage.

We propose a novel modeling framework for supply chain network design that models a prevailing trend in consumer choice in which demand is impacted by carbon footprint. To date, the literature lacks models that realistically account for and accurately calculate per unit emissions, i.e., carbon footprint. We develop a profit maximizing model that accounts for emissions at the different stages of the supply chain, locates facilities and selects their technology, and decides on the flow between echelons. To calculate the carbon footprint, fixed emissions are averaged over throughput, which results in a nonlinear optimization problem with fractional terms. To solve it, we provide a mixed integer second order cone programming reformulation. We perform extensive testing of the framework on a realistic case study and carry out detailed analysis. The proposed framework succeeds in capturing the trade-off between lost demand due to a high carbon footprint and investing in environmentally-friendly technology. The framework serves as a tool to induce organizations to invest in green technology and to allow regulating authorities to assess the impact of eco-labeling.