We present a new exact algorithm to solve a challenging vehicle routing problem with split pickups and deliveries, named as the single-commodity split-pickup and split-delivery vehicle routing problem (SPDVRP). In the SPDVRP, any amount of a product collected from a pickup customer can be supplied to any delivery customer, and the demand of each customer can be collected or delivered multiple times by the same or different vehicles. The vehicle fleet is homogeneous with limited capacity and maximum route duration. This problem arises regularly in inventory and routing rebalancing applications, such as in bike-sharing systems, where bikes must be rebalanced over time such that the appropriate number of bikes and open docks are available to users. The solution of the SPDVRP requires determining the number of visits to each customer, the relevant portions of the demands to be collected from or delivered to the customers, and the routing of the vehicles. These three decisions are intertwined, contributing to the hardness of the problem. Our new exact algorithm for the SPDVRP is a branch-price-and-cut algorithm based on a pattern-based mathematical formulation. The SPDVRP relies on a novel label-setting algorithm used to solve the pricing problem associated with the pattern-based formulation, where the label components embed reduced cost functions, unlike those classical components that embed delivered or collected quantities, thus significantly reducing the dimension of the corresponding state space. Extensive computational results on different classes of benchmark instances illustrate that the newly proposed exact algorithm solves several open SPDVRP instances and significantly improves the running times of state-of-the-art algorithms. History: Accepted by Andrea Lodi, Area Editor for Design and Analysis of Algorithms–Discrete. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72222011, 71971090, 71821001, 72171112], by the Young Elite Scientists Sponsorship Program by CAST [Grant 2019QNRC001], and by the Research Grants Council of Hong Kong SAR, China [Grant 15221619]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoc.2022.1249 .

The 3-dimensional bin packing problem (3D-BPP) is not only fundamental in combinatorial optimization but also widely applied in real world logistics. In the modern logistics industry, the complexity of constraints, heterogeneity of cargoes and scale of orders are dramatically increased, leading to great challenges to devise packing plans up to standard. While the tree search algorithm is proved to be a successful paradigm to solve the 3D-BPP, it is too time-consuming to be applied in the aforementioned large-scale scenarios. To overcome the limitation, we propose a data-driven tree search algorithm (DDTS) to tackle the 3D-BPP. The solution space with complicated constraints is explored by a tree search algorithm, and a convolutional neural network trained with historical data guides pruning the tree so as to accelerate the search process. Computational experiments on real-world datasets show that our algorithm outperforms the state-of-the-art approach with a loading rate improvement of 2.47%. Moreover, the deep learning technique increases searching efficiency by 37.14% with only 0.04% performance loss. The algorithm has been deployed in Huawei Logistics System, which increases the loading rate by 3% and could reduce the logistics cost by millions of dollars per year. To the best of our knowledge, we are the first to embed pruning networks into tree search for the large-scale 3D-BPP.

A solar power plant is a large-scale photovoltaic (PV) system designed to supply usable solar power to the electricity grid. Building a solar power plant needs consideration of arrangements of several important components, such as PV arrays, solar inverters, combiner boxes, cables, and other electrical accessories. The design of solar power plants is very complex because of various optimization parameters and design regulations. In this study, we address the cable-routing problem arising in the planning of large-scale solar power plants, which aims to determine the partition of the PV arrays, the location of combiner boxes, and cable routing such that the installation cost of the cables connecting the components is minimized. We formulate the problem as a mathematical programming problem, which can be viewed as a generalized capacitated minimum spanning tree (CMST) problem, and then devise a branch-and-price-and-cut (BPC) algorithm to solve it. The BPC algorithm uses two important valid inequalities, namely the capacity inequalities and the subset-row inequalities, to tighten the lower bounds. We also adopt several acceleration strategies to speed up the algorithm. Using real-world data sets, we show by numerical experiments that our BPC algorithm is superior to the typical manual-based planning approach used by many electric power planning companies. In addition, when solving the CMST problem with unitary demands, our algorithm is highly competitive compared with the best exact algorithm in the literature.

This article proposes a new approach to sales forecasting for new products (stock-keeping units [SKUs]) with long lead time but short product life cycle. These SKUs are usually sold for one season only, without any replenishments. An exponential factorization machine (EFM) sales forecast model is developed to solve this problem which not only takes into account SKU attributes, but also pairwise interactions. The EFM model is significantly different from the original Factorization Machines (FM) from two fold: (1) the attribute-level formulation for explanatory/input variables; and (2) exponential formulation for the positive response/output/target variable. The attribute-level formation excludes infeasible intra-attribute interactions and results in more efficient feature engineering comparing with the conventional one-hot encoding, while the exponential formulation is demonstrated more effective than the log-transformation for the positive but not skewed distributed responses. In order to estimate the parameters, percentage error squares (PES) and error squares (ES) are minimized by a proposed adaptive batch gradient descent method over the training set. To overcome the over-fitting problem, a greedy forward stepwise feature selection method is proposed to select the most useful attributes and interactions. Real-world data provided by a footwear retailer in Singapore are used for testing the proposed approach. The forecasting performance in terms of both mean absolute percentage error (MAPE) and mean absolute error (MAE) compares favorably with not only off-the-shelf models but also results reported by extant sales and demand forecasting studies. The effectiveness of the proposed approach is also demonstrated by two external public datasets. Moreover, we prove the theoretical relationships between PES and ES minimization, and present an important property of the PES minimization for regression models; that it trains models to underestimate data. This property fits the situation of sales forecasting where unit-holding cost is much greater than the unit-shortage cost (e.g., perishable products).

In this paper, a new branch-and-price-and-cut algorithm is proposed to solve the one-dimensional bin-packing problem (1D-BPP). The 1D-BPP is one of the most fundamental problems in combinatorial optimization and has been extensively studied for decades. Recently, a set of new 500 test instances were proposed for the 1D-BPP, and the best exact algorithm proposed in the literature can optimally solve 167 of these new instances, with a time limit of 1 hour imposed on each execution of the algorithm. The exact algorithm proposed in this paper is based on the classical set-partitioning model for the 1DBPPs and the subset row inequalities. We describe an ad hoc label-setting algorithm to solve the pricing problem, dominance, and fathoming rules to speed up its computation and a new primal heuristic. The exact algorithm can easily handle some practical constraints, such as the incompatibility between the items, and therefore, we also apply it to solve the one-dimensional bin-packing problem with conflicts (1D-BPPC). The proposed method is tested on a large family of 1D-BPP and 1D-BPPC classes of instances. For the 1D-BPP, the proposed method can optimally solve 237 instances of the new set of difficult instances; the largest instance involves 1,003 items and bins of capacity 80,000. For the 1D-BPPC, the experiments show that the method is highly competitive with state-of-the-art methods and that it successfully closed several open 1D-BPPC instances.

The split-delivery vehicle routing problem (SDVRP) is a natural extension of the classical vehicle routing problem (VRP) that allows the same customer to be served by more than one vehicle. This problem is a very challenging combinatorial optimization problem and has attracted much academic attention. To solve it, most of the literature articles adopted heuristic approaches in which the solution is represented by a set of delivery patterns, and the search operators were derived from the traditional VRP operators. Differently, our approach employs the combination of a set of routes and a forest to represent the solution. Several forest-based operators are accordingly introduced. We integrate the new operators into a simple tabu search framework and then demonstrate the efficiency of our approach by conducting experiments on existing benchmark instances.