This paper proposes a new approach to sales forecasting for new products 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 considers 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 variables and (2) exponential formulation for the positive response 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. Real-world data provided by a footwear retailer in Singapore is used for testing the proposed approach. The forecasting performance in terms of both mean absolute percentage error (MAPE) and mean absolute error (MAE) compares favourably 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.

Monotone submodular maximization with a knapsack constraint is NP-hard. Various approximation algorithms have been devised to address this optimization problem. In this paper, we revisit the widely known modified greedy algorithm. First, we show that this algorithm can achieve an approximation factor of $0.405$, which significantly improves the known factor of $0.357$ given by Wolsey or $(1-1/\mathrm{e})/2\approx 0.316$ given by Khuller et al. More importantly, our analysis uncovers a gap in Khuller et al.'s proof for the extensively mentioned approximation factor of $(1-1/\sqrt{\mathrm{e}})\approx 0.393$ in the literature to clarify a long time of misunderstanding on this issue. Second, we enhance the modified greedy algorithm to derive a data-dependent upper bound on the optimum. We empirically demonstrate the tightness of our upper bound with a real-world application. The bound enables us to obtain a data-dependent ratio typically much higher than $0.405$ between the solution value of the modified greedy algorithm and the optimum. It can also be used to significantly improve the efficiency of algorithms such as branch and bound.

This paper introduces a multi-period inspector scheduling problem (MPISP), which is a new variant of the multi-trip vehicle routing problem with time windows (VRPTW). In the MPISP, each inspector is scheduled to perform a route in a given multi-period planning horizon. At the end of each period, each inspector is not required to return to the depot but has to stay at one of the vertices for recuperation. If the remaining time of the current period is insufficient for an inspector to travel from his/her current vertex $A$ to a certain vertex B, he/she can choose either waiting at vertex A until the start of the next period or traveling to a vertex C that is closer to vertex B. Therefore, the shortest transit time between any vertex pair is affected by the length of the period and the departure time. We first describe an approach of computing the shortest transit time between any pair of vertices with an arbitrary departure time. To solve the MPISP, we then propose several local search operators adapted from classical operators for the VRPTW and integrate them into a tabu search framework. In addition, we present a constrained knapsack model that is able to produce an upper bound for the problem. Finally, we evaluate the effectiveness of our algorithm with extensive experiments based on a set of test instances. Our computational results indicate that our approach generates high-quality solutions.

The feasible solutions of the traveling salesman problem with pickup and delivery (TSPPD) are represented by vertex lists in existing literature. However, when the TSPPD requires that the loading and unloading operations must be performed in a last-in-first-out (LIFO) manner, we show that its feasible solutions can be represented by trees. Consequently, we develop a variable neighbourhood search (VNS) heuristic for the TSPPD with last-in-first-out loading (TSPPDL) involving several search operators based on the tree data structure. Experiments show that our VNS heuristic is superior to the current best heuristics for TSPPDL in terms of both solution quality and computing time.

This paper presents a project awarded by MGB HK to handle their inspection scheduling problem. MGB HK is the buying office of one of the largest retailers in the world, Metro Group. MGB HK handles all product procurement of Metro Group out of Europe. The inspection process is one of their critical processes along their entire procurement exercise. The objective of this project is to provide an effective scheduling engine so that in-house inspectors can handle as many inspections as possible using the least amount of time and costs. Meanwhile, we also help the company overcome their difficulties of data collection and maintenance as a result of the system we developed. Our engine will be deployed and integrated into the company’s IMS. The engine recorded an improvement in the scheduling of their inspections and initial prognosis indicates that delayed inspections have been greatly reduced by compared with previous schedule. The system can effectively schedule inspections by urgency, shipment value, and supplier’s historical performance. Other than the schedule, the AI engine can also generate solutions based on different strategies and criteria, which facilitate the decision-making process for the scheduling team and management at MGB HK.