## 1 Introduction  
Supplier selection and order allocation (SSOA) has always received considerable attention in the supply chain management (SCM) community [1]. Indeed, considering that an efficient selection of suppliers and a proper allocation of orders can reduce costs, improve product quality, and ensure timely delivery, its impact on the company's performance is evident. For many companies, the cost of raw materials and components represents 50% to 80% of the final cost of the finished product [2]. Moreover, small deliveries can decrease sales by up to 10%, and delays of up to 45 days can result in an almost 40% loss in sales [3]. In addition to its relevance, SSOA has gained interest among scholars because of the challenges the problem presents. Properly assigning orders to selected suppliers in future periods requires knowing in advance future supplier performance. Uncertainty about the future is thus one of the main challenges this problem presents. Secondly, when orders need to be allocated over multiple periods, the problem presents in the form of a sequential decision-making one, where past decisions affect future periods as well. Lastly, the presence of uncertainty about future supplier forecasts and the sequential nature of the problem present a third challenge. When forecasts are related to supplier performance, there is a peculiar interdependence between the possibility of obtaining forecast updates and how orders are allocated to suppliers. Updating forecasts related to supplier performance requires sending orders to suppliers themselves, as this is the only possibility for acquiring new supplier-related data. Due to the relevance of the problem and its challenges, researchers have started to develop mathematical formulations to solve it. First, approaches providing a solution for a single period in the future have been considered, and those dealing with multiple periods have also been generated. Similarly, deterministic models (i.e., not dealing with future uncertainty) have been investigated, while risk and uncertainty have been progressively considered. Indeed, multiperiod formulations that consider risk factors have become essential to effectively capture the dynamic nature of business. At the same time, the increased instability of supply chains has led to rethinking the SSOA not only to reduce cost but also to gain resilience and ensure business continuity. As a consequence, stochastic programming is now a widely adopted technique for building models for SSOA to cope with uncertainty. However, recent advancements in machine learning (ML) and deep learning (DL) have opened the door to alternative solutions in the management of supply chain problems [4; 5; 6; 7; 8]. Indeed, existing approaches for multiperiod SSOA present some limitations when addressing its main challenges. First, deterministic models are not able to deal with future uncertainty about supplier performance. Secondly, according to [9], although stochastic programming presents several benefits, it is limited in its application to real-life problems due to the high computational complexity that some scenarios can generate. Lastly, even if reinforcement learning has been proposed for solving several allocation problems in the supply chain [10; 11], it requires numerous interactions with the environment to learn the optimal way to allocate orders in SSOA, and, in real-world applications, this necessity is risky and expensive. Conversely, direct lookahead models (DLMs) are a potentially effective solution for real industrial problems. They can deal with the necessity of estimating future supplier performance and not require learning how to allocate orders recurring to a trial-and-error strategy. Indeed, DLMs assume the form of linear programming models where future decisions are taken considering the forecast provided by predictive models. The possibility of integrating ML and DL models in the predictive modules of these approaches has recently led several authors to consider this approach [12; 13; 14; 15; 16; 17].