## 1 Introduction  
By increasing competitiveness to retain market share, SC members need to access real-time data about customer preferences and other SC information in a timely manner [1]. In this regard, Industry 4.0 technologies, such as Cloud Computing (CC), Big Data Analytics (BDA), Internet of Things (IoT), Blockchain (BC), and Additive Manufacturing (AM), can assist SC members to connect processes by making them able to exchange information quickly and safely. For instance, [2] mentioned the potential applicability of IoT for gathering real-time data and storing them in a transparent manner by BC. Moreover, they employ the advantages of BDA to analyze the collected data for optimizing vehicle routing and reducing carbon emissions. Additionally, BDA can help enhance marketing activities and provide a better perception of customer needs, which leads to efficient resource usage in manufacturing [3, 4]. In addition, there is a mutual effect between applying Lean Manufacturing principles and Industry 4.0 technologies. As a matter of fact, Lean principles can pave the way for applying Industry 4.0 technologies, and digital practices can in turn support creating an operational environment with either zero or a limited amount of waste [5]. To this end, here Lean Digital Supply Chain (Lean DSC) is defined as a proper application of Industry 4.0 technologies in order to achieve Lean goals by reducing wastes in all SC echelons. Based on a classification by [6], there are seven types of wastes: transportation, inventory, motion, waiting, defect, over-production, over-processing. However, recently, under-utilized people are also considered as an eighth waste in the Lean principles [7]. However, the implementation of the different Industry 4.0 technologies together with the Lean principles is still a challenge for SC practitioners, and there is a need to have a clear roadmap and framework for applying them [8]. The present work aims to integrate the current state-of-the-art information about Lean Digital Supply Chain (DSC) by providing a broader perspective than the previous works, in order to assist both academicians in advancing theoretical outcomes on the topic and practitioners in real implementations. A Systematic Literature Review (SLR) is used to this end as a structured and scientific approach to identify and extract knowledge from the available contributions in a systematic way [9]. Previous SLRs mainly address the combined application of the Lean and Industry 4.0 notions to manufacturing as one of the SC echelons [10; 11; 12; 13]. Thus, studies on the effects of Lean and digital technologies on all the main SC processes other than manufacturing are needed. Furthermore, the perspective of the different SC members should be taken into account because they may have heterogeneous attitudes and viewpoints regarding the applicability of Industry 4.0 technologies and Lean [14]. Aside from the mentioned research gap, previous SLRs mainly deal with the relationship between Lean principles and Industry 4.0 by considering the latter as a general concept without focusing on its detailed technologies. However, it should be pointed out that each individual Industry 4.0 technology has specific features making it applicable to either be compliant with or foster a Lean SC environment. Therefore, the present work, by studying single Industry 4.0 technologies at an SC level, aims to answer the following research questions:  
1. Which SC processes can benefit from an integrated application of Lean and digital technologies? 2. Which Industry 4.0 technologies have the greatest potential to be combined with Lean principles in the main operational and organizational SC issues? 3. Which Industry 4.0 technologies can be jointly applied in order to support Lean principles in the SC? The results of the present work show the importance of investigating single processes in Lean DSC.