# Evaluating 3D Printers Using Data Envelopment Analysis
## 1 Introduction
Furthermore, the assessment of the efficiency of the available 3D Printers is by no means a trivial task and requires a high level of technological expertise and the evaluation of several factors. There is, therefore, from a buyer's/consumer's perspective, the need of having reliable tools for assessing the relative efficiency/value of 3D printers, which can be considered as a production and/or design tool. Assessing the efficiency of 3D Printers can also be useful for 3D printer manufacturers/developers, for constant benchmarking of their products against the competition. For evaluating a product's performance, several models, methods, and tools have been proposed. Indicatively, one could refer to the EVR (eco-cost value ratio) model [6], the Multiattribute Value Analysis method [7; 8], the Gestalt-Minimalism-based decision-making model [9], the Analytical Target Cascading method [10], and the Analytical Hierarchy Process method [11]. A basic characteristic of the above-mentioned methods is that they demand, as input, several claims and judgments that are based on subjective evaluations and complicated calculations [12]. Data Envelopment Analysis (DEA), first introduced by [PERSON], [PERSON], and [PERSON] [13], is a technique that can overcome such concerns. In DEA, the technical efficiency of a set of Decision-Making Units (DMUs) is evaluated by considering the amount of resources that have been employed by each DMU (inputs) for the production of certain products or outcomes (outputs) [14]. The analysis results are useful not only for comparing DMUs, but also for directing inefficient DMUs towards more efficient ways of production, defined in this context as transformation of inputs to outputs [15]. The method employs a linear non-parametric programming procedure in order to identify the most efficient DMUs, which collectively define the so-called efficient frontier. All other DMUs, i.e., those located below the frontier, are considered as inefficient. The method has the basic advantage of being a multi-dimensional method that can handle a large number of parameters, which may be functionally independent and/or evaluated in quite different measures and units. Moreover, DEA as a non-parametric comparative method, does not require all DMUs to balance the input and output parameters in a similar way. On the other hand, a disadvantage of the method is that it is quite sensitive to extreme data points and outliers. Despite the fact that DEA has been primarily developed and used as a benchmarking method for business and non-profit units and organizations [16; 17], it has also been extensively used for measuring the technical efficiency of consumer products, such as print ers [18], automobiles [19; 20], and cell phones [21; 22], as well as of advanced manufacturing technological systems and equipment, such as robots [23; 24; 25; 26; 27; 28; 29], CNC machines [30; 31; 32], expert systems [33], and flexible manufacturing systems [34; 35; 36; 37]. Based on the above, DEA seems a suitable method for assessing the relative efficiency of currently available 3D printers. The corresponding results and information could prove useful both for potential users of the technology, in order to navigate the rapidly changing and evolving landscape of available systems and manufacturers, as well as for developers and manufacturers of systems, in order to assess the technical efficiency of their systems compared with that of competitors and aptly adjust their market and product development strategy. In this context the application of DEA for the assessment of 3D printers is investigated in the present paper. Since it is difficult to compare 3D printing systems that are based on different technologies, mostly due to the associated material and technical differences, the study focuses on FDM/FFF technology, which is one of the most widely adopted and marketed 3D Printing methods.