## 1 Introduction  
From the business standpoint, predictability is an essential aspect of software development. In other words, before starting a project, it is important to understand how many resources and how much time the implementation will require. This is why estimation is an integral part of the software development life cycle. Following the cone-of-uncertainty concept [1], estimation is envisioned as a multistage process starting from an early phase of project ideation and finishing along with the implementation completion. At each project life cycle stage, estimation has certain goals, requires specific methods, and produces different outcomes. Most well-known and practically proven estimation methods were developed in the second half of the 20 th century. As a result, the application of those methods to modern software development projects causes difficulties or even is hardly possible. Such methods as COCOMO II [2] are quite complex and require special training. Another widely used method, PERT [3, 4], is relatively easy but does not take into account the agile nature of modern software development projects. Agile-oriented methods like planning poker, T-shirt sizing, affinity grouping, and their variations are rather applicable by agile teams at the implementation stage [5, 6, 7, 8]. A common downside of the existing methods (except COCOMO II) is that they do not cover the whole software development life cycle starting from project ideation and ending with production, including maintenance and support. To fill in this gap, the authors propose the concept of the estimation life cycle (ELC), tailoring estimation activities to the software development life cycle (SDLC) stages. According to the ELC, early project stages are accompanied by introductory, preliminary, and intermediate [9] estimations (listed in the order of increasing levels of details, reliability, and accuracy). The commonality of these estimations is that their outputs are not definitive enough to take on obligations. Instead, the following step--precise estimation--aims at providing outcomes that can be used for making commitments. Precise estimation takes place before the implementation start, when the analysis and design are completed. At the implementation stage, the estimates are compared with actual efforts, and a project team is responsible for keeping up-to-date the remaining estimates. After completing implementation, the ELC prescribes finalizing feedback on estimates. The current study is devoted to a method of preliminary estimation. The method's objective is to roughly understand the resources and time required to implement a project, minimizing the efforts spent on the estimation itself. Usually, this type of estimation is applicable in the initial steps of SDLC. The main outputs of the preliminary estimation are project scope (represented as an estimable-item breakdown structure, defined below), team composition, and project duration. Obviously, due to the quite high level of uncertainty, these outcomes are not supposed to be used for making commitments; instead, they will be elaborated on in the following stages: the intermediate and precise estimations [9; 10]. The method of preliminary estimation proposed in this study is based on a simplified version of a system of working-time balance equations [9; 10]. This applied simplification (in comparison with the intermediate estimation) aims, first of all, at the minimization of efforts spent on the estimation, intentionally sacrificing its accuracy. Additionally, the method is empowered with a decision support procedure based on a multiobjective optimization with the purpose of providing the involved experts with several estimate alternatives. For practical usage, the method of preliminary estimation involves a semistructured knowledge-intensive business process [11; 12], predefining steps to be performed and, at the same time, leaving enough space for flexibility and creativity.