# Software Portfolio Optimization: Access Rejection versus Underutilization
## 1 Introduction  
According to a Statista report [1], expenditures on global information technology (IT) by companies in various sectors grew annually between 2015 and 2022, as shown in Figure 1. Forecasts indicate an expected rise of 11% in 2023 due to the continued expansion of new technologies. In particular, several technological categories, including robotics and artificial intelligence, are likely to expand to represent more than 25% of IT spending worldwide, and next-generation security linked to those new technologies will also encourage significant growth (see IDC--Global ICT Spending Forecast [2]). Figure 1: International IT spending for 2015 through 2023. Software companies sell their products by transferring licenses of various software components to customers. Typically, a basic fee covers use of the software by a specified number of simultaneous or concurrent users, and annual maintenance fees ensure that purchasers receive maintenance and updates. Several types of license allow controlled access to software. MathWorks, for example, offers three different MATLAB(r) licenses:  
1. Network concurrent (floating) license. The network concurrent license makes MathWorks products available to anyone with access to the purchaser's network. Access is not limited to specific user names. Instead, users check out license keys when starting MATLAB or using its functions in other products. When all available keys have been checked out, the software's license manager denies further requests. 2. Network named user license. The network named user (NNU) license controls access via user name and costs four times less than the floating license. 3. Non-network licenses. Non-network licenses control access via either user name or computer identification. MathWorks also offers maintenance agreements, which provide an upgraded version twice a year, and technical support for an additional 25% of the license fee annually. Table 1 provides additional information about how users are typically distributed within a company under each type of license. Under common practice, heavy users (users occupying a license slot more than 25% of the time) are given personal user-name-based access. Light users (users occupying a license less than 25% of the time) usually rely on concurrent licenses. Non-network licenses are generally purchased only for users who cannot work on a network because of confidentiality concerns (laboratories, experiments) or because they are traveling. MathWorks also uses two types of activation: (i) a designated computer license designed for one computer, identified by its MAC (media access control) address, and any user of that computer can use the software; and (ii) user activation, in which specific user names are activated and can be used on up to four computers. It is also important to remember that many software licenses are offered with various sublicenses. The MATLAB license, for example, includes toolboxes intended for various content domains, such as code desecration, image processing, statistics, electronics, and mechanics. The cost of MATLAB sublicenses varies by type and ranges from USD 1000 to 50,000. Coder licenses are significantly more expensive than image processing and statistics licenses. Other software companies, such as nTopology, Ansys (e.g., Granta license, and Ansys Learning Hub license), and Solidworks, also offer both floating and named user licenses. These licenses control access to the software via user names or computer identification. Additionally, many of these companies also offer maintenance agreements that provide upgraded versions and technical support at an additional cost. In addition, similar to MathWorks, these companies offer various sublicenses for specific content domains, such as engineering, design, and analysis, with different costs. It is important to note that the