## 1 Introduction  
The primary application of wireless sensor networks (WSNs) is collecting measurement data from the area of operation of the network. Typically, the data is transmitted multi-hop to a specified node, a so-called gateway, which sends the data further to a repository, e.g., in the cloud. Frequent transmissions, unfortunately, consume device power, which determines the lifetime of the wireless sensor network. One solution to this problem is the use of periodic sensor networks (PSNs), in which measurement data are aggregated into packets and then transmitted periodically to the gateway according to an established schedule. Networks of this type can be built from devices having a memory buffer, in which the collected data can be stored until the scheduled transmission. Examples of PSN network applications are presented in the paper [1]. One of the crucial challenges in PSNs is to provide energy-efficient routing to collect data from selected devices within an assumed time window. In the literature, approaches using network clustering or data preprocessing and aggregation are most commonly proposed [2; 3; 4]. These algorithms must consider the limited energy resources of the nodes, the limited data buffers and the radio transmission range [2]. In [3] the authors proposed a two-level data aggregation technique to minimize the amount of data transmitted, thereby saving power consumption and bandwidth reduction. [PERSON] et al. [4] presented an energy-saving clustering algorithm based on a multi-criteria optimization method that enables using three different metrics for single-hop clustering. A similar problem may be solved by optimizing sensor location if an application allows this--see for example [5]. Additionally to routing, it is possible to adjust power settings of the nodes to suit processingand transmission needs which may be done by solving mathematical programming tasks resembling these used in static, backbone networks [6; 7]. We assumed that the location and energy profile of the sensors were known and that measurement data would be collected periodically. Thus, it is possible to formulate a mixed-integer programming problem (MIP) whose solution is the transmission schedule of the network nodes. In addition, the formulation considers the hidden node and exposed node problem to reduce interference and increase the quality and efficiency of network transmission. A significant problem is the computational complexity of the task. However, its solution can be obtained centrally before physically running the network and collecting data on an external machine or computing environment with adequate resources. The obtained solution can then be deployed on the network and reused many times. We analyze the infrastructure to monitor environmental data in some areas, e.g., farmland or dangerous waste dumps (see Figure 1 left). The sensors are located over the monitored site in a relatively dense, static network to facilitate the detection of anomalies like arid soil or change of toxic substance concentration. The sensors' locations are known and do not change during network operation. The monitored processes are typically slow, varying so that the sensors may report their measurements with relatively low frequency. Furthermore, taking advantage of dense network topology, it is possible to sample only part of the sensors periodically and use collected data to interpolate measurements for the whole area. Such operation allows for the conservation of network energy and provides more prolonged operation. Another application using periodic sampling of only part of the network to minimize communication and power consumption may be registering events for off-line analysis, e.g., monitoring animals moving around their territory (see Figure 1 right). The sensors activated by an animal may store data in their memory and transmit them in bulk at predefined time instants.