Railway rolling stock is one of the most significant cost sources for operators of passenger trains. The efficient circulation of rolling stock is therefore one of the main objectives pursued in practice. This paper focuses on the determination of appropriate numbers of train units of different types together with their efficient circulation on a single line. In order to utilize the train units on this line in an efficient way, they are coupled to or uncoupled from the trains in certain stations according to the passengers' seat demand in peak hours and off-peak hours. Since coupling and uncoupling train units has to respect specific rules related to the shunting possibilities in the stations, it is important to take into account the order of the train units in the trains. This aspect strongly increases the complexity of the rolling stock circulation problem. This paper presents a solution approach based on an Integer Programming model. The approach is applied to a real life case study based on the timetable of NS Reizigers, the main Dutch operator of passenger trains.

Maximizing system lifetime in battery-powered wireless sensor networks with power aware topology control protocols and routing protocols has received intensive research. In the past, this problem has been mostly studied from the indirect perspective of energy conservation. Although this leads to solutions that help extend network lifetime, energy conservation is not the same problem as network lifetime maximization. Some researchers have formally studied network lifetime maximization problems, based on the assumption that energy is only consumed by packet transmission. However, it is well known that in many cases energy is significantly consumed during overhearing and idle periods. In this paper, we try to present formal analysis of a variety of network lifetime maximization problems in different energy consumption models. In particular, we identify different energy consumption models, define a variety of fundamental network lifetime maximization problems in individual energy consumption models, and formally analyze their complexity. Polynomial time algorithms are presented for tractable problems, and NPhardness proofs are presented for intractable problems.

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