European Journal of Operational Research 252 (2016) 407–417 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor Discrete Optimization Robust scheduling of wireless sensor networks for target tracking under uncertainty Charly Lersteau a , André Rossi b , Marc Sevaux a,∗ a Université de Bretagne-Sud – Lab-STICC, CNRS, UMR 6285 Lorient, France b Université d’Angers – LERIA, Angers, France a r t i c l e i n f o Article history: Received 22 June 2015 Accepted 12 January 2016 Available online 18 January 2016 Keywords: Wireless sensor networks Target tracking Uncertainty Stability radius Robustness a b s t r a c t An object tracking sensor network (OTSN) is a wireless sensor network designed to track moving ob- jects in its sensing area. It is made of static sensors deployed in a region for tracking moving targets. Usually, these sensors are equipped of a sensing unit and a non-rechargeable battery. The investigated mission involves a moving target with a known trajectory, such as a train on a railway or a plane in an airline route. In order to save energy, the target must be monitored by exactly one sensor at any time. In our context, the sensors may be not accessible during the mission and the target can be subject to earliness or tardiness. Therefore, our aim is to build a static schedule of sensing activities that resists to these perturbations. A pseudo-polynomial two-step algorithm is proposed. First, a discretization step processes the input data, and a mathematical formulation of the scheduling problem is proposed. Then, a dichotomy approach that solves a transportation problem at every iteration is introduced; the very last step is addressed by solving a linear program. © 2016 Elsevier B.V. All rights reserved. 1. Introduction 1.1. Context Since wireless sensors are becoming more and more affordable, more and more applications are now possible such as traffic con- trol or battlefield surveillance (Akyildiz, Su, Sankarasubramaniam, & Cayirci, 2002; Yick, Mukherjee, & Ghosal, 2008). Low-cost sen- sors are usually autonomous, equipped with a sensing unit and a battery. Their typical purpose is to track targets in their sensing range. They can be randomly deployed from an airplane or an he- licopter in places lacking monitoring infrastructures. Sensors rely- ing on technologies like drones and radars are suitable in military or humanitarian assistance contexts, where the infrastructures are destroyed or non-existent. In this paper, the investigated mission is to monitor a target with a known trajectory, such as a train on a railway, a vehicle on a road or a plane in an airline route. Since accessing sensors can be difficult in some environments, we may have no control on them during the mission. Then, in order to save battery lifetime, sensors can be switched off and waken up later. To minimize the energy consumption, the target is moni- tored by only one sensor at a time. Moreover, the target is subject ∗ Corresponding author. Tel.: +33 297874564; fax: +33 297874527. E-mail addresses: charly.lersteau@univ-ubs.fr (C. Lersteau), andre.rossi@univ- angers.fr (A. Rossi), marc.sevaux@univ-ubs.fr (M. Sevaux). to perturbations on its path, that may cause advances and delays. Consequently, our challenge is to find a static schedule of sensing activities, able to monitor the target at any time, without target loss despite perturbation. A target loss happens when the target is outside the range of any active sensor. A sensing activity is iden- tified by a sensor, a starting date and a duration, to be computed offline, before the mission. During an activity, the corresponding sensor wakes up, collects information about the target for a cer- tain amount of time, and then gets back to sleep status. Our aim is to find the most robust schedule, i.e. the one that resists to the largest possible earliness and tardiness. 1.2. Related work There are plenty of WSN protocols for target tracking proposed in the literature, designed to achieve one or more goals. Usually, these protocols are dedicated to the optimization or management of different criteria. We present below a non-exhaustive list of the criteria addressed by those protocols: • Energy consumption: this is one of the most critical aspects since the sensors generally have a non-rechargeable battery. For example, the framework designed in Zhang and Cao (2004) configures min-cost convoy trees using dynamic programming in order to save energy. Many protocols that focus on this as- pect are based on LEACH (Handy, Haase, & Timmermann, 2002; Jindal & Gupta, 2013) or HEED (Younis & Fahmy, 2004). http://dx.doi.org/10.1016/j.ejor.2016.01.018 0377-2217/© 2016 Elsevier B.V. All rights reserved.