Investigating the benefits of re-optimisation while searching for two immobile entities on a network

We consider the problem of searching for two immobile entities on an undirected network where the entity locations are probabilistically known and dependent. This article extends the work by Jotshi, A. and Batta, R. (2008) 'Search for an immobile entity on a network', European Journal of Operational Research, Vol. 192, pp.347-359 - search for a single entity. The problem is first examined for the case where re-optimisation is not allowed, i.e. we are not allowed to change the path once we have started traversing it. In the second case, re-optimisation is allowed after the discovery of the first entity. For both cases, the objective is to minimise the expected search time to find both entities. Heuristic algorithms are introduced and computational results are presented showing the benefits of allowing re-optimisation.