A locating-dominating set of an undirected graph is a subset of vertices S such that S is dominating and for every u, v / ∈ S, the neighbourhood of u and v on S are distinct (i.e. N (u) ∩ S = N (v) ∩ S). Locating-dominating sets have received a considerable attention in the last decades. In this paper, we consider the oriented version of the problem. A locating-dominating set of an oriented graph is a set S such that for every u, v ∈ V \ S, N − (u) ∩ S = N − (v) ∩ S. We consider the following two parameters. Given an undirected graph G, we look forwhich is the size of the smallest (largest) optimal locating-dominating set over all orientations of G. In particular, if D is an orientation ofwhere γLD(D) is the minimum size of a locatingdominating code of D.For the best orientation, we prove that, for every twin-free graph G on n vertices, → γ LD (G) ≤ n/2 which proves a "directed version" of a widely studied conjecture on location-domination number. Moreover, we give some bounds for → γ LD (G) on many graph classes and drastically improve value n/2 for (almost) d-regular graphs by showing that → γ LD (G) ∈ O(log d/d • n) using a probabilistic argument. While → γ LD (G) ≤ γLD(G) holds for every graph G, we give some graph classes such as outerplanar graphs for which → ΓLD(G) ≥ γLD(G) and some for which → ΓLD(G) ≤ γLD(G) such as complete graphs. We also give general bounds for → ΓLD(G) such as → ΓLD(G) ≥ α(G). Finally, we show that for many graph classes → ΓLD(G) is polynomial on n but we leave open the question whether there exist graphs with → ΓLD(G) ∈ O(log n). * This work was supported by ANR project GrR (ANR-18-CE40-0032) † Research supported by the Finnish cultural foundation locating-dominating set of a directed graph D is a subset S of its vertices such that two vertices not in S have distinct and non-empty in-neighbourhoods in S. The directed location-domination number of D, denoted by γ LD (D), is the size of a smallest locating-dominating set of D.Two oriented graphs with the same underlying graph can have a very different behaviour towards locating-dominating sets. Let us illustrate it on tournaments that are oriented complete graphs. Transitive tournaments (i.e. acyclic tournaments) have directed location-domination number ⌈n/2⌉ whereas one can construct locating-dominating sets of size ⌈log n⌉ for a well-chosen orientation of K n [28]. Following the idea of Caro and Henning for domination [6] and the work started by Skaggs [28], we study in this paper the best and worst orientations of a graph for locating-dominating sets. A similar line of work has been recently initiated for the related concepts of identifying codes [9] and metric dimension [2].The two parameters that will be considered in this paper are the following. The lower directed location-domination number of an undirected graph G, denoted by → γ LD (G), is the minimum directed location-domination number over all the orientations of G. The upper directed locationdomination number of an undirected graph G, denoted by → Γ LD (G), is the maximum ...