en Mathematical Modeling and Applications of OR Mathematical Modeling and Applications of OR پژوهشی Original <span style="font-size:11pt"><span style="text-autospace:none"><span new="" roman="" style="font-family:" times=""><i><span style="font-size:10.0pt"><span style="letter-spacing:-.25pt">Traditional maximal p-hub covering problems focus on scenarios where network flow is constrained by resource limitations. However, many existing models rely on static parameters, overlooking the inherent randomness present in real-world logistics. This oversight can result in suboptimal network designs that are vulnerable to congestion and rising costs as demand varies. To address this issue, we propose a novel mathematical model for the capacitated single allocation maximal p-hub covering problem that takes into account stochastic variations in origin-destination flows. Although solving this model poses computational challenges, we utilize a Lagrangian relaxation algorithm to enhance efficiency. Computational experiments using the CAB dataset highlight the effectiveness of our approach in achieving optimal solutions while reducing computation time. This framework offers valuable insights for designing robust hub-and-spoke networks in the face of demand uncertainty.</span></span></i></span></span></span><br> &nbsp; Maximal hub covering, Demand uncertainty, Lagrangian Relaxation Method, Capacitated hubs 57 76 http://iors.ir/journal/browse.php?a_code=A-10-6055-1&slc_lang=en&sid=1 Yaser Khosravian y.khosravian@in.iut.ac.ir 00031947532846002867 00031947532846002867 Yes Ali Shahandeh Nookabadi ali-nook@iut.ac.ir 00031947532846002868 00031947532846002868 No Ghasem Moslehi moslehi@iut.ac.ir 00031947532846002869 00031947532846002869 No