The design of distribution networks that simultaneously consider location and inventory decisions seeks to balance costs and product availability. The most commonly observed measure of product availability in practical settings is the fill‐rate service level. However, the optimal design of a distribution network that considers the fill rate to control shortages of fast‐moving consumer goods (FMCG) is considered intractable and has only been addressed by heuristic methods. This paper addresses the optimal design of a distribution network for FMCG able to provide high fill‐rate service level under a continuous review policy. Considering the exact formulation for the provided fill rate, we formulated a joint location–inventory model with fill‐rate service level constraints as a convex mixed integer nonlinear problem for which a novel decomposition‐based outer approximation algorithm is proposed. Numerical experiments have shown that our solution approach provides good‐quality solutions that are on average 0.15% and, at worst, 2.2% from the optimal solution.

Private and public clouds are good means for getting on-demand intensive computing resources. In such a context, selecting the most appropriate clouds and virtual machines (VMs) is a complex task. From the user’s point of view, the challenge consists in efficiently managing cloud resources while integrating prices and performance criteria. This paper focuses on the problem of selecting the appropriate clouds and VMs to run bags-of-tasks (BoT): big sets of identical and independent tasks. More precisely, we define new mathematical optimization models to deal with the time of use of each VMs and to jointly integrate the execution makespan and the cost into the objective function through a bi-objective problem. In order to provide trade-off solutions to the problem, we propose a lexicographic approach. In addition, we introduce, in two different ways, capacity constraints or bounds on the number of VMs available in the clouds. A global limit on the number of VMs or resource constraints at each time period can be defined. Computational experiments are performed on a synthetic dataset. Sensitivity analysis highlights the effect of the resource limits on the minimum makespan, the effect of the deadline in the total operation cost, the impact of considering instantaneous capacity constraints instead of a global limit and the trade-off between the cost and the execution makespan.