For this work we study a multi-device network for multi-access ultra-reliable low latency communication (URLLC) services. In particular, we assume each device has a personalized latency requirement. Due to the low latency demand, we consider the impacts of finite blocklength (FBL) codes and formulate a weighted sum throughput maximization problem under certain quality-of-service (QoS) constraints, while the personalized latency requirements have been characterized as constraints on the assigned blocklength. To cope with the nonconvex blocklength allocation problem, we analyze the features for the optimal solution and find out that the optimum of such type of nonconvex problem occurs at the extreme points. Following the optimal solution feature, we propose an optimal algorithm via inspecting all possible extreme points in the feasible convex polytope. Furthermore, for reducing the design complexity for massive-device scenario, we also propose an efficient suboptimal solution based on a revised simplex tableau method, which is particularly modified for solving certain class of nonconvex problem. Finally, with numerical simulations, we verify the optimality of our proposed optimal design, and highlight the low complexity of our proposed efficient solution together with a superior throughput performance.