An algorithm is developed for solving a logistic optimization problem, in which product transportation occurs in two stages, using intermediate transportation waypoints whose optimal locations are determined during problem solving. Addressing complex transportation problems is crucial for optimizing logistic systems. Logistic problems reducible to two-stage continuous-discrete location-allocation problems involve two transportation stages and require assigning regions of continuously allocated product for transportation to the first-stage centers (waypoints). The solution also determines the optimal amounts of product transported from first-stage centers to second-stage centers to minimize total transportation costs from producers to consumers, including intermediate points. The proposed algorithm reduces the infinite-dimensional two-stage optimal location-allocation problem into a non-smooth finite-dimensional optimization problem in the first stage, which is solved using Shor’s r-algorithm for non-differentiable optimization. In the second stage, a UV method is applied to solve the transportation problem. The algorithm is implemented in C++ using the OpenCL platform for parallel computation, and its effectiveness is demonstrated through model problems.