Robot-Manual Forward-Reserve Allocation Problem

Abstract

In this paper, we consider the order-picking operations in which orders are picked either by humans or robots. A warehouse is configured with a manual-picking area and a robot-picking area. The robot-picking area is used for the forward-picking area to perform inexpensive picking operations, whereas the manual-picking area is used for the reserve-picking area to replenish the robot-area. We consider the problem to seek which SKUs are picked by human or robot, which SKUs are located by the manual-picking area or the robot-picking area, and how much volume is stored for each SKU in the robot area. The objective is to minimize the sum of the robot-picking cost, the manual-picking cost, and the replenishment cost. We formulate the decision problem as mixed-integer non-linear programming (MINLP). The problem is difficult to solve because it is nonlinear and has a large number of items. We proposed an efficient algorithm to solve the problem based on Lagrange relaxation to exploit the special structure of the problem. We theoretically prove convexity in the decomposed subproblem and derive an analytical solution, allowing efficient evaluation of the lower bound. The algorithm is applied to real-world data from a fashion e-commerce fulfillment center, involving over 15000 SKUs. The proposed method achieves substantial cost savings compared to benchmark policies. In addition, to assess scalability and robustness, the proposed method was evaluated on larger, artificially generated datasets and benchmarked against state-of-the-art metaheuristics. The results demonstrate that our method consistently outperforms these alternatives in both solution quality and computation time