Solving the forward-reserve allocation problem in warehouse order picking systems

Many warehouses store at least some goods in two areas, a reserve area that is efficient for storage and a forward area that is efficient for order picking. The forward-reserve allocation problem determines the set of Stock-Keeping Units and their space allocations in the forward area to maximize the forward area's benefit by trading off the relevant costs of order picking and internal replenishment. The mathematical model of this decision resembles the classical knapsack problem with the additional complexity that it has a discontinuous nonlinear cost function. A simple greedy heuristic has been proposed in the literature to solve this problem. This paper proposes an alternative branch-and-bound algorithm that can quickly solve the problem to optimality. Heuristic and optimal solutions are numerically compared using problem instances based on real warehouse data. Results suggest that the heuristic solutions are very close to the optimal ones in terms of both the objective value and the forward assignment.