Approximation procedures for the one-warehouse multi-retailer system

Two heuristic procedures for a one-warehouse multi-retailer system are developed. Based on the accuracy desired, the first heuristic evaluates a specified number of points. The relative error is within a bound that approaches . The complexity of the heuristics is O(n) for a fixed number of evaluations. Although the present bound only approaches the one of Roundy when only a small number of points are evaluated, the method is faster. The authors show that the bound for the present procedure and two bounds proposed by Roundy are tight. The second heuristic pertains to a class of policies called stationary interval policies. For this class of policies, the authors develop a fully polynomial-time approximation scheme where the relative error is within , and the computational effort ncreases as a linear function of . Computational experiments show that these heuristics perform well in practice.