A heuristic algorithm for managing inventory in a multi‐echelon environment
Authors: Bregman Robert L. , Ritzman Larry P. , Krajewski Lee J. 
Published: October 2002

The proper management of finished goods inventory in a multi‐echelon environment is an extremely difficult problem to solve. Optimization approaches for solving this problem are intractable, and currently available heuristic techniques have serious deficiencies. Pull systems and independent demand based push systems do not adequately deal with the lumpy demand caused by the dependent relationships of stocking locations in a multi‐echelon environment. Although distribution requirements planning (DRP) can be modified to handle uncertainties by adding safety stock, the process of deriving demands at lower echelons implicitly assumes deterministic conditions. In addition, no heuristic method directly considers the capacity of transportation and storage resources, or includes transportation costs. The incorporation of these additional complexities is left to the discretion of management.

This study introduces a new heuristic algorithm that addresses these additional complexities. The algorithm is an improvement heuristic that can be implemented as an add‐on module to a DRP system. At the core of this heuristic are two search routines (Savings and Change) for improving an initial solution determined by the DRP explosion process. We demonstrate this heuristic algorithm with two simple problems to provide some insight concerning its operation.

The heuristic algorithm is then tested against an alternative rolling horizon mixed‐integer linear programming (MILP) procedure that solves each linkage between locations optimally for each planning horizon. The example scenario used in this research consists of four distribution centers ordering from two regional warehouses, which in turn order from a central warehouse. Computer simulation is used to compare the two alternative procedures with rolling horizons and demand uncertainty. The performance of the procedures is compared for total costs, customer service, and the number of orders placed by locations within the control of the model. Multivariate analysis of variance (MANOVA) techniques are used to analyze these performance measures.

The experimental results suggest that the heuristic algorithm performs extremely well when compared to the MILP based procedure. Demand uncertainty is found to have a significant effect on customer service performance, but safety stock can be added to distribution centers in actual applications to control this situation. In addition, a qualitative comparison between the MILP approach and the heuristic algorithm in this study suggests that the introduction of demand uncertainty has the effect of reducing the experimental differences between the two techniques. This result suggests that the heuristic algorithm presented in this research works best (relative to the MILP approach) in the actual environments for which it is intended.

This study is of considerable value to managers concerned with the management of finished goods in a multi‐echelon environment. It represents an initial step toward the development of a heuristic algorithm that incorporates additional real‐world complexities and is tractable for realistically large problems. The findings from this study provide encouragement that similarly designed heuristics can be implemented within multi‐echelon inventory control systems in the future.