Stock positioning and performance estimation for distribution systems with service constraints

Abstract

The problem of minimizing average inventory costs in a distribution system consisting of one warehouse and multiple retailers subject to fill rate service constraints is studied. An effective algorithm to evaluate the optimal base-stock policy and cost under local control is provided. Properties of the optimal base-stock levels at each location are established. In addition, heuristics and closed-form approximations that yield insights into the drivers of system performance are also provided. An extensive numerical study to gain insight into the optimal solution, stock positioning and when to use the heuristics and approximations is presented. An example of how logistics postponement and fill-rate constraints affect the distribution system's performance is quantified. A discussion on how to study and allocate stocks across an arborescence system with more than two echelons is presented.

Keywords:

• Inventory/production
• multi-stage
• fill rate
• stock positioning
• newsvendor solution
• heuristics and approximations

Acknowledgements

The authors wish to thank the anonymous associate editor, the referees, Warren Hausman, and Rachel Zhang for their helpful suggestions. The discussions during the presentations at the November 2004 INFORMS Annual Meeting in Denver, Colorado, IBM in Summer 2004 and Case Western Reserve University in Fall 2004 were also beneficial.

Özalp Özer gratefully acknowledges financial support from National Science Foundation Grant No. 0556322 and Hellman Faculty Scholar Gift.

Notes

¹In addition to these two streams of research, there is another stream of research based on guaranteed service that does not trade-off backorder costs or service requirement with holding costs (Graves and Willems, 2000).

²Inventory position equals on-hand inventory plus inventory on order minus inventory backorders.

³ Graves (1996) suggests allocating most of the safety stock at the retailers. However, he does not test its performance.

⁴ Gallego et al. (2007) propose a similar method for the backorder cost model.

⁵See, for example, Chen and Zheng (1994) for a discussion of local and echelon base-stock polices for a serial system.

^†The numbers refer to one of the three feasible solutions of TSH that yields the lowest cost: (1) zero inventory; (2) zero safety stock; (3) maximum needed at the warehouse.

⁶Note that it makes little practical sense to operate or optimize a distribution system having less than 90% fill rates at each retailer. Nevertheless, this set of experiments is used to test the heuristics' sensitivity to fill rates.

⁷Recall from Table 4 that NVA and DFA yield similar regression results for cost analysis. Hence, they provide the same insights regarding the effect of system design parameters on costs.