Optimal inventory control with fixed ordering cost for selling by internet auctions

Shuren Liu; Qiying Hu; Yifan Xu

doi:10.3934/jimo.2012.8.19

Article Contents

2012, Volume 8, Issue 1: 19-40. Doi: 10.3934/jimo.2012.8.19

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Optimal inventory control with fixed ordering cost for selling by internet auctions

1.
School of Mathematics and Computational Science, Xiangtan University, Hunan, 411105
2.
School of Management, Fudan University, Shanghai 200433

Received: June 30, 2009

Revised: May 31, 2011

Published: December 2011

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Abstract

We study an optimal inventory control problem for a seller to sell a replenishment product via sequential Internet auctions. At the beginning of each auction, the seller may purchase his good from an outside supplier with a fixed ordering cost. There is a holding cost for inventory and backordering is not allowed. We address the total expected discounted criteria in both finite and infinite horizons and the average criterion in an infinite horizon. We show that the classic $(j, J)$ policy is optimal for each criterion. Moreover, we obtain integer programming with bounded decision variables $j$ and $J$ for computing the optimal $(j, J)$ policies for both the discounted and average criteria in an infinite horizon. Finally, numerical results show that it is meaningful for the seller to reduce randomness in the number of buyers with certainly remaining the average number of arriving buyers, but to enhance randomness in the buyers' valuation.

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Mathematics Subject Classification: Primary: 90B05; Secondary: 90C40.

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