The inventory billboard effect on the lead-time decision

Zhengping Wu, Xin Zhai and Zhongyi Liu

International Journal of Production Economics, 2015, vol. 170, issue PA, 45-53

Abstract: This research brings together two important research streams: lead-time management and the inventory billboard effect. While traditional inventory theory, which assumes that demand is independent of the average on-hand inventory, recommends that lead-time be reduced to the lowest level possible, it is clearly not the case when inventory exhibits the billboard effect, which refers to the demand stimulating effect of inventory. We use analytical models to examine the firm׳s optimal lead-time decision in the presence of the inventory billboard effect in two scenarios: with and without inventory based competition. We begin with the single firm scenario, where a firm employs the base stock policy for the infinite horizon continuous-review inventory problem with a deterministic lead-time and inventory dependent demand. The firm׳s decisions are to choose the optimal lead-time and the corresponding base stock level to maximize its expected profit rate. We find that the inventory billboard effect favors a long lead-time, because a long lead-time results in a higher inventory level, which in turn induces more demand. We then consider the case where two firms compete on inventory for customer demand. We completely characterize the unique Nash equilibrium and provide closed-form solutions, which allow us to conclude that inventory based competition pressures both firms to increase the lead-time. Our numerical studies show that the extent to which demand depends on inventory amplify the impact of competition on the optimal decisions and the associated profit. Our findings suggest that lead-time reduction, although widely advocated by popular production philosophies such as Just-in-Time, has to be carefully evaluated when inventory exhibits billboard effect.

Keywords: Lead-time decision; Billboard effect; Inventory management; Competition; Game theory (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:proeco:v:170:y:2015:i:pa:p:45-53

DOI: 10.1016/j.ijpe.2015.09.008

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