Threshold incentives over multiple periods and the sales hockey stick phenomenon

Abstract

In this paper we study threshold-based sales-force incentives and their impact on a dealer's optimal effort.A phenomenon, observed in practice, is that the dealer exerts a large effort towards the end of the incentive period to boost sales and reach the threshold to make additional profits. In the literature, the resulting last period sales spike, is sometimes called the hockey stick phenomenon (HSP.) We show that lack of information leads to the HSP and characterize its form over multiple time periods. Under perfect information it is possible to completely eliminate the HSP, however, this may be difficult in practice. We show that the manufacturer can control the HSP by using imperfect information to set the threshold and delay its computation until the last period. We discuss an implementation plan that allows the manufacturer to do so. We then study the impact of competition on the HSP and show conditions under which the HSP can be dampened or exacerbated. We also characterize the variance of the total sales across all the periods and demonstrate conditions under which offering a bonus contract may be beneficial in controlling the variance.

Hockey Stick Phenomenon: Supply Chain Management Challenge in Brazil

“…Three sources were utilized to identify alternative policies to cope with the hockey stick phenomenon: ideas proposed by the theoretical framework (Bradley & Arntzen, 1999;Buzzell, Quelch, & Salmon, 1990;Chen, 2000;Poddar & Donthu, 2013;Sohoni et al, 2010), ideas suggested by Consumption Ltd executives and scenarios that arose while the study was being carried out. In all, nine different policies were found that were able to eliminate invoicing spikes at the end of the month (see Table 2).…”

“…Adapted from Sohoni et al (2010) Increase logistics flexibility Eliminate or reduce the impact of the spike on logistics by increasing production capacity and inventories…”

“…The hockey stick sales or hockey stick phenomenon, a sales spike at the end of the sales period, is an important characteristics of many markets in Brazil but not exclusive to this country. There are references in the literature to companies in highly diverse industries and countries suffering from the effects of the hockey stick phenomenon (Bradley & Arntzen, 1999;Chen, 2000;Hines, Holweg, & Sullivan, 2000;Hoole, 2005;Lee, Padmanabhan, & Whang, 1997a;Neale & Willems, 2009;Nyaga, Closs, Rodrigues, & Calantone, 2007;Oyer, 1998;Shaw, 1996;Singer, Donoso, & Konstantinidis, 2009;Slone, Mentzer, & Dittmann, 2007;Sohoni, Bassamboo, Chopra, Mohan, & Sendil, 2010;Stank, Dittmann, & Autry, 2011;Sterman, 2006;Umble & Srikanth, 1990;Villegas & Smith, 2006;Zotteri, 2013).…”

“…Agency theory (Chen, 2000), non-cooperative game theory (Singer et al, 2009) and dynamic stochastic (Sohoni et al, 2010) theoretical models have been employed to study this phenomenon. One of our goals is to evaluate the adequacy, with an empirical study, of the policies proposed by previous authors to eliminate the hockey stick phenomenon and also to test new alternatives.…”

“…In order to eliminate the sales spike, the sales quota was required to perfectly mimic market demand (Sohoni et al, 2010). Utilizing non-cooperative game theory, Singer et al (2009) constructed a theoretical model that indicated the fact that retailers use knowledge of future demand and stocks to force suppliers to give discounts to reach sales target is the primary cause for end of month sales spike (Singer et al, 2009).…”