Sales Effort Management under All-or-Nothing Constraint

47 Pages Posted: 9 Jan 2020 Last revised: 23 Sep 2020

See all articles by Longyuan Du

Longyuan Du

University of San Francisco - School of Management

Ming Hu

University of Toronto - Rotman School of Management

Jiahua Wu

Imperial College Business School

Date Written: December 18, 2019

Abstract

We consider a sales effort management problem under an all-or-nothing constraint. The seller will receive no bonus/revenue if the sales volume fails to reach a predetermined sales target at the end of the sales horizon. Throughout the sales horizon, the sales process can be moderated by the seller through her costly effort. We show that the optimal sales rate is non-monotone with respect to the remaining time or the outstanding sales volume required to reach the target. Generally, it has a watershed structure that for any needed sales volume, there exists a cutoff point on the remaining time above which the optimal sales rate decreases in the remaining time and below which it increases in the remaining time. We then study easy-to-compute heuristics that can be implemented efficiently. We start with a static heuristic derived from the deterministic analog of the stochastic problem. With an all-or-nothing constraint, we show that the performance of the static heuristic hinges on how the profit-maximizing rate fares against the target rate, which is defined as the sales target divided by the length of the sales horizon. When the profit-maximizing rate is higher than the target rate, the static heuristic adopting the optimal deterministic rate is asymptotically optimal with negligible loss. On the other hand, when the profit-maximizing rate is lower than the target rate, the performance loss of any asymptotically optimal static heuristic is of an order greater than the square root of the scale parameter. To address the poor performance of the static heuristic for the latter case, we propose a modified resolving heuristic and show that it is asymptotically optimal, and achieves a logarithmic performance loss.

Keywords: revenue management, optimal control, salesforce management, all-or-nothing constraint

Suggested Citation

Du, Longyuan and Hu, Ming and Wu, Jiahua, Sales Effort Management under All-or-Nothing Constraint (December 18, 2019). Available at SSRN: https://ssrn.com/abstract=3506499 or http://dx.doi.org/10.2139/ssrn.3506499

Longyuan Du

University of San Francisco - School of Management ( email )

San Francisco, CA 94117
United States

Ming Hu (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada
416-946-5207 (Phone)

HOME PAGE: http://ming.hu

Jiahua Wu

Imperial College Business School ( email )

Tanaka Building
South Kensington Campus
London, SW7 2AZ
United Kingdom
02075949851 (Phone)

HOME PAGE: http://www3.imperial.ac.uk/people/j.wu

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