Sales effort management under all-or-nothing constraint
File(s)rm_aon_accepted.pdf (646.92 KB)
Accepted version
Author(s)
Du, Longyuan
Hu, Ming
Wu, Jiahua
Type
Journal Article
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 water shed structure that for any needed sales volume, there exists a cut off 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.
Date Issued
2021-10-06
Date Acceptance
2021-04-13
Citation
Management Science, 2021, 68 (7), pp.5109-5126
ISSN
0025-1909
Publisher
Institute for Operations Research and Management Sciences
Start Page
5109
End Page
5126
Journal / Book Title
Management Science
Volume
68
Issue
7
Copyright Statement
© 2021 INFORMS
Identifier
https://pubsonline.informs.org/doi/10.1287/mnsc.2021.4142
Subjects
Social Sciences
Science & Technology
Technology
Management
Operations Research & Management Science
Business & Economics
revenue management
dynamic programming-optimal control
applications
marketing
salesforce
all-or-nothing constraint
REVENUE MANAGEMENT
DEVELOPMENT COMPETITION
COMPENSATION PLANS
ALLOCATION
CONTESTS
Operations Research
08 Information and Computing Sciences
15 Commerce, Management, Tourism and Services
Publication Status
Published
Date Publish Online
2021-10-06