Sales Effort Management under All-or-Nothing Constraint
43 Pages Posted: 9 Jan 2020
Date Written: December 18, 2019
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. 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 static heuristics derived from the deterministic analog of the stochastic problem. With the existence of an all-or-nothing constraint, we show that the performance of static heuristics hinges on how the profit-maximizing rate fares against the target rate, which is defined as the sales target divided by the length of 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 or equal to the target rate, the performance loss of any asymptotically optimal static heuristic is greater than the square root of the scale parameter. To address the poor performance of static heuristics 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
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