Deconvolving the Productivity of Salespeople via Constrained Quadratic Programming

Abstract

With the present market trend, businesses and organisations with large salesforces are experiencing much turnover among their sellers. Movement of salespeople from one company to another is a continual process as long as there is market demand. In the traditional sense, a salesperson’s productivity is directly proportional to the revenue that he or she brings to the company. Importantly, the senior leaders in organisations are interested in knowing the variations in sales productivity as a result of hiring and attrition in the salesforce. In this paper we focus our attention on the characterisation of sales productivity based on four categories. When an existing salesperson leaves, what is the sales productivity over time if replaced by a new hire from a university, an experienced new hire, or a transfer from another division in the company? In addition if an organisation ventures into acquisition, what is the anticipated sales productivity from this? We model the sales productivity of new hires as a linear time-invariant system and estimate productivity profiles with a least-squares deconvolution formulation. By applying business constraints on productivity profiles for regularisation, we are left with a constrained quadratic program to solve. We demonstrate the estimation technique on real-world sales data from a global enterprise, finding productivity profiles under the four different cases listed above.