Fast approximation methods for sales force deployment

Sales force deployment involves the concurrent resolution of four interrelated subproblems: sizing the sales force, salesman location, sales territory alignment, and sales resource allocation. The first subproblem addresses the topic of selecting the appropriate number of salesman. The salesman location aspect of the problem involves determining the location of each salesman in one sales coverage unit. Sales territory alignment may be viewed as the problem of grouping sales coverage units into larger geographic clusters called sales territories. Sales resource allocation refers to the problem of allocating scarce salesman time to the aligned sales coverage units. All four subproblems have to be resolved in order to maximize profit of the selling organization. In this paper a novel nonlinear mixed-integer programming model is formulated which covers all four subproblems simultaneously. For the solution of the model we present approximation methods which serve to solve large-scale problem instances arising in practise. The methods which provide lower bounds for the optimal objective function value are benchmarked against upper bounds. On the average the solution gap, i.e. difference between upper and lower bound, is roughly 3%. Furthermore, it is shown, how the methods can be used to analyze various problem settings which are of highly practical relevance. Hence, the methods presented in this paper are effective and efficient and will be very helpful for marketing management.