Fast approximation methods for sales force deployment

Sales force deployment involves the simultaneous resolution of four interre lated subproblems: sales force sizing, salesman location, sales territory a lignment, and sales resource allocation. The first subproblem deals with se lecting the appropriate number of salesman. The salesman location aspect of the problem involves determining the location of each salesman in one sale s 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 subprobl ems have to be resolved in order to maximize Profit of the selling organiza tion. Ln this paper a novel nonlinear mixed-integer programming model is fo rmulated which covers all four subproblems simultaneously. For the solution of the model we present approximation methods capable of solving large-sca le, real-world instances. The methods, which provide lower bounds for the o ptimal objective function value, are benchmarked against upper bounds. On a verage the solution gap, i.e., the difference between upper and lower bound s, is about 3%. Furthermore, we show how the methods can be used to analyze various problem settings of practical relevance. Finally, an application i n the beverage industry is presented.