Modeling and optimization of multilevel marketing operations

This paper models the resource allocation problem arising in multilevel marketing (i.e., network) operations. The supervisor of a network of salespersons has a limited resource (her own time). She must decide on the (i) optimal number of “direct contacts” to recruit, train and develop; (ii) optimal number of lower levels she should be responsible for helping to hire, train and develop their own direct contacts, and (iii) optimal allocation of her time at each level in the network. We use tools from branching processes and find general results for the probability distribution of the number of lower level contacts with non‐identical distributions for any given number of initial contacts. Using these results, we present an optimization model for contacts with different characteristics and determine the optimal number of initial contacts, the number of lower levels and the supervisor's optimal effort at each level using tools from nonlinear programming, in particular, Kuhn‐Tucker conditions and Lagrangian duality. We generalize our models, (i) to allow for the randomness of time spent by the supervisor; and (ii) the possibility of supervisor generating her own direct sales. Several examples illustrate our findings.