Grouping customers for better allocation of resources to serve correlated demands

In this paper, we discuss a common decision-making problem arising in the allocation and decentralization of resources under uncertain demand. The total resource requirements for a given service level equals the sum of mean demands plus a safety factor multiplied by the standard deviations of demands. Since the demand means are unaffected by any customer groupings, we attempt to exploit demand correlations for developing customer groups such that the sum of the standard deviations over all groups is minimized. A concave minimization model with binary variables is developed for this purpose and a heuristic partitioning method is proposed to efficiently solve the model. The model is appropriate for both manufacturing and service management with potential applications in salesforce allocation, grouping of machines in job shops, and allocation of plant capacities.