The efficient use of resources is of paramount importance in any organization, and
this is especially true of the use of human resources. We are considering an organization
with a fixed number of workers over a network of subunits. The relative efficiency
of these units can be uncovered using Data Envelopment Analysis (DEA) methods. How
do we overcome efficiency differences when resources are constrained? Motivated by
concerns for quality assurance, we use a method that lexicographically minimizes the
tasks per worker. We present a fast algorithm to calculate the optimal allocation.
Connections to the apportionment literature — mostly focusing on the fair allocation
of voting districts among geographical or administrative regions, — are discussed.
The allocation can be validated using DEA: efficiency indicators are now levelled.
The method is illustrated using data from salary administrators at the Hungarian State
Treasury’s 19 county-level subsidiaries. Knowing the number of standard administrative
tasks for each subsidiary and each month, we allocate workers proportionally to the
busiest months. After the reallocation, the relative efficiency of the worst-performing
counties moves from about 60% to over 90%.
