Expected behavior in the min max random assignment problem Consider the standard assignment problem: $n$ people are assigned to n jobs (one person to one job) so to minimize the sum of costs. When the costs are generated randomly (using the exponential (1) distribution), it is known that the expected sum of costs is $\pi^2/6$.
An alternative solution to the assignment problem is to choose an allocation that instead minimizes the largest cost incurred by any individual, in the spirit of the John Rawls fairness criteria. Is it known what is the random sum of costs in the random version of the problem?
See Michael Z. Spivey, &quot;Asymptotic Moments of the Bottleneck Assignment Problem,&quot; Mathematics of Operations Research, 36 (2): 205-226, 2011.