Document Type


Date of Award



Prisons, Mathematical models, Criminals, Rehabilitation

Degree Name

Doctor of Philosophy (PhD)



First Advisor

A. G. Holtmann

Second Advisor

T. G. Cowing

Third Advisor

D. H. Newlon


Social Sciences


This paper is an attempt to apply economic analysis to the management of prisons. In particular, we analyze the operations of the U.S. Federal Bureau of Prisons. Using a linear programming framework we create a model of how the Bureau generates costs and benefits for society, and the model is then run to maximize the net social benefits available from the resources devoted to the federal prison system. More specifically, we define thirty six inmate types, six major types of prisons, and allow sentence lengths of one, three, and five years. The model is then asked to solve for the optimal inmate-prison-sentence length combinations, in the context of a five year planning horizon.

The prison system is assumed to create social benefits by confining and rehabilitating dangerous criminals. To value captivity we use some recently available, and relatively high quality, data to project how many crimes each type of inmate would be committing per year were he not in prison. To value rehabilitation, we attempt to estimate the reforming effect of each major type of federal prison, and then add up the expected number of future crimes-not-committed due to rehabilitation. In the standard version of the model each crime which the prison system prevents either through confinement or offender reform is valued at the average amount which society spends to protect itself from the type of crime which has been prevented.

The prison system is assumed to be restricted in its activities by three major sets of constraints: (1) a fixed budget in each year of the horizon; (2) an upper bound on its capacity to hold each type of inmate; and (3) each year we assume that a new batch of offenders is given to the Bureau by the courts, and the prison system must either confine these new people, or decide to put them on “probation,” i.e. the model is allowed the option of throwing some offender types out of prison altogether.

The results of this exercise, based on a problem structure with 2700 original (non-slack) decision variables and 565 constraints, are consistent with initial expectations. Young, violent offenders are given long terms, and older inmates, especially those convicted of non-violent crimes, are given generally short sentences. In fact, no offender over age forty is allocated to any confinement at all. Clearly the model is able to see and respond to the obviously high opportunity cost of putting a non-dangerous offender in prison when that means, generally, that a more dangerous person must be kept out of prison, or kept in for a shorter term, given the fixed supply of cells and budget. Shadow values on the constraints indicate that providing the Bureau with more resources may be quite worthwhile.

These general results remain largely unchanged under nine variations on the standard model. These various alternative specifications of the problem allow us to consider a wide range of values for the model's two most important parameters: the value of each crime prevented, and the rehabilitative capability of each major type of federal prison.

The major drawback of this model is that the deterrence and "social revenge” value of prison operations are not explicitly valued. There is of course considerable debate on whether or not these values are zero, but further inquiry here is certainly warranted. Another flaw in the model is the aggregation required.

Available for download on Tuesday, April 01, 2025