Optimal Allocation of Students to Naval Nuclear-Power Training Units
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Optimal Allocation of Students to Naval Nuclear-Powe
Training Units
Michael R. Miller, Robert J. Alexander, Vincent A. A
ige, Robert F. Dell, Steven R. Kremer,
Brian P. McClune, Jane E. Oppenlander, Joshua P. Tomlin
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ige, Robert F. Dell, Steven R. Kremer, Brian P. McClune, Jane E.
Oppenlander, Joshua P. Tomlin XXXXXXXXXXOptimal Allocation of Students to Naval Nuclear-Power Training Units. Interfaces
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INTERFACES
Vol. 47, No. 4, July–August 2017, pp. 320–335
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Optimal Allocation of Students to Naval Nuclear-Powe
Training Units
Michael R. Miller,a Robert J. Alexander,a Vincent A. A
ige,a Robert F. Dell,b Steven R. Kremer,a Brian P. McClune,a
Jane E. Oppenlander,c Joshua P. Tomlina
aNaval Nuclear Laboratory, Kesselring Site, Schenectady, New York 12301; bOperations Research Department, Naval Postgraduate School,
Monterey, California 93943; c School of Business, Clarkson University, Schenectady, New York 12308
Contact: XXXXXXXXXX (MRM); bo
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Received: November 12, 2015
Revised: July 11, 2016; December 1, 2016
Accepted: March 24, 2017
Published Online in Articles in Advance:
June 27, 2017
https:
doi.org/10.1287/inte XXXXXXXXXX
Copyright: This article was written and prepared
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and is therefore in the public domain.
Abstract. The U.S. Navy operates an impressive fleet of nuclear-powered submarines and
aircraft ca
iers andhas safely operated its nuclear fleet formore than 60 years,while steam-
ing over 154 million miles. Rigorous training has been key to maintaining such an impres-
sive record. The U.S. Naval Nuclear Propulsion Training Program develops, certifies, and
delivers the nuclear-operator qualification training for enlisted and officer personnel oper-
ating its nuclear fleet. This training finishes at one of four nuclear-power training units
(NPTUs), operates under a complex set of hard and soft constraints, varies depending on
the type of student, and requires significant personnel and equipment resources.We devel-
oped and implemented a mixed-integer linear program (MILP) that prescribes how many
students of each type to allocate to each NPTU at the start of each class (a group of stu-
dents who train together) and how allocated students complete NPTU training. The use of
MILPhas improved student allocationbyan estimated eight percent and led to significantly
improveduse of bothNPTUpersonnel and equipment resources. In this paper,we describe
this unique optimization application, the MILP formulation, its path to adoption, its use
interface, and impacts from its development and use over the past three years.
History: This paper was refereed.
Funding: The submitted manuscript has been authored by contractor of the U.S. Government [Contract
DE-NR XXXXXXXXXX]. Accordingly, the U.S. Government retains a non-exclusive, royalty-free license to
publish or reproduce the published form of this contribution, or allow others to do so, for U.S.
Government purposes.
Keywords: military • personnel: programming • integer • applications: education systems • planning: decision analysis • applications
Nuclear-powered submarines and aircraft ca
iers (Fig-
ure 1) are key elements for the defense of the United
States and for the maintenance of free and open com-
merce across the world’s oceans (Department of the
Navy and Department of Energy XXXXXXXXXXThese vessels
are staffed by highly trained enlisted and officer per-
sonnelwhooperate andmaintain the power-generation
and propulsion systems capable of extended unsup-
ported operations. The U.S. Naval Nuclear Propulsion
Training Program develops, certifies, and delivers the
nuclear-operator qualification training for enlisted and
officer personnel who operate its nuclear fleet. This
training finishes at one of four Nuclear Power Train-
ing Units (NPTUs). This paper describes the benefits
achieved by using a MILP to prescribe the number of
students of different types to allocate to each NPTU at
the start of each class and the activity sequence for allo-
cated students to complete NPTU training.
Certifying Nuclear Operators
Certification as a naval nuclear operator requires rig-
orous training that lasts at least one year for each of
five student types refe
ed to by the name of the certi-
fication: electrician’s mate; machinist’s mate; electron-
ics technician; engineering laboratory technician; and
engineering officer of the watch. Each student type
completes a unique training track consisting of knowl-
edge and hands-on requirements. A student is cer-
tified (i.e., qualified) to operate a specific area of a
naval nuclear-propulsion plant only after demonstrat-
ing mastery of propulsion plant equipment.
320
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XXXXXXXXXX
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Miller et al.: Optimal Allocation of Students to Naval NPTUs
Interfaces, 2017, vol. 47, no. 4, pp. 320–335 321
Figure 1. The Nuclear-Powered Aircraft Ca
ier USS JOHN C STENNIS (CVN 74), with Destroyer Escort (to Left), and the
Nuclear-Powered Submarine USS SEAWOLF (SSN 21) Operates on Deployment in the Pacific Ocean
Notes. Operating the nuclear power plants on these ships requires highly trained enlisted and officer personnel. (Photo from http:
navy.mil.)
Depending on the student type, students attend one
or more schools prior to beginning NPTU training.
While required schools vary by student type, all stu-
dent types must satisfactorily complete a six-month
program (i.e., nuclear-power school), consisting pri-
marily of classroom instruction, prior to six additional
months of NPTU training. Ideally, upon completion of
this classroom instruction, students immediately begin
training at one of four NPTUs at one of two training
sites; each site has two units. During NPTU training,
students engage in a mix of classroom, simulator, and
hands-on training. Delays in starting NPTU training
often occur due to limited resources; this produces a
acklog of students waiting to begin NPTU training.
Navy leadership carefully monitors this backlog.
Each NPTU is a self-contained training facility com-
posed of a nuclear reactor, simulators, classrooms, staff
instructors, and other training assets. Each NPTU class
consists of a group of students who train together,
which is designated by a sequential number based on
the fiscal year. For example, class 1501 co
esponds to
the first class started in fiscal year 2015. The starting
week of each NPTU class is known, and all plants start
classes on the same day; therefore, each plant runs
classes with the same class number. With rare excep-
tions, a new class starts every eight weeks and three
classes normally train simultaneously at each NPTU.
Students are assigned (i.e., allocated) to a NPTU class
and train together as a class.
NPTU training consists of a classroom phase (seven
weeks) followed by a hands-on phase (17 weeks).
Hands-on activities at the NPTU are critical because
they teach students to perform the tasks that are
equired to safely operate nuclear reactors. Much of
this hands-on training (refe
ed to as “watchstand-
ing”) takes place at “watchstations” located in eithe
a plant that contains a nuclear reactor or at a simula-
tor. Training conducted outside of the plant is refe
ed
to as “off-watch” training. Although extremely real-
istic, simulator training can only satisfy a fraction of
the required watchstanding. A qualified staff instruc-
tor must be present at each watchstation in both the
plant and a simulator to ensure proper plant operation.
During operations, students are able to performwatch-
standing. Simulators require staff time onlywhen oper-
ating for training.
There are five types of staff instructors, each per-
forming different training functions. Whereas students
a
ive in batches at defined intervals as part of a class,
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http:
navy.mil
Miller et al.: Optimal Allocation of Students to Naval NPTUs
322 Interfaces, 2017, vol. 47, no. 4, pp. 320–335
staff instructors continuously flow in and out of a
NPTU based on their individual military assignments.
Typically, a staff instructor is assigned to a NPTU fo
three years consistent with the typical length of othe
Navy assignments. In addition to supporting hands-
on training in the simulator and plant, staff instruc-
tors engage in a variety of other duties, including
plant operation, providing classroom instruction, and
administrative tasks. The amount of time devoted to
each duty depends on staffing levels and the numbe
of students being trained.
It is generally desirable to allocate as many students
as possible to a class, while satisfying a variety of con-
straints and assuring the efficient use of limited staff
instructors, equipment, and