Optimizing Marine Security Guard Assignments

ABSTRACT

The Marine Corps Embassy SecurityGroup (MCESG) assigns 1,500 Ma-rine Security Guards (MSGs) to 149

embassy detachments annually. MCESGattempts to balance MSG experience levelsat each detachment and assign MSGs totheir preferred posts while fulfilling severalbillet requirements. Historically, assign-ments have been made manually in a labor-intensive process requiring more than 6,000person-hours per year. This article describesthe Marine Security Guard AssignmentTool (MSGAT). MSGAT is an Excel-baseddecision support tool that utilizes a systemof workbooks to guide MCESG through astreamlined data collection process and pro-vide high-quality assignments. Assignmentsare optimized using a multicommodity net-work flow formulation. This article comparesassignments generated by MSGAT to as-signments generated manually by MCESGand demonstrates that MSGAT assignmentsare superior with regard to several measuresof effectiveness.

INTRODUCTIONThe Marine Security Guard program

has existed in its current form since Decem-ber 1948. Marine Security Guards (MSGs)are responsible for providing ‘‘internal se-curity services at designated United StatesDiplomatic and Consular facilities to pre-vent the compromise of classified informa-tion and equipment that is vital to nationalsecurity’’ (Department of State, 1999).MSGs currently serve at 149 embassiesand consular facilities, henceforth referredto as detachments. An MSG’s tour typicallyconsists of three one-year posts at three dif-ferent detachments. Prior to serving at hisor her first detachment, each MSG (typi-cally a Lance Corporal with three years ofservice) receives two to three months oftraining at MSG School in Quantico, Vir-ginia. MSG School graduates five classes of80–100 students annually. Following eachMSG School graduation, a rotation occursin which new graduates enter their firstposts, MSGs who have served one or twoyears rotate to new detachments, and MSGswho have served three years leave the MSGprogram. Thus, there are five rotations of ap-proximately 250–300 MSGs every year, with

each rotation corresponding to a graduatingclass. The life cycle of MSGs is described indetail in the ‘‘Attributes’’ subsection of thisarticle.

Prior to each rotation, MSGs are as-signed to available billets. Historically, as-signments have been generated manuallyby the Marine Corps Embassy SecurityGroup (MCESG). In assigning MSGs toavailable billets, MCESG takes into accounta number of attributes of MSGs, billets, anddetachments.

This article describes a decision sup-port tool designed to assist in the assign-ment process: the Marine Security GuardAssignment Tool (MSGAT). The goal ofMSGAT is to expedite the assignment pro-cess while maintaining or improving solu-tion quality relative to manual assignment.The MSG assignment problem is addressedusing two integer linear programs (ILPs)that seek to optimize the overall qualityof the assignments made. This article de-scribes these models and uses historicaldata to compare assignments producedby MSGAT to those produced manuallyby MCESG.

RELATED WORKA large body of prior work has estab-

lished the utility of decision support sys-tems for military applications. This sectionexamines recently employed personnel as-signment optimization models within theUS military and focuses on developmenttechniques that make them successful. It alsoexamines integration of such models with in-formation management systems.

Extensive research has examined theuse of network flow models for personnelassignment. Bausch et al. (1991) address as-signment optimization with respect to theimmediate mobilization of Marine Corpsofficers. The authors designed and built theManpower Assignment RecommendationSystem (MARS). MARS is a decision supporttool based on a network flow model thatworks in conjunction with Marine Corps da-tabases to complete a wartime mobilizationinvolving 40,000 officers and 27,000 billets(Bausch et al., 1991). MARS combines threeobjectives:

1. Maximize the number of billets filledwith qualified officers.

OptimizingMarineSecurityGuardAssignments

Maro D. Enoka

United States Marine [email protected]

E. M. Craparo

Naval Postgraduate [email protected]

OR METHODS:(Integer) linearprogramming,Multiobjectiveoptimization, Networkmethods

APPLICATION AREAS:Resources readiness andtraining, Manpower andpersonnel

Military Operations Research, V19 N2 2014, doi 10.5711/1082598319205 Page 5Military Operations Research, V19 N2 2014, doi 10.5711/1082598319205 Page 5

2. Maximize the fit of the officer to the billet.MARS attempts to obtain a perfect officer-billet fit and avoids sending over- or under-qualified officers to any billet. MSGAT alsoseeks to maximize the fit of each Marine-billet assignment using similar fit criteria,such as rank and gender.

3. Minimize the amount of movement whenfilling the billets. That is, MARS aims to keepas many officers in the unit to which theywere assigned prior to mobilization.

Two files are critical to the functionality ofMARS: the Wartime Officer Slate File (WOSF)and the Wartime Authorized Strength Report(WASR). The WOSF contains information onMarines, whereas the WASR describes billetsand their requirements. A conceptual networkmodel of the Marine Corps mobilization problemdepicts each officer as a supply node and eachbillet as a demand node (Bausch et al., 1991). Be-cause a literal implementation of the conceptualmodel is computationally impractical, MARS em-ploys several important simplifications to theconceptual model (Bausch et al., 1991). Prior tothe development of MARS, the previous MarineCorps system took up to four days to completea mobilization and produced substandard re-sults. MARS produces results in less than 10 min-utes and with a significant improvement in allmeasures of effectiveness (MOEs).

Tivnan (1998) also presents a network flowmodel, Enlisted Assignment Model-Global(EAM-GLOBAL), that serves to optimize the as-signment of enlisted Marines to billets. EAM-GLOBAL seeks to optimize Marine-to-billet fitwhile balancing staffing shortages, allowinggrade and MOS substitutions, and minimizingthe monetary cost associated with moving Ma-rines (Tivnan, 1998). Four MOEs are used to de-termine how well EAM-GLOBAL’s assignmentssatisfy US Marine Corps (USMC) staffing goals:

1. Percentage of filled billets.2. Number of transcontinental United States

transfers.3. Percentage of filled billets with a perfect fit.

The authors define ‘‘perfect fit’’ as an exactgrade and MOS match between Marine andbillet.

4. Number of Marines available but notassigned.

EAM-GLOBAL verifies that the current inven-tory of enlisted Marines can achieve over 99 per-cent of the staffing goals.

In a similar model, Dell et al. (2008) use aninteger linear program, Optimally StationingArmy Forces (OSAF), to provide optimal sta-tioning of Army units as weapons systems, mis-sions, and operations change over time. TheOSAF model prescribes optimal Army station-ing by using the existing starting locations, setof installations, and unit requirements to mini-mize cost associated with Base Realignmentand Closure (BRAC) decisions, while maximiz-ing military value (Dell et al., 2008). Each station-ing plan satisfies a number of unit requirements,such as the availability of buildings and land forunit training. OSAF has assisted with BRAC de-cisions since 2005 and has successfully providedthe Army with reliable stationing analysis forseveral years. Although OSAF is a stationinganalysis tool, it shares many features with per-sonnel assignment models such as MSGAT (Dellet al., 2008). For example, each assignment solu-tion generated by MSGAT satisfies various MSGand billet requirements identified by MCESGand the region commands.

Similarly, Loerch et al. (1996) develop an in-teger program to determine efficient stationingsolutions for the United States Army in Europe.The authors design their model to achieve thedesired objectives of minimizing monetarycosts, maintaining unit integrity, and fulfillingunit support requirements (Loerch et al., 1996).Model results were provided as a basis for de-veloping stationing plans throughout Europe.

In a related approach that uses mixed inte-ger programming, Baumgarten (2000) developsthe Marine Corps Manpower System (MCMS)to maximize the Marine Corps’ operationalreadiness through the assignment of officers tobillets. While attempting to fulfill billet require-ments, MCMS simultaneously develops theprofessional skills that each officer must possessto be assigned to billets as their careers progress(Baumgarten, 2000). Thus, career paths must bedesigned to reflect the balance of fulfilling billetrequirements and developing professional skills.Baumgarten (2000) presents a mixed integer pro-gram, the Officer Career Path Selection (OCPS)model, that assigns officers to acceptable careerpaths in order to meet billet requirements while

OPTIMIZING MARINE SECURITY GUARD ASSIGNMENTS

Page 6 Military Operations Research, V19 N2 2014

satisfying professional skill development. OCPSassists in determining the number of officers toassign to various Military Occupational Special-ties (MOSs) each year.

Goldschmidt and Boersma (2003) also useinteger programming to assign MOSs to allnewly commissioned Marine Corps second lieu-tenants at the Basic School (TBS). The assignmentof an MOS is based on the officer’s ordinal rankwithin his or her cohort at TBS and the de-mands of the Marine Corps. Ordinal rank is aranking based on academic and leadershipgrades attained throughout TBS. To ensure qual-ity distribution of officers, each cohort withinTBS is divided into thirds based on ordinalrank (Goldschmidt and Boersma, 2003). TheMOS vacancies are divided into thirds as well.Goldschmidt and Boersma (2003) develop aninformation management system, MyMOS,for use by TBS personnel, that assists in the col-lection of information and the assignment ofMOSs to newly commissioned officers. EachMOS assignment model is an integer linearprogram that optimally assigns an MOS to anofficer using the officer’s ordinal rank, MOSpreferences, the third in which the officerfinished within their cohort, and MOS avail-ability. In addition to the numerical im-provements realized by linear programming,Goldschmidt and Boersma (2003) achieve sub-stantial cost savings by reducing human in-volvement in the assignment process.

Many of the models discussed thus far aresuccessful, in part, because they incorporatepersistence. That is, these models account forany existing solution and attempt to minimizedisruptions to that solution while meeting newrequirements. Incorporation of persistence isbeneficial because optimization has the poten-tial to amplify small input changes into drasti-cally different solutions (Brown et al., 1997).This is especially troublesome in a cyclic processsuch as the MCESG assignment process. In thisprocess, MCESG produces an assignment, theassignment is published, revised MSG or billetdata becomes available, MCESG produces a re-vised assignment, and the revised assignment ispublished. New assignments that retain fea-tures of prior assignments are more desirableto MCESG, as this limits the amount of disrup-tion to MSGs’ planned rotations. Thus, MSGAT

utilizes a user-defined parameter that limitsnumber of changes between any two sequentialassignments.

OPTIMIZATION MODELSMSGAT implements a multicommodity

network flow model called the Balance Model(BALMOD) to optimally assign MSGs to bil-lets. It also implements the Assignment Mod-ification Model (ASMOD), which is an extensionof BALMOD that is capable of generating similarassignments using varying sets of input data. Be-fore describing models BALMOD and ASMOD,we first discuss the attributes of MSGs and billetsthat are relevant in the assignment process.

AttributesMSGAT considers several attributes when

determining goodness of fit between an MSGand a billet. These attributes are summarized inTable 1. Most attributes are applicable to individ-ual MSG/billet pairs; however, two attributes arerelevant at the detachment level. The first is MSGexperience level. Rotating MSGs can be placed intoone of four experience levels:

1. First posters are transitioning from MSGSchool to their first detachment.

2. Second posters are transitioning from theirfirst detachment to their second detachment.

3. Third posters are transitioning from their sec-ond detachment to their third detachment.

4. OPCs are going Off Program Completely(OPC; i.e., leaving MSG duty).

An individual leaving MSG duty may bedoing so for one of three reasons: (1) the MSGmay have successfully completed his or her ser-vice and is rotating OPC; (2) the MSG may bephysically unable to continue duty and is beingdischarged for the Good of the Service (GOS); or(3) the MSG may be removed from duty for legalreasons or Removed for Cause (RFC). For thepurposes of the decision support tool, the termOPC encompasses the OPC, GOS, and RFCconditions. In assigning MSGs to detachments,MSGATattempts to ensure that each detachmentreceives a balanced distribution of first, second,and third posters, taking into account any MSGs


Military Operations Research, V19 N2 2014 Page 7Military Operations Research, V19 N2 2014 Page 7

who are not rotating in the current cycle as wellas any OPCs leaving MSG duty.

The second attribute that is relevant at thedetachment level is MSG rank. MSGs range inrank from Lance Corporal (E3) to Staff Sergeant(E6). MSGAT attempts to ensure that each de-tachment receives a balanced rank structure,again taking into account any MSGs who arenot rotating in the current cycle as well as anyOPCs leaving MSG duty.

All remaining attributes can be modeled atthe level of individual MSG/billet pairs. Thefirst such attribute is detachment tier. Each de-tachment is categorized into one of three tiersbased on desirability. Tier designations are de-termined by the Department of State (1999). Tier1 detachments are in desirable locations, such asParis, Rome, and Munich. Tier 3 detachmentsare in less desirable locations, such as Port AuPrince, Rangoon, and Kiev. Tier 2 detachmentsare in intermediate locations, such as MexicoCity, Ankara, and Kuwait. One goal of the as-signment process is to ensure that each MSG re-ceives an equitable distribution of Tier 1, Tier 2,and Tier 3 assignments during his or her 3-yeartour of duty; ideally, one year should be spent ineach tier.

MSGAT also takes into account any post re-strictions that may make an MSG ineligible toserve at a particular detachment. One example

of a condition that would result in a post restric-tion is the presence of a close relative of the MSG(e.g., an aunt or an uncle) living near the detach-ment. For security reasons, MSGs are not per-mitted to serve at such detachments.

Each detachment belongs to one of ninegeographic regions, and MSGs are prohibitedfrom serving at more than one detachment inthe same region. Thus, MSGATattempts to avoidassignments that would result in an MSG servingin a repeat region. This attribute is modeled sepa-rately from the post restriction attribute because,in some cases, it may be desirable to relax the re-peat region requirement while enforcing any re-strictions on individual posts.

Most detachments are configured to houseboth male and female MSGs; however, some de-tachments are configured for males only. There-fore, MSGAT considers gender when assigningMSGs to detachments. Again, gender is consid-ered separately from the post restriction attri-bute to allow attributes to be emphasized ordeemphasized individually.

Three attributes relate to specific designa-tions MSGs may hold. Some detachments, lo-cated in designated countries and referred to asDC posts, require that posted MSGs have a specialtype of security clearance. Thus, MSGAT consid-ers each MSG’s DC qualification status. Similar toDC qualification, MSGs must receive a special

Table 1. The set of goals that MSGAT attempts to satisfy when making MSG-billet assignments.

Entity Attribute Goal

Detachment Experience level MSG experience level should be balanced across all detachments.Rank MSG rank should be balanced across all detachments.

MSG/billet Tier MSGs should not be assigned to the same tier more than once.Post restrictions MSGs should not be assigned to detachments in which

they are restricted from serving.Repeat region MSGs should not be assigned to the same region more than once.Gender Female MSGs should not be assigned to detachments that are

not configured for females.DC Only DC-qualified MSGs should be assigned to DC detachments.A/ Only MSGs qualified to serve as an A/ should be assigned

to billets requesting an A/.SSgt select Billets needing SSgt selects should receive MSGs selected

for the rank of SSgt.1/5 posts All billets in 1/5 posts have priority over billets in more populous

detachments.Preferences MSGs should be assigned to one of three detachment preferences

or one of two region preferences.



designation to serve as an assistant detachmentcommander (A/). Accordingly, MSGAT con-siders each MSG’s A/ status when making assign-ments to detachments requesting a new A/.Finally, detachments may also request an MSGwho has been selected for promotion to Staff Ser-geant (SSgt); these MSGs are referred to as SSgtselect.

Inevitably, personnel shortages sometimesresult in some billets going unfilled. When thisoccurs, it is desirable that unfilled billets be lo-cated at large embassies with many MSGs ratherthan small embassies with few MSGs. The small-est embassies are configured for one detachmentcommander and five watchstanders; these are re-ferred to as 1/5 posts. MSGAT attempts to fill allbillets at 1/5 posts.

Finally, MSG preferences are taken into ac-count. In each rotation, each MSG is allowed tospecify two regions and three individual detach-ments in which he or she would most like to serve.MSGAT attempts to honor these preferences.

Limitations of the ClassicalAssignment Model

The classical assignment model matchespersonnel to billets while minimizing a sum ofpenalties (or, equivalently, maximizing a sum ofutilities) defined for each person-billet pair. Asshown in Table 1, MSGAT must satisfy two de-tachment-level goals: each detachment must re-ceive an equitable distribution of first, second,and third posters, as well as a balanced rankstructure. Fortunately, with the exception ofrank and experience level, all other attributesare either constant throughout a detachment orare linked to rank. Thus, each detachment candesign its billet requests to ensure that it receivesa balanced rank structure. However, the classicalassignment model must be modified to balanceexperience levels across detachments. We nowdescribe such a modification.

Model BALMODBALMOD solves a multicommodity net-

work flow problem in which MSG experiencelevels serve as commodities. A schematic dia-gram of this network is shown in Figure 1.

This network contains four sets of nodes:a set representing MSGs, G; a set representingbillets, B; a set representing detachments, D;and a set representing experience levels, E. Thefirst layer of this network, consisting of the nodesin G and B and the arcs connecting them, behavesas a classical assignment model. It assigns MSGsto billets based on attributes unique to MSGs/billet pairs. The second layer of the network cap-tures the balance of MSG experience levels acrossdetachments.

In this multicommodity model, flow com-modities represent MSG experience levels. Thearcs connecting nodes in D to nodes in E incurpenalties based on the commodity of flow(MSG experience level) and the experiencelevel represented at the destination node. Thearc connecting node det in D to node e in Ehas capacity cape

det, which indicates the numberof MSGs with experience level e required at de-tachment det to balance experience levels acrossdetachments.

The capacities capedet are calculated as fol-

lows. Denote the overall fraction of MSGs withexperience level e, including rotating and non-rotating MSGs but not OPCs, by frace. Denotethe number of MSGs with experience level e thatare not rotating out of detachment det by Sdet

e . Fi-nally, denote the set of open billets at detach-ment det by B(det). MSGAT uses the followingcalculation to set the detachment experience de-mands cape

det:

cap3det 5 max 0;b f rac3jBðdetÞjc2 S

det3

� �

cap2det 5 max 0;b f rac2jBðdetÞjc2 S

det2

� �

cap1det 5 jBðdetÞj2 cap

2det 2 cap

3det

This demand calculation attempts to evenlydistribute experience levels over all detach-ments. Future improvements to MSGAT may in-clude a more sophisticated calculation of cape

det.We will henceforth refer to each unit of MSG ex-perience demand as a slot. In other words, ifcap

3A 5 5, we say that there are five slots available

for third posters at detachment A.BALMOD allows the user to control as-

signments of individual MSGs to detachmentsthrough the use of a binary matrix f, which has



components fg,b. This matrix, called the force/forbid matrix, allows the user to either force orforbid the assignment of an MSG to a specificdetachment by placing capacities on the arcsconnecting nodes in G to nodes in B. Initially,the force/forbid matrix allows any MSG to beassigned to any billet, i.e., fg,b¼ 1 "g,b. However,the user may enter certain requirements that re-sult in modifications to the force/forbid matrix:

• If the user forces MSG g to be assigned to de-tachment det, then fg,b ¼ 1 for all b 2 B(det),and fg,b ¼ 0 for all b ; B(det). This allowsMSG g to be assigned to any billet within de-tachment det and not to any billet outside de-tachment det. Because each MSG is requiredto be assigned to some billet, the net resultis that MSG g must be assigned to detach-ment det.

• If the user forbids MSG g from being as-signed to detachment det, then fg,b ¼ 0 forall b 2 B(det).

Note that the force/forbid matrix gives the usera great deal of control; in fact, an inexperienceduser may inadvertently render the problem in-feasible. Therefore, MSGAT executes infeasibil-ity corrections prior to solving if the userperforms one of the following actions:

• Forces more MSGs to a particular detach-ment than the number of available billets atthat detachment, or

• Forces and forbids an MSG to the samedetachment.

In addition to these feasibility checks, a post-processing step also verifies solution qualityand notifies the user of any potential problemwith MSGAT’s output.

We now describe BALMOD’s mathematicalformulation. For simplicity, the formulation de-scribed in this article assumes that the numberof MSGs rotating is equal to the number of bil-lets available. In reality, the number of rotating

Figure 1. BALMOD solves a two-layer multicommodity network flow problem. The network contains four setsof nodes (G, B, D, and E) and three edge sets. The first layer minimizes MSG-billet cost with respect to attributesunique to MSGs and billets. The second layer balances MSG experience across detachments.



MSGs and available billets are not necessarilyequal in every assignment cycle. Thus, MSGATexecutes a preprocessing step to handle unequalnumbers of MSGs and billets.

Indices and sets:

g 2 G MSGb 2 B Billetk 2 K MSG or billet attributedet 2 D Detachmente 2 f1,2,3g Experience levelc 2 f1,2,3g Flow commodityBdet 4 B Set of billets located in detachment

det

Input data:

det(b) Parent detachment of billet bvk

g ;b Penalty incurred by MSG g and billetb for attribute k

wk Weight given to attribute kwbal Weight given to the experience balance

attributepenc

e Penalty for assigning an MSG withexperience c to a slot requiring experi-ence level e

fg,b Binary input for manually specifyingassignment of MSG g to billet b.

expcg 1 if guard g has experience level c, 0

otherwise

Calculated data:

costg ;b 5Pk

wkvkg ;b Cost of assigning MSG g to

billet b, excluding the experi-ence penalty

capedet Slots available for MSGs with

experience level e at detach-ment det

Decision variables:

ASSIGN cg ;b Decision to assign MSG g with

experience level c to billet b[binary]

BILLET cb;detðbÞ Decision to assign billet b in de-

tachment det(b) to a guard withexperience c [binary]

EXSLOT cdet;e Number of MSGs with experi-

ence level c assigned to detach-ment det and assigned to slotsrequiring experience e

Formulation: BALMOD

minASSIGN

EXSLOT

ASSIGN

Xg;b

�costg;b �

Xc

ASSIGNcg;b

�

1 wbal �Xdet

Xc;e

pence �

EXSLOTcdet;e

maxc;e

pence

� �� jBdetj

s:t:X

b

ASSIGNcg;b 5 exp

cg "g; c (1)

Xg;c

ASSIGNcg;b 5 1 "b (2)

Xg

ASSIGNcg;b 5 BILLET

cb;detðbÞ "b; c (3)

Xb2Bdet

BILLETcb;det 5

Xe

EXSLOTcdet;e "det; c

(4)Xc

EXSLOTcdet;e # cap

edet "det; e (5)

Xc

ASSIGNcg;b # fg;b "g; b (6)

ASSIGNcg;b 2 f0;1g "g; b; c (7)

BILLETcb;det 2 f0;1g "b; det; c (8)

EXSLOTcdet;e $ 0 "det; e; c (9)

BALMOD’s objective function contains twoterms. The first term calculates costs associatedwith attributes unique to MSGs and billets. Theparameter costg,b is a goodness-of-fit measurethat is calculated using parameters wk and vk

g;b.The weight parameter wk is tunable by the user;it is designed to allow the user to emphasize ordeemphasize particular attributes in the costcalculation. Weights wk take on values between0 and 100. The penalty parameter vk

g;b is incurredby MSG g and billet b for attribute k. Penaltiesvk

g;b take on values between 0 and 1. A fulldescription of penalties vk

g;b can be found inEnoka’s master’s thesis (Enoka, 2011).

The second term in the objective functioncalculates penalties related to the balance ofexperience levels across detachments. Each arc



connecting a node in D to a node in E has a costthat depends on the level of mismatch betweenMSG experience level (flow commodity) and ex-perience level represented by the target node inE. Note that a normalization factor is includedin the objective function term relating to the bal-ance penalty. This is done to ensure that theresulting balance penalty is between 0 and 1,as the penalties for the other attributes are alsobetween 0 and 1.

BALMOD’s constraints function as follows.Constraint set 1 ensures that each guard g is as-signed to exactly one billet b while assuring thatthe flow originating from node g is of the correctcommodity. (Note that for each guard g, expc

g isequal to 1 for exactly one experience level c.)Constraint set 2 ensures that each billet b isassigned one MSG g. Constraint set 3 enforcesflow conservation at each billet node b 2 B. Con-straint set 4 enforces flow conservation at eachdetachment node d 2 D. Constraint set 5 ensurescorrect calculation of the experience balance pen-alty, given detachment experience demands.Constraint set 6 enforces conditions expressedby the force/forbid matrix. Constraint sets 7–9impose binary and nonnegativity restrictionson the decision variables, as appropriate.

Note that BALMOD is an integer linear pro-gram rather than a linear program (LP), as wouldbe required in a classical assignment model. Con-straints 6 and 7 are required because multicom-modity network flow problems do not alwayshave integer optimal solutions. However, empir-ical observations suggest that the LP relaxationof BALMOD very often has an integer optimalsolution.

Assignment ModificationIn addition to making good initial assign-

ments, MCESG assignment personnel need tohave the ability to make small changes to existingassignments. It is not uncommon for publishedassignments to undergo several modificationsthroughout an assignment cycle due to changesin MSG or billet input data. Typically, modifica-tions impact several MSG-billet pairs. Becausemodifications often occur after an assignmenthas been published, it is important to limit thenumber of MSG-billet pairs impacted. To thisend, MSGAT uses the Assignment Modification

formulation ASMOD to generate modified as-signments. ASMOD has the same functionalityas BALMOD and uses all of the data, decisionvariables, and constraints that BALMOD uses.However, ASMOD also introduces several newpieces of data, decision variables, and con-straints. Key among these is the parameter dmax,which allows the user to select the maximumnumber of MSG-billet pairs that can be modified,thus enabling MCESG to define the degree ofpersistence required between assignments. Wenow describe the remaining data, decision vari-ables, and constraints introduced by ASMOD(in addition to the data, decision variables, andconstraints used in BALMOD).

Input data:

dmax Maximum number of changes be-tween the existing assignment andthe new assignment

assignoldg ;b MSG-billet assignment in the assign-

ment being modified

Constraints:Xg;bð Þ:assign

oldg;b 5 0

Xc

ASSIGNcg;b

1X

g;bð Þ:assignoldg;b 5 1

1 2X

c

ASSIGNcg;b

!

# 2 � dmax (10)

The objective function in formulationASMOD is the same as that in BALMOD. Like-wise, ASMOD also contains constraint sets 1–9,as well as one additional constraint set. The left-hand side of constraint set 10 calculates thenumber of MSG-billet pairs that differ in as-signment status between the incumbent assign-ment and the new assignment. The first termcounts the number of MSG-billet pairs forwhich an assignment was not made in the in-cumbent assignment and is made in the new as-signment, whereas the second term counts thenumber of MSG-billet pairs for which an as-signment was made in the incumbent assign-ment and is not made in the new assignment.The total number of changes between the in-cumbent assignment and the new assignmentis restricted to be at most 2 � dmax. Note that ifguard g was previously assigned to billet b and



is now assigned to billet b#, then two MSG-billetpairs ((g,b) and (g,b#)) have changed.

RESULTSHaving described the optimization models

implemented by MSGAT, we now turn our atten-tion to an analysis of MSGAT’s performance. Tofacilitate comparison of MSGAT with manual as-signments, MCESG provided all available inputdata from assignment cycles 4–10, 5–10, 1–11, 2–11, and 3–11, where cycle N–YZ is the Nth assign-ment cycle in fiscal year 20YZ. Actual assignmentsmade manually during those cycles were also pro-vided. We now compare assignments producedby MSGAT to MCESG’s manually-generated as-signments using the following MOEs:

1. Percentage of billets that received a requestedexperience level. Although MSGAT attemptsto balance experience levels across detach-ments, individual detachments are also ableto request particular experience levels. MCESGdid not document the number of first, second,and third posters at each detachment in anyof the assignment cycles, making it impossibleto evaluate the degree to which experiencelevels were balanced among detachments.Thus, this MOE measures the number of bil-lets that received a requested MSG experiencelevel instead.

2. Percentage of billets that receive a requestedrank.

3. Percentage of MSGs who are assigned toa new tier (i.e., a tier to which the MSG hasnot previously been assigned).

4. Percentage of billets requesting an A/ quali-fied MSG that receive such an MSG.

5. Percentage of billets at 1/5 posts that receivean MSG. Recall that a 1/5 post is a post withone detachment commander and five watch-standers; in other words, a small embassy.Filling a billet in a 1/5 post is preferred overfilling a billet in a post with more MSGs.

6. Percentage of MSGs who receive a detach-ment preference.

7. Percentage of MSGs who receive a regionpreference.

For each MOE, a high percentage is pre-ferred over a low percentage. Note that this list

of MOEs does not utilize all of the attributeslisted in Table 1; this is because the input datanecessary to consider these attributes was notrecorded by MCESG in previous assignmentcycles.

Attribute WeightsFor each assignment cycle, we used MSGAT

to generate three assignments using attributeweights as shown in Table 2. Each set ofweights was designed by subject matter expertsat MCESG in such a way as to favor the inter-ests of a particular entity within the MCESGorganization.

Recall that a higher weight indicates a moreimportant attribute. The MSG-centric weightsfavor MSG interests such as the MSG’s regionand detachment preferences while maintaininghigh weights on factors that impact MSG safety,such as A/ status and billets at 1/5 Posts. TheRegion-centric weights emphasize attributes thatfavor the interests of regional leadership, suchas experience and rank. The Headquarters (HQ)-centric weights emphasize attributes important atthe HQ level of MCESG, such as assigning MSGsto new tiers. These weights most closely reflectthe decision process and priorities that MCESGcurrently uses when creating assignments.

AnalysisWe now examine MOE satisfaction in assign-

ments generated using MSGAT as compared to

Table 2. Attribute weights for the three MSGAT-generated assignments.

AttributeMSG-centric

Region-centric

HQ-centric

A/ 90 100 1001/5 70 70 70Tier 5 5 40Experience-Request 15 25 15Rank 15 30 5Preferences 50 5 5

Note: Weights for the gender, DC, SSgt select, andexperience-balance attributes are set to 0 becausethe corresponding input data was not documentedfor any of the historical assignment cycles.



MCESG-generated manual assignments. In addi-tion to assignments generated using the attributeweights given in Table 2, several ‘‘single-MOE’’assignments were generated for each set of as-signment cycle data. The single-MOE assign-ments were created to determine the maximumpossible satisfaction of each MOE in each assign-ment cycle; in other words, to determine anupper bound on performance. In single-MOE as-signments, all attribute weights are equal to zeroother than the weight for the MOE being opti-mized; this weight is strictly positive. Figures 2and 3 summarize the performance of MSGAT as

compared to MCESG’s manually generated as-signments for each assignment cycle. We nowdiscuss each MOE and assignment cycle in turn.Note that not all assignment cycles are shown foreach MOE; the assignment cycles presented arethose for which historical data was available.

Billets requiring A/-qualified MSGs: Figure 2ashows the percentage of billets requesting anA/ that received an A/-qualified MSG. MSGATassigns at least 20 percent more A/-qualifiedMSGs to billets requiring them than the manualassignment in every historical comparison. Inthe 4–10 cycle, MSGAT successfully fills the

Figure 2. MSGAT assignments compared with actual (manual) assignments for assignment cycles 4–10, 5–10,1–11, 2–11, and 3–11 with respect to A/ assignments, billets at 1/5 posts, nonrepeat tier assignments, and embassiesreceiving requested experience levels.



maximum percentage of billets requesting anA/ for every MSGAT assignment; the manualassignment satisfies only 78 percent of billetsrequesting an A/. In the 5–10 cycle, MSGATfills the maximum possible percentage of bil-lets with the HQ-centric weights, whereas theMSG-centric and embassy-centric weights fill92 percent of the billets and the manual assign-ment fills only 77 percent. In the 1–11 cycle, themanual assignment satisfies only 67 percent ofbillets requesting an A/, whereas the MSG-centric and embassy-centric assignments eachsatisfy the maximum percentage of the A/-requesting billets.

Billets at 1/5 posts: Figure 2b illustrates thefill percentage of billets at 1/5 posts. Althoughthe manual assignment performs relatively wellaccording to this MOE, MSGAT assignments fillmore billets at 1/5 posts for nearly every assign-ment cycle comparison. In the 4–10 cycle, everyMSGAT assignment results in the maximumpercentage of 1/5 billets being filled, whereasthe manual assignment assigns only 92 percent.In the 5–10 cycle, the HQ-centric assignmentsatisfies the maximum percentage of 1/5 billets,whereas the MSG-centric and embassy-centricassignments result in 83 and 81 percent of billetsat 1/5 posts being assigned, respectively. The

Figure 3. MSGAT assignments compared with actual (manual) assignments for assignment cycles 4–10, 5–10,1–11, 2–11, and 3–11 with respect to embassies receiving requested ranks and MSG preference satisfaction.



manual assignment for 5–10 results in 81 percentof 1/5 billets being filled. The 1–11 manual assign-ment fills 93 percent of 1/5 billets, whereas theembassy-centric and HQ-centric assignments fillthe maximum percentage of 1/5 billets. The man-ual assignment performs the best in cycle 3–11,assigning 98 percent of the possible 1/5 billets.However, all 3–11 MSGAT assignments outper-form the manual assignment by filling the maxi-mum possible percentage of 1/5 billets.

Nonrepeat tier: Figure 2c shows the percent-age of Marines assigned to a nonrepeat tier.MSGAT performs comparably to the manualMCESG assignment in cycles 4–10 and 5–10,while outperforming it significantly in cycle2–11. With respect to the MSGAT assignments,the MSG-centric weights produce solutions thatassign the lowest percentage of MSGs to a non-repeat tier level in all cycles. This occurs becauseMSGs often request to be assigned to a repeattier, even if this tier is undesirable, and in thiscase their requests are honored. Excluding theMSG-centric assignment, the manual assign-ment results in the lowest percentage of MSGsbeing assigned to a nonrepeat tier for every cycle.In assignment cycle 4–10, the embassy-centricand HQ-centric assignments outperform themanual assignment and assign nearly the maxi-mum possible percentage of MSGs to a nonrepeattier level. The MSGAT assignments slightly out-perform the manual assignment in cycle 5–10;however, all assignments assign nearly the max-imum possible number of MSGs to nonrepeattiers. In assignment cycle 2–11, the manual as-signment results in only 75 percent of MSGs be-ing assigned to a nonrepeat tier level, whereasthe HQ-centric assignment results in the maxi-mum percentage of MSGs being assigned to anonrepeat tier level.

Requested experience level: This MOE exam-ines the percentage of billets that receiveda requested MSG experience level and is illus-trated in Figure 2d. As the figure indicates,MSGAT assignments significantly outperformthe manual assignment for all assignment cyclesexcept the 1–11 cycle, in which all assignmentsperform comparably. Note that in general, expe-rience requests are difficult to satisfy, as indicatedby the upper bounds. This is because detach-ments tend to prefer second posters over firstposters and third posters, and there are generally

not enough second posters to satisfy all detach-ment requests.

Requested rank: Figure 3a depicts the percent-age of billets that received a requested MSG rankfor cycles 4–10 and 2–11; MSGAT performs com-parably to the manual assignment in cycle 4–10and outperforms it in cycle 2–11 when using theembassy-centric and HQ-centric weights. Eachof these 2–11 MSGATassignments nearly satisfiesthe maximum percentage of rank requests.

MSG preferences: MSGATassigns two to threetimes more MSGs to their requested posts thanthe manual MCESG assignment. The percentageof MSGs who received a detachment preferenceappears in Figure 3b. As expected, the MSG-centric assignment generates the highest percent-age of MSGs whose detachment preferences aresatisfied, although other MSGAT assignmentsalso assign a high percentage of MSGs a preferreddetachment. The 4–10, 5–10, 1–11, and 2–11 man-ual assignments assign only 18, 23, 33, and 1 per-cent of MSGs to a preferred detachment. With theexception of the 1–11 cycle, the manual assign-ments are significantly outperformed by MSGATassignments. The MSG-centric assignment fromcycle 2–11 results in the highest percentage ofMSGs receiving a detachment preference; it isinteresting to note that this outstanding level ofdetachment preference satisfaction occurs in theassignment cycle with the lowest level of satisfac-tion in the manual assignment implemented.

Figure 3c depicts the percentage of MSGswho receive a region command preference. Incontrast to Figure 3b, the MSG-centric assign-ments do not always result in the highest num-ber of MSGs receiving a region preference. Thishappens because in the MSG-centric weight set,the preference attribute is given the highestweight with respect to the other weight sets.The preference penalties are organized suchthat MSGAT assigns an MSG to a detachmentpreference before a region preference; furtherdetails can be found in Enoka’s master’s thesis(Enoka, 2011). Thus, the MSG-centric weightset has a higher number of MSGs going to a de-tachment preference than a region preference.The manual assignments result in the lowestpercentage of MSGs receiving a region prefer-ence for every historical comparison.

A summary of overall preference satisfac-tion appears in Figure 3d. This figure indicates



the percentage of MSGs who are assigned to atleast one of their preferences (detachment or re-gion). The manual assignment is significantlyoutperformed by the MSGAT assignments inevery historical comparison. Although satisfy-ing MSG preferences is not necessarily a top pri-ority for MCESG, these results demonstrate thatit is possible to satisfy many MSGs’ preferenceswithout sacrificing solution quality with regardto the other MOEs.

Table 3 summarizes the aggregate perfor-mance of MSGAT and the manual assignmentsacross all assignment cycles. We denote the totalpercentage of billets filled satisfactorily with re-spect to attribute k by method m as Pm

k , wheremethod m represents either MSGAT with a par-ticular set of attribute weights, or the actual(manual) assignment. Let Mk,t denote the maxi-mum number of billets that could be filled satis-factorily with respect to attribute k in assignmentcycle t, as indicated by appropriate the single-MOE assignment. Furthermore, let Fm

k;t denotethe number of billets filled satisfactorily withrespect to attribute k in assignment cycle t bymethod m. Then, we calculate Pm

k as

Pmk 5

100 �X

t

Fmk;tX

t

Mk;t

:

DiscussionMSGAT assignments provide solutions that

result in a higher overall satisfaction level thanmanually generated assignments. In nearly allhistorical comparisons, the manual assignmentis significantly outperformed by every MSGATas-signment with respect to every MOE. Performanceis most similar for those MOEs for which themanually generated assignment performs well.

In addition to solution quality, it is also im-portant to consider the time required to producean assignment. The time taken to enter the re-quired input data for an assignment cycle intothe decision support tool was approximately12 hours of work, by one individual. Once thedata was entered and the problem formulated,the computational time was approximately 30seconds on a personal computer. This can becompared with the 1,200 hours it takes for threeMarines within the assignments section atMCESG to enter the data and reach a viable so-lution. Additionally, the time taken to generatea second solution with MSGAT is very low; usu-ally on the order of 60–120 seconds on a personalcomputer. This can be compared with the 1–2weeks required for assignment personnel to gen-erate a second solution.

The main finding of this analysis is thatMSGAT is able to provide solutions that satisfythe MOEs more favorably than the manual as-signment process at MCESG for data frommost historical assignment cycles. The deci-sion support tool provides ‘‘better-fitting’’ as-signments using fewer resources, and in ashorter time period than the current manualassignment process.

SUMMARY AND CONCLUSIONSThis article describes a personnel assignment

tool called the MSGAT. MSGAT implements twointeger linear programs to optimally assign (orreassign) MSGs to billets while balancing MSGexperience across embassies.

MSGAT offers the user a great deal of con-trol over the assignment process. In particular,MSGAT solves the integer linear programsBALMOD and ASMOD to generate assignments.

Table 3. Summary of MSGAT performance and manual assignments. Total percentage of possible billets filledsatisfactorily by manual MCESG assignments and by MSGAT across all assignment cycles (P m

k ).

Attribute Actual MCESG MSG-centric Embassy-centric HQ-centric

A/ 74.7 96.7 95.6 1001/5 90.7 94.0 94.7 100Tier 89.3 86.3 95.6 97.2Experience-Request 57.3 88.0 92.4 91.1Rank 79.3 71.3 96.0 92.7Preferences 27.9 84.7 76.2 73.3



These models solve a minimum-cost networkflow problem on a two-layer multicommoditynetwork in which MSG experience level servesas the commodity. BALMOD is used to make ini-tial assignments, whereas ASMOD is used tomodify existing assignments.

To validate MSGAT and illustrate its useful-ness in facilitating the assignment process, wehave compared MSGAT’s assignments to histor-ical manual assignments from assignment cycles4–10, 5–10, 1–11, 2–11, and 3–11. Assignmentsproduced by MSGAT are superior to the manualassignments on nearly all MOEs for every histor-ical comparison.

The most significant benefit that MSGAT of-fers is a substantial improvement in quality ofMSG security at each detachment. On average,when compared with historical assignments,MSGAT assignments result in more embassiesreceiving A/-qualified MSGs, a higher rate ofbillets at 1/5 posts being filled, a smaller per-centage of MSGs being assigned to repeat tiers,a higher percentage of embassies receivingrequested MSG experience levels, a higher per-centage of embassies receiving required MSGranks, and a higher percentage of MSGs beingassigned to one of their preferences. These fac-tors combine to make a more satisfactory assign-ment picture at all levels. Not only does MSGAToutperform the manual assignments with respectto overall MOE satisfaction, but it also signifi-cantly reduces the amount of time spent byMCESG creating assignments and allows MCESGto focus on other important responsibilities.

ACKNOWLEDGEMENTSThis study was sponsored by the Marine

Corps Operations Analysis Division (OAD)with additional support from the Office of Na-val Research (ONR). The authors would like tothank the Marine Corps Embassy SecurityGroup (MCESG) Assignments Section for theirassistance.

AUTHOR STATEMENTThe authors’ views expressed in this arti-

cle are made available for the purpose of peer

review and discussion and do not necessarilyreflect the views of the United States MarineCorps, the Department of the Navy, the De-partment of Defense, or the United Statesgovernment.

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Optimizing Marine Security Guard Assignments