2013 Optimizing Intratheater Military Airlift in Iraq …Calhoun: The NPS Institutional Archive Faculty and Researcher Publications Faculty and Researcher Publications 2013 Optimizing

Calhoun: The NPS Institutional Archive

Faculty and Researcher Publications Faculty and Researcher Publications

2013

Optimizing Intratheater Military Airlift in

Iraq and Afghanistan

Brown, Gerald G.

Brown, G.G., Carlyle, W.M., Dell, R.F., Brau, J.W., 2013, "Optimizing Intratheater Military Airlift

in Iraq and Afghanistan," Military Operations Research, 18(3), pp. 35-52.

http://hdl.handle.net/10945/38129

ABSTRACT

The Air Tasking and Efficiency Model(ATEM) has been used since 2006. Itsdevelopment was motivated by an

urgent need to plan and evaluate intratheaterairlift of passengers and palletized freightfor Operation Iraqi Freedom in Iraq andOperation Enduring Freedom in Afghani-stan. ATEM plans routes and aircraft config-urations (capacity of passenger seats andpallet positions) for a heterogeneous fleet ofaircraft flying between multiple airfields.ATEM respects limits on crew duty periods,times and abilities of each airfield to handleand fuel each aircraft type, and aircraft speedand carrying capacity. Initially, ATEM ad-vised improving daily and weekly routeensembles, conveying more passengers andpallets and using fewer aircraft than priormanually generated solutions. This earlyuse reduced the required number of groundconvoys and thereby exposure to impro-vised explosive devices. Later, ATEM advisedwhere to advantageously move aircraft tonew home airfields, how to shift aircraftbetween theaters, and when to bring aircrafthome from war.

That I have hoisted sail to all the winds,which should transport me farthest

from your sight.Shakespeare, Sonnet

INTRODUCTIONThe logistics of transporting, arming,

feeding, clothing, sheltering, and fueling hun-dreds of thousands of personnel involvedwith our military operations in Iraq andAfghanistan has been a daunting challengefor US Central Command (CENTCOM),the unified combatant command whose areaof responsibility includes those countries.The CENTCOM Deployment and Distribu-tion Operations Center (CDDOC) at CampArifjan, Kuwait, receives specific demandsignals and manages what is essentially thelast echelon in a world-wide supply chain.This echelon conducts intratheater move-ment of materiel, using convoys of trucksand, when possible, airlift, to move person-nel and their equipment to where they areneeded in support of military operations.

In 2005 the CENTCOM commander di-rected US military leaders to do everything

within their powers to reduce the number ofground convoys and thus reduce exposureof personnel to the ever-increasing numberof improvised explosive devices. The direc-tor of CDDOC pressed his staff, ‘‘We cannotfly everything, but we need to fly every-thing we can.’’

The United States Transportation Com-mand divides intratheater air routes intotwo broad categories, frequency channelroutes and requirements channel routes(United States Transportation Command,2005). Frequency channel routes are pub-lished in a schedule, much like an airline,based on anticipated demands for a giventime period. Requirements channel routesare decided each day, and move emergentdemand as necessary. Author Brau wasstationed at Camp Arifjan in October 2005,and at that time he found that air plannerswere manually scheduling CENTCOMintratheater airlift using basic tools such aswhiteboards and simple Microsoft Excelspreadsheets to keep track of assets and ma-teriel. He immediately started working onan optimization model to assist planners increating the requirements channel routesand prescribing air and ground movementof passengers (PAX) and air freight pallets(PALS), hereafter referred to collectively ascargo. He contacted the other authors soonafter he started this effort, and by December2005 our team had begun development ofa decision support tool called the Air Trans-portation and Efficiency Model (ATEM) forquickly creating requirements channel routes,to help clear backlogged cargo, and to designhigh-quality weekly frequency channel routesfor future demands. The solutions providedby ATEM maximize the flow of PAX andPALS on intratheater airplanes: by analyzingdaily operations data, we realized this pre-sented the greatest opportunity to make asignificant near-term improvement.

ATEM would be of little utility withoutan interface making it easy for nonanalystplanners to understand and use. So, we de-veloped a portable, laptop-based graphicaluser interface using Microsoft Excel andVisual Basic (Microsoft, 2012a,b), and amathematical modeling suite includingthe General Algebraic Modeling System(http://www.gams.com) and several com-mercial optimization packages. A trip toKuwait by two of our co-authors confirmedthat such a decision support tool would bea significant improvement in both frequency

OptimizingIntratheaterMilitaryAirlift inIraq andAfghanistan

Dr. Gerald G. Brown,Dr. W. Matthew Carlyle,and Dr. Robert F. Dell

Naval Postgraduate [email protected],[email protected],[email protected]

John W. Brau, Jr.

USTRANSCOM / [email protected]

APPLICATION AREAS:Airlift, Vehicle Routing,Convoy Mitigation,IED Mitigation,Decision Support

OR METHODS:Optimization,Spreadsheets, Heuristics

Military Operations Research, V18 N3 2013, doi 10.5711/1082598318335 Page 35Military Operations Research, V18 N3 2013, doi 10.5711/1082598318335 Page 35

and requirements channel planning, and helpedsolidify the structure of the model based on ourdirect experience with air logistics in Iraq andon our discussions with planners in theatre.

MILITARY AIRLIFT PLANNING TOOLSOur intratheater distribution problem is

a variant of the vehicle routing problem (VRP)(Dantzig and Ramser, 1959). The objective ofVRP is to design a set of routes for a given fleetof vehicles that satisfies customer demands atdispersed locations from one or more depots,at lowest cost. Side constraints added to the ba-sic VRP create variants of the problem. Typicalvariants include the capacitated vehicle routingproblem, where vehicles have limited capacity,the vehicle routing problem with pickups anddeliveries, where customers can both receivematerial from and return material to a depot,the vehicle routing problem with time win-dows, where visits to customers must be madewithin a specified time epoch, and the shuttlingproblem, where each customer is both an originand a destination for shipments from and toother customers, and the dial-a-ride problem,where customer pickups and drop-offs aremerged into a set of vehicle routes. See Tothand Vigo (2002) for a survey of VRP problemsand solution techniques.

We find intratheater airlift as required inOperation Iraqi Freedom (OIF) and OperationEnduring Freedom (OEF) to be a unique VRP.Feillet, Dejax, and Gendreau (2005) present theprofitable arc tour problem that shares muchin common, but in addition to the features theydescribe we also must plan for multiple depots,multiple (here, two) types of cargo capacity oneach vehicle, and a limited heterogeneous vehi-cle fleet.

Joint Pub 3-0 (Joint Chiefs of Staff 2001) de-fines three levels of war: strategic, operational,and tactical. Military logistics must enable oper-ations at all three levels. The Joint Staff andservice staffs concentrate on strategic logisticsmatters. Combatant Commanders (COCOM)link strategic- and operational-level logistics.Finally, subordinate commanders blend oper-ational and tactical logistics to accomplishmissions assigned by the COCOM (Joint Chiefs

of Staff 2000). Strategic distribution, the move-ment of forces from Continental US (CONUS)bases into a theater of operations, flows alongintertheater distribution channels. Operationaldistribution, the movement of materiel withina COCOM theater, flows along intratheater logis-tics channels. VRPs are inherent in both inter-theater and intratheater distribution, and theDepartment of Defense employs many tools tosolve both these problems.

The major strategic distribution models inuse when we started ATEM and still in use to-day are the Global Deployment Analysis Sys-tem (GDAS), Joint Flow and Analysis Systemfor Transportation (JFAST), Model for Inter-theater Deployment by Air and Sea (MIDAS),the Mobility Simulation Model (MobSim), andthe Consolidated Air Mobility Planning System(CAMPS). Barnes and McKinzie (2004) surveythese systems. In addition to these, other simu-lation models in use today include the AirMobility Operations Simulation (AMOS) andthe Analysis of Mobility Platform (AMP).

GDAS uses alternating greedy cargo andgreedy vehicle heuristics combined with routeinsertion to assign passengers to modes of trans-portation (air, ground, and sea) for transportbetween points of CONUS embarkation topoints of debarkation in some area of operations.JFAST employs local search to plan strategiclift from CONUS to some deployment area ofoperations (see Koprowski [2005], and his refer-ences for a summary). MIDAS is a simulationthat represents strategic deployment of unit per-sonnel and equipment by air and sealift intotheater ports of debarkation (Military SurfaceDeployment and Distribution TransportationEngineering Agency Command, 2005). MobSimis a network-based discrete event stochasticmodel. CAMPS, the replacement for both ADANS(Air Mobility Command Deployment AnalysisSystem) and CMARPS (Combined Mating andRanging Planning System), is a heuristic plan-ning tool (Becker et al., 2004). AMOS is a rule-based, discrete-event simulation of worldwideairlift with the ability to model detailed air toair refueling and airfield congestion (see Mason[2009] and Wu and Powell [2009]). AMP is a sim-ulation that includes MIDAS and other legacysimulation models (Raytheon, 2013). Noel andStratton (2012) catalog the portfolio of more

OPTIMIZING INTRATHEATER MILITARY AIRLIFT IN IRAQ AND AFGHANISTAN

Page 36 Military Operations Research, V18 N3 2013

than 40 models (including those referencedabove) that have had some use at Air MobilityCommand.

Intratheater distribution tools are less com-mon. Barnes et al. (2004) provide approximatesolutions to an intratheater VRP with a tabusearch metaheuristic, but we know of no instal-lation of their product. They claim that, at thetime of publication of their paper, all other the-ater distribution tools were simulation-based.These include ELIST (Enhanced Logistics Intra-theater Support Tool), TRANS (TransportationResource Assessment Network Simulator), andMASS (Mobility Analysis Support System).Transway (Pohl 2006) uses a tabu search meta-heuristic to help plan intertheater (and intra-theater) distribution. Burks et al. (2010) alsotackle intratheater distribution with tabu search.We have no evidence that either of theseproducts were ever used by the Departmentof Defense.

ATEM INTEGER LINEAR PROGRAMFORMULATION

We present an integer linear program (ILP)formulation of ATEM. ATEM takes as input a listof airport pairs and the number of PAX andPALS traveling between them; each of thesepairs and associated demands is known asa demand line, because it is represented by a sin-gle line on a demand spreadsheet used by theplanners.

ATEM also takes as input a (typically verylarge) list of routes, each of which is specific toan airplane type and to a particular configurationof that airplane. A route for one airplane onone day consists of a sequence of flight legs,where each leg is a single nonstop flight be-tween an origin and a destination airfield. Thefirst leg departs from the airplane’s home airfield,and the last leg returns to this same home air-field. Each route consists of a feasible sequenceof flight legs, in that the associated aircraft can,in one day, make all of the flights on the routein the sequence given without violating any op-erational restriction or resource requirement(such as fuel and total flight time).

This route and configuration data allowsATEM to determine which demand lines can

be served by each route and what capacity, interms of PAX and PALS, it can lift on each flightin that route: any cargo from a demand linewhose origin precedes its destination on thatroute could conceivably be carried by an aircraftflying that route, although it might require sev-eral flight legs to get there. ATEM allows suchloading of cargo and carrying it through oneor more intermediate airfields before unloadingit at its destination (planners call this through-put); the number of legs per load is controlledby a single parameter, maxloadhops, (where thenumber of hops a particular piece of cargo makesis just the number of consecutive flight legs be-tween its origin and destination), and settingthis parameter to one prevents any throughput(i.e., every passenger or pallet can travel on atmost one leg in a route).

Finally, for each airport ATEM needs toknow the maximum number of landings allowedeach day, and the number of aircraft of each typethat are based at that airport. Given an enumera-tion of every admissible route for each aircrafttype, configuration, and home airport, ATEMseeks an optimal assignment of a single routeto each aircraft and an allocation of cargo to thoseroutes that maximizes (prioritized) PALS andPAX conveyed. It may not always be possibleto fill each flight on a route with cargo. For in-stance, an empty flight (a deadhead) may be neces-sary to reposition an airplane, or to bring it backhome at the end of its route.

Indices [;cardinality]a 2 A set of airfields (alias ai ,aj ) ;20½ �c 2 C set of cargo types (passengers

and cargo pallets) ;2½ �p 2 P set of airplane types ;5½ �p 2 Pai

set of airplanes of type p basedat airfield ai

g 2 Gp set of configurations for air-plane type p ;5½ �

ai ; aj

� �2 L set of possible flight legs or

segments (airport of embarka-tion (APOE), airport of debar-kation (APOD) pairs) ;100½ �

r 2 Rpaiset of routes for airplane type pstarting at airfield a # 100; 000½ �

s 2 1; 2;.; Sf g ordinal of stop on a route (aliass#,so) [;7]


Military Operations Research, V18 N3 2013 Page 37Military Operations Research, V18 N3 2013 Page 37

Datalenr number of stops on route raðr ; sÞ airfield at stop number s on route

r, where 1 # s # lenr

carryaiaj cr amount of cargo c on leg ai ; aj

� �that

can be airlifted by route rcpaiaj c priority of cargo c on leg ai ; aj

� �

demaiaj c demand units on leg ai ; aj

� �for

cargo ccaprc capacity on route r of cargo type clanding a maximum number of landings in

airfield aplanespa number of airplane type p starting

from airfield amaxloadhops the maximum number of consecu-

tive legs the cargo from a singledemand line can travel on one route

Calculated Setsðs; s#Þ 2 Hr stop s’ comes after, and within

maxloadhops of, stop s on route r:1 # s , s# # lenr , s# 2 s # maxloadhops

VariablesSELECTr integer number of times airplane

type p(r) is flown on route rLOADrss#c integer cargo units airlifted by air-

plane type p(r) flying route r fromAPOE airfield s to APOD airfields#of cargo type c

ATEM-ILP Formulation

MaximizeX

r;ðs;s#Þ2Hr;c

cpaðr;sÞaðr;s#ÞcLOADrss#c (1)

Subject to:X

r2Rpai

SELECTr # planespai"ai 2 A; p 2 Pai

(2)

X

r; s; s#:ðs; s#Þ2Hr;aðr; sÞ5ai;aðr; s#Þ5aj

LOADrss#c # demaiajc "ðai; ajÞ 2 L; c

(3)

X

ðs; s#Þ2Hr :

s# so, s#

LOADrss#c # caprcSELECTr

"r; 1 # so, lenr; c (4)

X

r; s#:1, s## lenr;aðr; s#Þ5aj

SELECTr # landingaj"aj 2 A (5)

The objective function (1) calculates thepriority-weighted value of all cargo conveyedon all routes. For each airfield and each air-plane type based there, constraint (2) limitsthe number of routes selected to the numberof airplanes available. For each demand lineand cargo type, constraint (3) prevents air-planes from lifting more that the demandavailable and accounts for any extra lift capac-ity available. For each route, and each stop onthat route that is not the last stop, and each cargotype, constraint (4) limits loading on the flightdeparting that stop by the airplane capacity foreach cargo type, for the configuration used onthat route. For each airfield, constraint (5) limitstotal daily landings by all routes selected; notethat each route may land at an airfield morethan once, and may carry portions of some de-mand line on two or more legs.

In the special case where maxloadhops ¼ 1,the capacity available on each flight leg on a routeis just the capacity of the aircraft assigned to theroute, because the aircraft is completely emptiedat each stop on the route. We can simplify themodel and eliminate many constraints and allof the LOAD variables by defining a new set ofvariables, called EXTRA, that measure the un-used capacity on each leg of each route selected.The ‘‘Solving ATEM’’ section of this papermore fully discusses the benefits of thissimplification.

New VariablesEXTRAaiajc unused capacity of selected routes

for cargo c, on leg ai; aj

� �

With these variables accounting for the overallloading of each leg on the route we can removethe LOAD variables and replace constraints (3)and (4) with:



X

r

carryaiajcrSELECTr # demaiajc

1 EXTRAaiajc "ðai; ajÞ 2 L; c; (6)

which explicitly accounts for unused space oneach flight in a route, and replace the objectivefunction with:

MaximizeX

ðai;ajÞ2L;c;r

cpaiajccarryaiajcr SELECTr

2X

ðai;ajÞ2L;c

cpaiajc EXTRAaiajc; (7)

which calculates the total carrying capacity ofeach route, and then subtracts any unused capac-ity to arrive at the total amount of cargo lifted.

ATEM also allows, for each aircraft, the selec-tion of a different route on each day of a multidayplanning horizon (e.g., one week). For simplicityof exposition, we have not included a day index,although one exists in ATEM. However, becauseairplanes return to their home airbase after eachday of flying, the days in a plan are only linkedby the cargo remaining to be lifted.

Figure 1. Map of Iraq indicating a sample of airfield locations by dots. Al Udeid (located 350 nautical miles to the south-east) in Qatar, and Incirlik (located 325 nautical miles to the northwest) in Turkey, are not shown. (After National Im-aging and Mapping Agency, 2003; http://www.lib.utexas.edu/maps/middle_east_and_asia/iraq_planning_2003.jpg)



CENTCOM INTRATHEATER AIRLIFTWe consider the frequency and requirement

channel route selection problems faced by theCENTCOM Combined Air Operations Center(CAOC), located at Al Udeid Air Force Base,near Doha, Qatar in 2005 and 2006.

Airfield Locations and Demand DataWe used about 20 airfields to support intra-

theater air distribution in Iraq, including severaloutside the country; Figure 1 shows locations ofsome of these for distribution in Iraq. Table 1 pro-vides an excerpt from a longer sheet of demandlines. Each demand line expresses the numberof PALS and PAX that need to be transportedbetween an APOE and an APOD. A standard‘‘463L’’ pallet is 88 inches long by 108 incheswide, and each carries a maximum of 10,000pounds (Department of the Army, 1993). A pas-senger represents a single person and personalgear.

Our overall objective is to maximize the pri-oritized number of PAX and PALS lifted, wheresome PAX and PALS have different prioritythan others (e.g., delayed, or frustrated, cargomight be given a higher priority to encourageclearing out the backlog). Each cargo type andeach individual demand line is assigned a pri-ority. ATEM multiplies each demand by its cargotype priority and by its line priority, and maxi-mizes the total resulting prioritized demandthat is moved. Table 1 is an example of such de-mand data, including demand line priorities.Data presented in this table and the remainingtables are a sample of possible ATEM inputvalues provided by CENTCOM planners for un-classified use. Planners can change the values ofthese ATEM input parameters at will as the situ-ation dictates. Figure 2 presents a summary ofone week of demand for pallets and passengersin Iraq.

Airplanes and Load ConfigurationsThe number and types of airplanes available

for distribution also varies, but usually consistedwhen ATEM was first used of about 35 airplanesof five different types for CENTCOM intra-theater airlift, including C-130E (see Figure 3),

C-130J1, C-130J2, C-17 (see Figure 4), and IL-76.Each airplane type, with the exception of theIL-76, can be flown in any of a number of alter-nate configurations, with each configuration pro-viding the passenger seat and pallet positioncapacities. Table 2 lists configurations by airplanetype (with the exception of C-130J2) along withassociated passenger and pallet capacities.

Airplane and aircrew endurance limit thelength of a route, as shown in Table 3, which alsoshows a sample of possible fuel and crew con-straints that limit routes. ‘‘Max #landings in

Table 1. Example of demand lines, each with an or-igin and destination airfield, a number of PAX andPALS to carry, and a priority. There are 126 passengersand one pallet to fly from Al Salem to Alasad, with pri-ority one. By contrast, the 44 passengers and one palletto fly from Al Salem to Tallil have priority 100, signi-fying each of these PAX and PALS is 100 times moreimportant to carry than a priority 1 demand. Priorityis a simple way to highlight frustrated cargo. This de-mand may be for a day, a week, or some longer plan-ning epoch.

APOE AOPD PAX PALS PRIORITY

Al Salem Alasad 126 1 1Al Salem Al Taq 159 1 1Al Salem Balad 108 5 1Al Salem Baghdad 273 3 1Al Salem Mosul 47 4 1Al Salem Kirkuk 33 2 1Al Salem Q West 5 3 1Al Salem Al Sahra 51 1 1Al Salem Tallafar 52 2 1Al Salem Tallil 44 1 100Al Salem Al Udeid 113 8 1Alasad Al Salem 117 1 1Alasad Al Taq 17 3 1Alasad Balad 7 2 1Alasad Al Udeid 5 2 1Al Taq Al Salem 135 6 1Al Taq Kuwait 1 7 1Al Taq Alasad 14 17 1Al Taq Balad 2 2 1Al Taq Baghdad 2 1 1Al Taq Al Udeid 3 1 1Balad Al Salem 288 3 1Balad Kuwait 4 8 1Balad Alasad 6 2 1Balad Al Taq 7 5 1Balad Baghdad 13 7 1Balad Mosul 10 6 1



box before recrew’’ represents the number oflandings into a combat area, where approachand departure involve evasive tactical maneu-vers, and may be conducted at night withoutlighting. In addition to these constraints, plan-ners also limit the maximum number of stopsan airplane can make during a route. For exam-ple, a C-17, which is nominally based outsideIraq, can make no more than three landings inIraq before it needs to return to its home base.However, it can recrew, and return to land in Iraqat most three more times before returning to itshome airfield.

Airfield CapabilitiesTable 4 is a sample of ground times at air-

fields by airplane type. Similarly, Table 5 samplesairfield refuel times by airplane type. Table 6 lists

airplane home airfields and the numbers of air-planes based at each. Flying times between air-fields are given for each airplane type. Otherinput includes the number of landings permit-ted at each airfield per day, as well as the abilityof each airfield to accommodate each airplanetype.

ROUTE GENERATIONGiven demand data, a fleet of airplanes with

their home airfields, and a time horizon, ATEMprescribes a configuration and a route for eachairplane on each day in the planning horizon thatmoves as much cargo as possible.

A complete flight ensemble specifies a routefor each airplane on each day in the planninghorizon. We have discovered, by hand, that

Figure 2. PALS and PAX demand for a seven-day Iraq scenario. Pallet demands are depicted in the upper,darker bar segments. There are about 20x20¼400 airfield pairs, but only 85 of these have demand lines here. De-mand lines vary widely in magnitude, and include some pure-passenger and some pure-pallet demands. Airfieldpairs are suppressed for brevity.

Figure 3. C-130E at Al Udeid. The tail ramp is positioned to transfer cargo pallets by fork lift or roll-on, roll-offk-loader vehicle. The C-130 has a single roller-rail track for manually pushing cargo pallets forward, or aft, or off.For scale, author Dell is standing under the inboard starboard engine. In the image on the right, an aircrew mem-ber folds up hammock seats in a configuration change to make room for another cargo pallet.



conjuring these routes while synchronouslydetermining their joint feasibility and effective-ness is the crux of solving this problem. Manualplanning experience suggests thumb rules thatcan be a good guide here, but no manual plannercan be expected to solve this complex problemevery day with anything approaching optimality.There are a number of well-known ways to auto-mate route construction. In this case, there arefew enough airfields, and few enough demandlines, and each route can include at most fewenough hops, that we can enumerate every feasi-ble route, and thus not worry about missing anygood one. For each airplane and its origin air-field, ATEM successively constructs every possi-ble permutation of airfield-hops that can bevisited in one duty period, ending with a returnto the origin airfield. Simple rules, such as neverflying two deadhead legs in a row, help limit thenumber of routes. Additional rules eliminateroutes lacking a required refuel or crew replace-ment event.

We define a directed graph G ¼ (N, A) withnode set N defined by a start node s, an endnode t (here, s ¼ t), and an intermediate eche-lon of nodes for every stop on a route up tomaxroutehops-1. For specificity, each of these in-termediate nodes is named (airfield, hop num-ber). We specify a directed arc in A connectingeach node with ‘‘hop number’’ with every othernode with ‘‘hop number11’’ to which we mightfly directly.

Given a flight time tij . 0 for each arc (i, j) inA, and a threshold value T[MAX ROUTE HRS,the pseudocode in Figure 5 enumerates the fi-nite number of s-t paths of length bounded by T.

For simplicity of exposition, we do not clut-ter this algorithm with the admissibility tests forrefueling requirements along the route, the min-imum and maximum route lengths, or the max-imum number of flights (hops) per route (seeTable 3 for examples of these data). However,these tests are easily included at the same pointin the algorithm as the test for total route time.Although in general the number of paths in asingle graph can be exponential in the numberof nodes in the graph, for the OIF and OEF caseswe have examined we can accommodate exhaus-tive enumeration. With data similar to that pre-sented here, we generate on the order of a fewhundred thousand feasible routes.

Filtering routes to limit the minimum num-ber of hops, the maximum number of landings‘‘in the box,’’ and so forth, is a simple matterof keeping track of these numbers, suppressingthe complete routes that do not meet the lowerthresholds and fathoming enumeration of par-tial paths as soon as they exceed the upperthresholds.

Routes are generated separately for eachairplane type and each origin home airfield forthat airplane type. Any route longer than thegiven maximum time before refueling for thatairplane type requires a (single) stop at a refueling

Figure 4. C-17 at Al Udeid. The aft k-loader vehicles are receiving rows of passenger seats pushed off (and aban-doned until a later evolution here) in a configuration change to accommodate more cargo pallets. The C-17 hastwo, parallel roller-rail tracks for manually pushing cargo pallets forward, or aft. For scale, on the right, authorsBrau and Dell appear standing on the tail ramp, working through the details of load configuration changes withthe airplane’s loadmaster.



airfield between minimum time before refuel andmaximum time before refuel. Similarly, for an air-plane type with a crew replacement restriction(i.e., maximum number of landings in the box be-fore crew replacement is a small integer, such asthree) any route must return to its origin airfieldbefore the number of landings at airfields ‘‘in thebox’’ following the last landing at the origin air-field exceeds this limit. Routes violating either re-quirement are suppressed.

We find that selecting a feasible ensemble ofroutes that moves a large amount of cargo isrelatively straightforward once we have enu-merated all the feasible routes. This feasible

ensemble could be used as an initial incumbentfor a local search heuristic. However, we seeka certificate of optimality for our solutions, sowe use the integer linear program in the ‘‘ATEMinteger linear program formulation’’ section tochoose an optimal set of routes (out of all feasibleroutes) and to establish an upper bound on howmuch additional cargo could have been moved.

SOLVING ATEMThe ATEM integer linear programming

model has hundreds of thousands of variablesand constraints for the optimization model withthroughput, and tens of thousands of constraintsfor the reformulation without. If throughput isnot allowed we can solve all of our problem in-stances using, e.g., GAMS/CPLEX [2012]. If weallow throughput (i.e., maxloadhops . 1), thenthe integer programs become significantly largerdue to the quadratic dependence on maxloadhopsof the number of LOAD variables. Some casescan still be solved with CPLEX, but we find thatthe execution times are much longer than in thecase of no throughput. Schedulers do not haveimmediate access to commercial solvers, so wedeveloped a companion heuristic algorithm toprovide good solutions to ATEM in a veryshort runtime. Our basic heuristic consists ofdata preprocessing followed by greedy selec-tion of routes. The preprocessing reduces de-mand lines that appear on routes that mayhave been fixed by the planner. After generat-ing all of the routes a greedy heuristic makesa single pass through the list of aircraft (andtheir home cities) and for each of those andfor each day in the planning horizon it choosesthe route that maximizes lift of remaining cargo(without throughput) on that route, assigns thatroute to that aircraft on that day, and thenremoves that lifted cargo from those demandlines. In contrast with the ILP, the heuristic doesnot consider throughput. Bridges [2006] de-scribes two additional iterative improvementsteps to improve a greedy solution. He also con-siders generalizing relaxations including air-plane configuration changes during a route,and throughput.

The results worksheet (Figure 6) serves asboth an output display and an important input.

Table 2. Load configurations by airplane type withpassenger and pallet capacities. A C-130E has passen-ger hammock seats that can be folded up or moved outof the way to make room for cargo pallets to be pushedaboard on a roller rail and can carry between zero andfive cargo pallets with each additional pallet configura-tion reducing passenger capacity in discrete steps from72 down to nine. Configuration changes don’t takelong, and some can be completed in-flight in anticipa-tion of the next load. By contrast, the C-17 has two par-allel cargo pallet roller rails, and some configurationchanges require rows of passenger seats mounted onthese rails to be rolled off and left on airfield, to be re-covered later. These configuration changes are betterassisted by special ground vehicles called k-loaders.The IL-76 is chartered to carry pallets only. (Notlisted: C-130J2.)

ConfigurationAirplane

typePassengercapacity

Palletcapacity

Acp2 C-130E 9 5Acp3 C-130E 25 4Acp4 C-130E 42 3Acp5 C-130E 56 2ap1 C-130E 72 0jac2 C-130J1 0 8Jacp2 C-130J1 18 7Jacp3 C-130J1 34 6Jacp4 C-130J1 50 5Jacp5 C-130J1 60 4Jacp6 C-130J1 74 3Jacp7 C-130J1 94 2jap1 C-130J1 115 1C17c C-17 0 18C17cp C-17 54 11C17p C-17 189 4Ilc IL-76 0 9



The planner can use ATEM repeatedly to refinea plan. The planner can designate the first col-umn of a favored route with ‘‘fix’’ and the num-ber of days the route will be repeated by aspecific airplane. Subsequent ATEM route revi-sions will honor this guidance. These distin-guished routes have either been automaticallygenerated by ATEM, or manually entered bythe planner. Because ATEM considers all admis-sible routes, the only reason for a planner to keyin a route is to violate some business rule ATEMwould honor.

The routes selected worksheet in Figure 7will indicate a planned refueling by a prefix,for example, ‘‘F_Al_Salem.’’ A planned crew-replacement event would appear ‘‘C_Al_Salem.’’If any passenger or cargo is carried for more thanone hop, this exception would appear as an inter-mediate line tracing the throughput in additionto the customary one-hop results shown.

EXAMPLESWe present four representative scenarios of

intratheater airlift for Iraq and Afghanistan in2005 and 2006. The first and smallest of theseis a single-day requirement for logistics distri-bution to and within Afghanistan. Our secondscenario is for a seven-day planning horizonthat suggests frequency channels in Iraq. Next,we test a large, single-day distribution require-ment within Iraq. Finally, we show how toparametrically remove airplanes from a chan-nel design. The ATEM-ILP integer linear pro-gram is generated by GAMS (2012) and solvedwith GAMS/CPLEX 12.3 (2012) on a 3-GHz lap-top, using a value of 0.01 for the relative optimal-ity criterion (CPLEX terminates after finding asolution that is guaranteed to be within 1% ofoptimal).

Table 3. Route limitations by airplane type. Limitations include the maximum time an airplane can operate, timebetween refueling, number of landings in the box, and number of times an airplane can replace aircrews. Eachroute for each airplane type is also limited by some Max Route Hops number of landings.

Airplane type C-17 C-130E C-130J1 C-130J2 IL-76

Max route time (hrs) 12.00 9.50 9.50 9.50 12.00Max time before refuel (hrs) 12.00 5.00 5.00 5.00 12.00Min time before refuel (hrs) 12.00 3.00 3.00 3.00 12.00Max #landings in box before recrew 3 20 20 20 20Max number recrews 1 0 0 0 0

Table 4. Sample of airfield ground times. Groundtime varies by airfield and airplane type. In this exam-ple, a C-17 requires 45 minutes on the ground at Balad,while all other airplane types require 30minutes there.

Ground time (mins)

Airfield C-17 C-130E C-130J1 C-130J2 IL-76

Alasad 45 60 60 60 60Al Taq 45 30 30 30 30Balad 45 30 30 30 30Baghdad 45 60 60 60 60Mosul 45 30 30 30 30Kirkuk 45 45 45 45 45Basrah 45 45 45 45 45Q West 45 45 45 45 45Al Sahra 45 30 30 30 30

Table 5. Sample of airfield refueling times. Refuel-ing is concurrent with ground time. For example, ifa C-17 requires refueling in Balad, its total groundtime is 90 minutes. All other airplanes require 75minutes on the ground to refuel at Balad. An ‘‘n’’ in-dicates that the airplane type cannot refuel atthat airfield.

Refuel time (mins)

Airfield C-17 C-130E C-130J1 C-130J2 IL-76

Alasad 90 60 60 60 60Al Taq 90 60 60 60 60Balad 90 75 75 75 75Baghdad 90 90 90 90 90Mosul n n n n nKirkuk 90 75 76 77 77Basrah n n n n nQ West n n n n nAl Sahra n n n n n



Afghanistan ScenarioOur Afghanistan scenario has a total de-

mand of 404 PAX and 844 PALS on 40 demandlines that require transport among 14 airfields.Figure 8 provides an overview of the initial de-mand distribution among these 40 demand lines.The maximum demand line represents 152 PAXand PALS, and the minimum has just one PAXor one PAL. There are 14 airplanes available;six C-130Es at Bagram and eight C-17s at AlUdeid. Route limitations by airplane type are asshown in Table 3. For example, the maximumroute time for a C-130E is 9.5 hours and the max-imum route time for a C-17 is 12 hours. Enumer-ation yields 1,916 possible routes.

ATEM ILP solves in about three seconds,and uses all 14 airplanes. This solution trans-ports 155 of 404 PAX and 398 of 844 PALS, airlift-ing 44.3% of unit demand. Our greedy heuristictakes slightly less time to solve, and does just aswell in this case. Even though we do not moveall the demand, ATEM-ILP certifies that this isan optimal solution: we know this is the bestthat can be done with this airplane fleet. Havingsuch a certificate was important in early testingand acceptance of ATEM, especially given thatsome air planners evaluate a route ensembleby the fraction of available PAX seats and PALspots filled.

Seven-Day Iraq ScenarioOur seven-day Iraq scenario has 17,704 cargo

units on 85 demand lines that require movementamong 17 airfields. Of this demand, 15,677 arePAX, and 2,027 are PALS. Figure 2 provides anoverview of this demand. For this scenario, wehave 30 airplanes available, and Table 7 lists the

number of airplanes available by airplane typeand home airfield. We assume that each airplanecan fly each of the seven planning days. Table 3provides route restrictions for each type of air-plane. There are 272,024 possible routes to fly sat-isfying these restrictions.

Generating all routes takes less than a min-ute. The ATEM-ILP solves in about two minutesand the heuristic takes about the same amountof time. Both the ILP and HEURISTIC move al-most all the demand.

Single-Day Iraq ScenarioOur single-day Iraq scenario has 505 pas-

sengers and 645 pallets on 82 demand linesconnecting 17 airfields. Figure 9 provides anoverview of this demand. Table 8 lists the typesand home airfields of the 29 airplanes available.Airplane restrictions are the same as those inthe Iraq seven-day scenario. ATEM generates207,121 feasible routes.

Generating all routes takes less than a min-ute. ATEM-ILP solves in about 16 minutes andthe ATEM-HEURISTIC takes about a minute.The ILP plan moves 1,059 of the required 1,150demand units (92.1%); 445 PAX (88%) and 614PALS (95%). The ATEM-HEURISTIC plan moves1,044 demand units (90.8%); 456 PAX (90%) and588 PALS (91%).

Removing Airplanes from the Seven-Day Iraq Frequency Channel Design

Table 9 shows a sequence of planning runsthat successively restricts the available aircraftfleet for the frequency channels. Depending onexigent priorities, and how accurate you thinkthe general future demand forecast is, such

Table 6. Home airfields with associated airplanes. In this example, there are two C-130Es and four C-17s at AlUdeid, six C-130Es at Balad, 14 C-130Es at Al Salem, two IL-76s at Kuwait International, and one C-17 at Incirlik.Each airplane starts and ends each daily duty cycle at its home airfield.

Homebase C-17 C-130E C-130J1 C-130J2 IL-76

Al Udeid 4 2 0 0 0Balad 0 6 0 0 0Al Salem 0 14 0 0 0Kuwait International 0 0 0 0 2Incirlik 1 0 0 0 0



a study can help commanders decide where andwhen to draw down (i.e., reduce the number of)airplanes.

Table 9 also shows how quickly ATEM canprovide decision support by either solving thefull integer linear program or by using thegreedy heuristic. We use ATEM to check onthe performance of our heuristic, and to get a so-lution quality certificate on any feasible solutionwe have, whether generated automatically byATEM or the heuristic, or manually by a planner.

WHAT ATEM DOESN’T DO, AND WHYATEM suggests a set of routes, and we use

the term ensemble, rather than ‘‘schedule,’’ as acollective noun for these. We are not produc-ing a complete, minute-by-minute enumerationof flight events. ATEM limits landings-per-dayby airfield as a surrogate for details such asmovement-on-ground constraints. In practice,airlift planners revised ATEM proposals as nec-essary to produce a detailed, timed schedule,

Figure 5. Algorithm enumerating all the (finite number of) s-t paths of length bounded by T. (See Byers andWaterman [1984] and Carlyle and Wood [2005].)



and did this better than we could, based onexpert knowledge that we cannot access bycomputer.

ATEM does not discriminate below pallet-level detail. Although current, official planningdoctrine dictates we consider the actual contentsof each pallet (in US military vernacular, this isTime-Phased Force Deployment Data level IVdetail), we could not do this, because such detailwas simply not available. We assume safelyloaded air pallets, have witnessed careful assem-bly of such pallets, but have also seen the finalarbiter, an airplane’s loadmaster, reject pallets.‘‘In-transit visibility’’ is a noble goal we admireas much as anyone, but, lacking such detail, weprefer to suggest good cargo airlift plans for thedemand we can see, rather than require detailthat is not available.

ATEM does not change configurations dur-ing a route, even though our airplanes do this.We adopt this conservative assumption becauseconfiguration changes require time, aircrew ef-fort, and sometimes also require support fromground crews and equipment, and storage of,

for instance, passenger seats. Some configura-tion changes are influenced, or even precluded,by the current aircraft load. We know how to ac-commodate all this, but the result might be a lit-tle too clever, and the planner might be puzzledby the mysterious route time lost here.

Passengers board with bag pallets holdingtheir personal gear. Depending on the type ofpassenger and the mission, the per-passengervolume of personal gear varies. ATEM cannotsee this variation, and does not discriminate be-tween bag pallets and cargo pallets. Plannersadjusted configuration capacity as necessary toaccommodate this complication.

We only plan direct deliveries. We do notsuggest relay conveyance, where some cargo ispicked up, left at some intermediate airfield,and thence conveyed by some other airplane toa subsequent destination. Planners can do thisby adjusting demands to draw intermediateshipment. In practice, when an airplane is aboutto depart with an empty seat or cargo pallet po-sition, airfield ground personnel will seize thisopportunity to relay passengers or pallets. Many

Figure 6. Portion of the Results worksheet. The prefix ‘‘fix’’ tells ATEM the planner wants to preserve the routein that line. This route may have been constructed by ATEM, or may have been manually designed by the planner(and thus may violate business rules ATEM would honor). The planner has fixed the first route here, which isused just one day for the airplane with tail number p1, indexed route catalog number r19959, configurationc1d, airplane type C_130E, taking off from Al_Salem and making hops as shown until returning there.

Figure 7. Portion of the Routes_Selected worksheet. This shows more detail than the Results worksheet, includingthe planned numbers of PAX and PALS carried on each leg. Throughput (multihop deliveries) would be distin-guished from single-hop deliveries, any fueling event would be indicated by an ‘‘F,’’ and any crew-replacementevent by a ‘‘C.’’ There is no such event here. All planned legs shown here are completely full, except for a deadheadhop on route r19975 repositioning airplane p1 from Balad to Kirkuk, followed by another leg returning to Balad with46 of 52 passenger seats occupied.



routes resemble hub-and-spoke operations, andrelaying to a hub is a good tactic.

CONCLUSIONIn early February 2006, Brown and Dell trav-

eled to Kuwait to deliver a prototype planner,and to iron out first-hand any details we mighthave overlooked concerning demands or signify-ing their importance. The trip to theater con-firmed key features that planners needed, andisolated those of less importance. It also con-firmed that no other tool was being used by theCAOC planners to help solve this difficult prob-lem. CAOC planners were aware of a few soft-ware packages that advertised the ability tohelp with this planning, but the planners werenot satisfied with the usability of these tools ortheir effectiveness.

During late February and early March,daily email exchanges provided ATEM updates

and modeling support. ATEM was used exten-sively by CAOC planners to help answer a num-ber of questions about fleet mix and size, and toverify the channel routes. ATEM was particu-larly helpful when used to justify stationingmore airplanes in Afghanistan.

In late March and April, ATEM was used todevelop the ‘‘star’’ routes of a hub-and-spokedistribution system and incorporated ATEM intodaily scheduling. CAOC planners were able tofix the channel and star routes, optimize demandcarried by these routes and then optimize assign-ment of the remaining demand to the remainingairplanes. Cargo was consistently moved withinthe 72-hour hold-time standard while leavingairplanes on the ground. This allowed much-needed crew rest and additional maintenancetime. Prior to this, air planners rarely left opera-tional airplanes on the ground.

Airlift operations became so efficient thatCENTCOM reduced the C-130 fleet by 10 with-out increasing the number of other airplanes,while at once increasing the amount of cargomoved. As a telltale of this change, the USArmy’s 3rd Corps Support Command at CampAnaconda, 50 miles north of Baghdad, moved6,500 pallets by air in October 2005. By the sum-mer of 2006, this command moved nearly 16,000pallets per month by air (Santana 2006).

By May 2006, we had developed a fast,purpose-built heuristic to solve ATEM modelsquickly (but approximately), permitting ATEMto be installed directly on machines connectedwith the Secret Internet Protocol Router network(SIPRnet). Comparisons such as those shown in

Figure 8. Demand for Afghanistan test case broken down by pallets (PALS) and passengers (PAX). For brevity,individual airfield pairs are not labeled on the horizontal axis.

Table 7. Number of each type of airplane availableat each home airfield for the seven-day Iraq scenario.We assume each airplane can fly every day.

Aircraft HomebaseOne dayavailable

Seven daysavailable

C-17 Al Udeid 4 28C-17 Incirlik 1 7C-130E Balad 6 42C-130E Al Salem 16 112C-130E Al Udeid 1 7IL-76 Kuwait 2 14



this paper between our heuristic and the exactmathematical solutions have reassured us thatthe heuristic quickly and reliably delivers high-quality route ensembles, but we maintainedSIPRnet reach-back to true optimization at NavalPostgraduate School should any doubt arise.

In June, we issued a technical report (Brownet al. 2006) with planner guidance.

In November 2006, ATEM was conveyed toUSTRANSCOM, Air Mobility Command. Wehave also distributed copies to other militaryagencies and civilian universities. In 2007,DeGrange (2007) used ATEM for CENTCOMCDDOC to justify withdrawing six more C-130sfrom theater with no reduction in service levels.As CAOC planners rotated every four months,we soon lost visibility of ATEM’s use within theCAOC but ATEM has seen continued use in AirMobility Command. One of the highlights in-cludes its use in 2009 to help determine theproper mix of CH-47s and C-130s in both Iraq

and Afghanistan with recommendations pro-vided to the Chairman of the Joint Chief of Staffand fully implemented. Most recently, ATEMwas used for the congressionally mandatedMobility Capabilities Assessment for the year2018 (MCA-18). Air Mobility Command alsoplans to use ATEM to assist with the congressio-nally mandated Mobility Requirements and Ca-pability Study that will commence in February2013 (Anderson, 2013).

Wray (2009), working with the authors, cre-ated the Marine Assault Support HelicopterPlanning Assistance Tool (MASHPAT), an EXCEL-based, computer system with fast heuristicsolver to schedule helicopter operations, espe-cially those in Afghanistan. MASHPAT includesseveral helicopter-specific details ATEM lacks,such as: load templates by helicopter type tocarry combinations of own fuel, passengers,bags, internally loaded tri-wall pallets, and ex-ternal loads; restrictions to carry all passengersin a complete unit; ground and airborne fuelconsumption rates; density altitude; require-ments to conduct certain operations with mul-tiple helicopters; day and night operationalrestrictions; and weather. Wray redeployed toIraq and to Afghanistan and used MASHPATin theater, and MASHPAT has been deliveredto and used by Air Mobility Command.

Breitbach (2012) has recently developedcustom demand data processing subroutinesand used ATEM as part of his thesis to planglobal air transport policies in Afghanistan withboth intertheater and intratheater legs.

Figure 9. Demand broken down by PALS and PAX for the single-day Iraq test scenario. Demand line airfieldpairs are intentionally omitted.

Table 8. Number of each type of airplane availableat each home airfield for the single-day Iraq scenario.

Aircraft Homebase Aircraft available

C-17 Al Udeid 4C-17 Incirlik 1C-130E Balad 6C-130E Al Salem 14C-130E Al Udeid 2IL-76 Kuwait 2



ATEM has saved taxpayers considerablemoney. One CDDOC study determined thatthe daily operating cost of a deployed C-130 is$250,000, so 10 airplanes amounts to $2.5 millionper day.

However, the most important impact ofATEM has been its contribution to convoy miti-gation and the reduction of personnel casualties.(See, e.g., recounting of these reports by Briga-dier general M.J. Saunders 2006.)

ACKNOWLEDGEMENTSA previous version of this paper was pre-

sented to the 2007 Military Operations ResearchSociety annual meeting, and was awarded theBarchi Prize. The Navy awarded each of the ci-vilian authors with the Superior Civilian ServiceMedal for this work. John Brau was awardedthe Joint Service Commendation Medal for histour of duty at CDDOC. We withheld this paperfrom general circulation until after withdrawal ofour combat forces from Iraq in December 2011.

Brown thanks the Air Force Office of Scien-tific Research and the Office of Naval Researchfor long-term, pure research support, with en-couragement to find important problems andsolve them. Carlyle also acknowledges supportfrom the Office of Naval Research.

The authors also thank Don Anderson, As-sistant Director, USAF AMC A9/AA9, who con-tinues to commute to theater to conduct studieswith ATEM to improve aircraft utilization.

REFERENCESAnderson, D., 2013, personal communication

dated 14 January.

Barnes, J., and McKinzie, K. 2004. A Review ofStrategic Mobility Models Supporting theDefense Transportation System, DefenseTransportation: Algorithms, Models, and Appli-cations for the 21st Century, Brigantic, R. T., andMahan, J. M., eds. Elsevier. pp. 839–868.

Barnes, J., Crino, J., Moore, J., and Nanry, W.2004. Solving the Theater Distribution Vehicle

Table 9. Removing airplanes from the seven-day Iraqi frequency channel design. Starting with the airplanefleet shown in Table 8, top-down, each row represents an increasingly restricted airplane fleet. The C-17 atIncirlik and the two IL-76s at Kuwait remain in service throughout all these restrictions. For instance, run7 has no C-130E at Al Salem, only one remaining C-130E and one C-17 at Al Udeid, but all six C-130Es at Balad.From 212,816 routes by airplane-type and home base, ATEM-HEURISTIC finds a route ensemble that lifts85.5% of demand, ATEM-ILP lifts 89.7%, contributes an upper bound of 90.9% for any airlift ensemble thatmay yet be found, but requires 90 minutes to do this. (An asterisk indicates the solver reached a preset 90 min-ute limit used for runs in this table.)

Al Salem Al Udeid Balad

Run C-130E C-130E C-17 C-130E Routes Heu % ILP % ILP bnd Solve mins

All 16 1 4 6 272,024 100.0% 99.4% 100.0% 2.61 3 1 4 6 272,024 100.0% 100.0% 100.0% 4.12 2 1 4 6 272,024 100.0% 99.7% 100.0% 5.13 1 1 4 6 272,024 100.0% 99.2% 100.0% 79.04 0 1 4 6 212,816 100.0% 99.4% 100.0% 40.05 1 3 6 212,816 99.5% 99.2% 100.0% 47.96 1 2 6 212,816 96.7% 98.1% 100.0% 90*7 1 1 6 212,816 85.5% 89.7% 90.9% 90*8 1 0 6 178,010 67.0% 71.3% 72.0% 15.59 0 6 176,846 63.1% 66.9% 67.6% 4.010 5 176,846 59.7% 63.4% 64.1% 3.311 4 176,846 56.3% 59.6% 60.2% 13.712 3 176,846 52.7% 55.4% 56.0% 10.513 2 176,846 48.3% 50.8% 51.3% 2.714 1 176,846 43.3% 44.8% 45.3% 0.715 0 18,344 35.7% 37.0% 37.2% 0.2



Routing and Scheduling Problem UsingGroup Theoretic Tabu Search, Defense Trans-portation: Algorithms, Models, and Applicationsfor the 21st Century, Brigantic, R. T., andMahan, J. M., eds. Elsevier. pp. 599–616.

Becker, M., Kramer, L., and Smith, S. 2004.Continuous Management of Airlift andTanker Resources: A Constraint-BasedApproach, Defense Transportation: Algorithms,Models, and Applications for the 21st Century,Brigantic, R. T., and Mahan, J. M., eds.Elsevier. pp. 581–598.

Breitbach, T. 2012. Air Cargo Routing intoAfghanistan: An Inter/Intra-Theater Ap-proach. MS Thesis in Operations Research,Air Force Institute of Technology, Wright-Patterson AFB, Ohio.

Bridges, J. A. 2006. Planning United StatesCentral Command Intra-Theater AirliftRoutes. MS Thesis in Operations Research,Naval Postgraduate School, Monterey,California.

Brown, G., Carlyle, W., Dell, R., Brau, J.,S. Sanford, and Bridges, J. 2006. Air Taskingand Efficiency Model (ATEM). Report Num-ber NPS-OR-06-006-PR, Naval PostgraduateSchool, Monterey, California.

Burks, R., Moore, J., Barnes, W., and Bell, J. 2010.Solving the Theater Distribution Problemwith Tabu Search, Military Operations Re-search, Vol 15, No 4, pp. 5–26.

Byers, T, and Waterman, M. 1984. DeterminingAll Optimal and Near-optimal SolutionsWhen Solving Shortest Path Problems byDynamic Programming, Operations Research,Vol 32, No 6, pp. 1381–1384.

Carlyle, W., and Wood, R. 2005. Near-Shortestand k-Shortest Simple Paths, Networks, Vol 46,No 2, pp. 98–109.

Dantzig, G., and Ramser, R. 1959. The TruckDispatching Problem, Management Science,Vol 6, No 1, pp. 80–91.

DeGrange, W. 2007. Air Tasking and EfficiencyModel (ATEM) Demonstration of Feasibilityfor Redeployment of Six C-130s fromCENTCOM, Centcom Deployment & Distri-bution Operations Center.

Department of the Army. 1993. Field Manual55-9 Unit Air Movement Planning. Washing-ton, DC.

Feillet, D., Dejax, P. and Gendreau, M. 2005. TheProfitable Arc Tour Problem: Solution witha Branch-and-Price Algorithm, TransportationScience, Vol 39, No 4, pp. 539–552.

GAMS/CPLEX. 2012. CPLEX 12, http://www.gams.com/dd/docs/solvers/cplex.pdf.

Joint Chiefs of Staff. 2000. Joint Pub 4-0 Doctrinefor Logistic Support of Joint Operations.Washington, DC.

Joint Chiefs of Staff. 2001. Joint Pub 3-0 Doctrinefor Joint Operations. Washington, DC.

Koprowski, P. 2005. Interdicting a ForceDeployment: Two-Sided Optimization of As-set Selection, Lift Scheduling, and Multi-Commodity Load Planning, M.S Thesis inOperations Research, Naval PostgraduateSchool, Monterey, California. March.

Mason, D. 2009. Design Specifications for theAir Mobility Operations Simulation Envi-ronment (Air MOOSE), Proceedings of the2009 Spring Simulation Multiconference,Article #60.

Microsoft Corporation. 2012a. Microsoft VisualBasic, http://msdn.microsoft.com/en-us/vstudio/hh388568.

Microsoft Corporation. 2012b. Microsoft Office,http://office.microsoft.com/en-us.

Military Surface Deployment and DistributionTransportation Engineering Agency Com-mand. 2005, http://www.tea.army.mil/tools/amp.htm.

Noel, R., and Stratton, W. 2012. JointDistribution Process Analysis Center(JDPAC). Modeling, Simulation,Optimization, and Analysis (MSO&A) Sys-tems, JDPAC Software Catalog, draft unpub-lished document.

Pohl, J. 2006. TRANSWAY, System Architectureand Components, report number TW-DESIGN-03, CDM Technologies, Inc., SanLuis Obispo, California.

Raytheon. 2013. Analysis of Mobility Platform(AMP), http://www.bnn.com/technology/knowledge/amp.

Santana R. 2006. US Military IncreasinglyUsing Air Lifts, Washington Post. August 3.http://www.washingtonpost.com/wp-dyn/content/article/2006/08/03/AR2006080300130_pf.html.



Saunders, M. 2006. Officer Evaluation Report ofLTC John Brau, 28 February.

Toth, P., and Vigo, D. 2002. The Vehicle RoutingProblem, Society for Industrial and AppliedMathematics, Philadelphia.

United States Transportation Command. 2005.USTRANSCOM Handbook 24-2 Understandingthe Defense Transportation System. Scott AirForce Base, Illinois.

Wray, J. 2009. Optimizing Helicopter Assault

Support in a High Demand Environment (U),MS Thesis in Operations Research, Naval Post-graduate School, Monterey, California. June.

Wu, T., and Powell, W. 2009. The Optimizing-Simulator: An Illustration Using the MilitaryAirlift Problem, ACM Transactions on Modelingand Computer Simulations, Vol 19, No 3, pp.14:1–14:31.



Documents

2013 Optimizing Intratheater Military Airlift in Iraq …Calhoun: The NPS Institutional Archive Faculty and Researcher Publications Faculty and Researcher Publications 2013 Optimizing