Vol. 35, No. 5, September–October 2005, pp. 381–392issn 0092-2102 �eissn 1526-551X �05 �3505 �0381

informs ®

doi 10.1287/inte.1050.0156©2005 INFORMS

Maximizing Federal Natural Gas Royalties

Steven A. StoddardCenter for Army Analysis, Fort Belvoir, Virginia 22060, steven.stoddard@us.army.mil

I conducted research to enable the US Minerals Management Service (MMS) to maximize natural gas royalties.MMS is the agency of the US Department of the Interior responsible for managing mineral royalties. As part ofmanaging royalties, MMS decides whether to accept royalties in value (cash payment, RIV) or in kind (physicaltransfer of gas, RIK). When MMS collects RIK, it also decides how to transport, process, and sell the natural gas.RIK is a fairly new program for MMS, which began continuous collection of RIK under a pilot study in 1998. Asits RIK program grew, MMS sought my assistance to improve its decision processes for converting RIV to RIKand for choosing among transportation, processing, and sales options. (This is not an army matter; I workedon this project while I was a doctoral student at the Colorado School of Mines.) I provided data-processingapplications to improve predictions of royalty volumes and assessments of existing royalty values. To supportdecisions concerning conversion of royalties from RIV to RIK, I developed a goal-price metric that accounts for avariety of market conditions. This metric compares favorably to alternatives that MMS was using or considering.I used an optimization model to evaluate conversion and contract alternatives so as to maximize total royalties.MMS began using the results of this research in 2002 and continues its use today. The first project it analyzedusing these results provided a net royalty increase of $3.4 million over the first contract year.

Key words : industries: petroleum, natural gas; networks, graphs: applications.

The United States has substantial natural gasreserves. Much of this natural gas is on federal

property, especially in US territorial waters in the Gulfof Mexico. On federally owned property, the gov-ernment owns the mineral rights. Commercial nat-ural gas companies produce natural gas from thesefederally owned reserves under leases from the fed-eral government. They do so when they believe theycan profitably produce (by drilling), transport (viapipeline), process (to remove impurities and separatethe components), and sell the natural gas from theseleases (most typically to energy companies). Commer-cial companies that drill for natural gas on leases fromthe federal government pay royalties based on theMineral Leasing Act of 1920 and the Outer Conti-nental Shelf Lands Act (OCSLA) of 1953 (Price 2000).The Department of the Interior, specifically, the Min-erals Management Service (MMS), manages the min-eral rights on behalf of American citizens and collectsthese royalties.

Most natural gas companies pay royalties in value(cash payments, RIV). After producing and sellingnatural gas, these companies pay MMS for the royalty

share of the gas (typically one-sixth or one-eighth,depending upon the lease location) minus allowabledeductions for transportation and processing. MMS,however, has the option of taking a percentage of thenatural gas and selling it. This is known as takingroyalties in kind (RIK). Since 1998, MMS has beentaking RIK with the goal of saving administrativecosts while maintaining revenue (General Account-ing Office 2004). Whenever MMS chooses to take RIKfrom a lease, it may or may not combine the natu-ral gas with royalties from other leases. When MMScombines natural gas from various leases, it does soat a facility measurement point (FMP). An FMP isa meter that measures natural gas flow early in thejourney from the well to the sales point. FMPs com-prise RIV-or-RIK decision points for MMS. WheneverMMS takes RIK, it must arrange to transport, pro-cess, and sell the gas just as if it were a commercialnatural gas company (Minerals Management Service2001).

In 1998, MMS adopted its RIK program. Underthis program, it manages all RIK leases and makesdecisions concerning conversion of leases from RIV

381

Stoddard: Maximizing Federal Natural Gas Royalties382 Interfaces 35(5), pp. 381–392, © 2005 INFORMS

to RIK. Prior to adopting its RIK program, MMScompleted the 1997 Royalty in Kind Feasibility Study.The authors of this study concluded that an RIK pro-gram for natural gas could be advantageous for boththe government and commercial entities because ofpotential administrative savings. That is, MMS wouldrequire fewer administrators to oversee RIK (such asmarketers, credit personnel, and accountants) thanit requires to ensure compliance with RIV (accoun-tants, auditors, and legal personnel). Commercial nat-ural gas companies would save on costs primarilybecause RIK leases do not carry the costly audit andlitigation burden associated with RIV. I accepted asgiven the conclusions of the 1997 Royalty in KindFeasibility Study. I did not analyze the relative mer-its of RIK and RIV and the impact each has on theglobal economy. Instead, I accepted that MMS hasan obligation to maximize royalties given producer-determined levels of production and that MMS mustchoose the course of action (RIK or RIV) that willreturn the greatest royalties to the treasury of theUnited States. MMS recently reiterated this obliga-tion in its business-model extension by publishing itsstrategies for optimizing processing, transportation,and market opportunities for RIK (Minerals Manage-ment Service 2004).

I further assumed that such decisions have noimpact on producers’ revenues. Consider a simpleexample: A natural gas company produces 600 mil-lion British thermal units (MMBtu) of natural gas andsells it at a net price of $10 per MMBtu, or $6,000.Assuming RIV and a royalty rate of 1/6, the com-pany pays MMS a royalty of $1,000 and keeps $5,000.If MMS had chosen to convert this lease to RIK, thecompany would turn over 100 MMBtu of natural gasto MMS and sell the remaining 500 MMBtu for (onehopes) $5,000. MMS makes such decisions to con-vert from RIV to RIK whenever it believes it canobtain $1,000 or more in royalties (Minerals Manage-ment Service 2001). The company’s royalty paymentsare the same regardless of MMS’s decision. Anypotential losses to the company are likely negated asit is freed from the audit burden that comes withRIV. MMS may have gained, however, by poolingthe natural gas from that lease with royalty vol-umes from other nearby leases and perhaps gainingfavorable transport, processing, or sales arrangements

because of the large volume (Minerals ManagementService 2004).

RIK is a fairly new program for MMS. Prior to 1998,all natural gas companies paid RIV expect for thosein a few small pilot studies conducted between 1995and 1997 (Minerals Management Service 2001). MMScontinues to increase in measured increments the pro-portion of natural gas leases that pay RIK (GeneralAccounting Office 2003, Minerals Management Ser-vice 2004). My research was one of several that MMSinitiated to help it make appropriate decisions con-cerning RIK.

In response to congressional inquiries aboutwhether MMS was receiving appropriate values forits natural gas royalties in its RIK program, the Gen-eral Accountability Office (GAO, congress changedthe name from “Accounting” to “Accountability”in July 2004) studied the RIK program and pub-lished its results in January 2003 and April 2004. TheGAO’s mission is to provide independent evaluationof the federal government. Shortcomings identified inits 2003 report provided some of the impetus for myresearch.

ObjectiveWhen MMS takes natural gas royalties in kind, it con-tracts for the most lucrative transportation, process-ing, and sales arrangements that it can find (MineralsManagement Service 2001, 2004).

Prior to this research, MMS did not have a sys-tematic process for determining whether the pricesit received from commercial natural gas companieswere accurate or fair. Its data-processing methodrestricted it to examining short time periods to esti-mate unit prices. Because revenue from RIV can differconsiderably from month to month, one needs a longperiod of evaluation to determine whether RIK salescan yield at least as much as RIV (General AccountingOffice 2004). Also, fluctuating market conditions biasmonthly price estimations. My data-processing toolsenabled MMS to broaden the analytical time period,and my goal-price metric gave unprecedented fidelityto its RIV estimates. MMS can now verify a $10 perMMBtu price or determine that the price was really$9.95 per MMBtu. Five cents makes a difference indecisions about natural gas royalties.

Stoddard: Maximizing Federal Natural Gas RoyaltiesInterfaces 35(5), pp. 381–392, © 2005 INFORMS 383

Also, prior to my research, MMS enumerated allpossible decision choices to determine its course ofaction. That is, it listed every possible combination oftransportation, processing, and sales options for eachlease it was considering for conversion from RIV toRIK. Then it compared all of these combinations to itsexisting RIV revenue. I used a network model withside constraints (based on the physical network of thenatural gas pipelines) to determine the solution thatmaximizes royalties.

My objective in this study was to maximize royal-ties from natural gas production on federal property.Specifically, this research provides tools that

—improve the existing process for quantifying RIVlease quantity and production,

—offer royalty-maximizing decisions regardingwhether to convert existing RIV leases to RIKleases, and

—offer royalty-maximizing decisions for RIK leasesby identifying optimal transportation, processing, andsales arrangements.

Data-Processing ApplicationsThe first step in my research was to provide MMSwith tools for analyzing natural gas production androyalty information, OGOR Calc and RIV Calc.

To make proper RIV-or-RIK decisions for each lease,MMS conducts a historical analysis of the RIV at thelease. It does so to estimate future production vol-umes and to assess royalty values that commercialleaseholders have paid. Prior to my research, MMSperformed all such analyses by manipulating spread-sheet data manually. Because this process was timeconsuming, MMS could examine only selected leasesand had to base its analyses on examining short timeperiods. The tools I developed automated MMS’s pro-cess and enabled it to analyze more leases over longerperiods.

These tools do not provide any earth-shatteringoperations research revelations, but their develop-ment and implementation was very important to theoverall project:

—I gained a deep understanding of the real prob-lems MMS faced daily, including the parameters thatinfluenced its decisions, where it obtained data, andhow good the data were. This knowledge was critical

to my development of the goal-price metric and opti-mization technique.

—By delivering a working tool that users reallyneeded in the first month on the job, I gained enor-mous credibility at MMS. That credibility was criti-cal in gaining acceptance of the goal-price metric andoptimization technique. I built these tools throughdaily interaction with the users so that they affectedevery feature.

OGOR Calc (oil and gas operations report calcula-tor) enables MMS to determine the volumes of nat-ural gas associated with various production leases(Figure 1).

RIV Calc converts downloaded royalty data intooutput tables that MMS can use for analysis andcan import into the optimization model. The programaccomplishes several data-processing tasks that MMSused to perform manually, including removing dupli-cate reports, aggregating separated reports, and cor-recting erroneous data. RIV Calc creates summarizedoutput tables that enable users to examine sales pricesand to compare them to market indices that MMSselects. Users can also examine summarized data ontransportation and gas-processing costs.

Because OGOR Calc and RIV Calc have greatlyreduced the time it takes to conduct historical analysisfor each lease, MMS now prospects for new oppor-tunities to convert RIV leases to RIK leases. Instead

100,000

10,000

1,000

100Jul

1997Jan

1998Jul

1998Jan

1999Jul

1999Jan

2000Jul

2000Jan

2001

Roy

alty

vol

ume

(MM

Btu

/day

)

Figure 1: OGOR Calc summarizes natural-gas production data and chartsit over time. This chart shows how OGOR Calc displays production data fora single lease. It plots production using a log scale because most naturalgas production declines in a log-linear pattern. Such charts enable MMSto predict future royalty volumes.

Stoddard: Maximizing Federal Natural Gas Royalties384 Interfaces 35(5), pp. 381–392, © 2005 INFORMS

of restricting its analyses to selected leases, it ana-lyzes several leases simultaneously to find leases withrelatively low RIV (implying that it could increaseroyalties with RIK) and with high enough productionvolumes to be good candidates for RIK.

New Price GoalBefore proceeding to maximize royalties using anoptimization model, I examine the valuation parame-ter associated with keeping an FMP in RIV.

For each FMP, MMS assigns a value to RIV thatis relative to a goal price. This goal price is usuallya differential from a published market index priceor a combination of several indices. MMS does thisbecause it must compare the royalties it received inthe past (in RIV) to potential RIK receipts in thefuture. Because market prices for natural gas changedaily, it cannot directly compare RIV prices in thepast to future RIK prices. Instead, it compares RIVto RIK by examining their differentials from somebenchmark that changes with market conditions. RIKand RIV differ month to month because market pricesdiffer from month to month and because RIV and RIKmay have different market bases (General AccountingOffice 2004).

To develop a goal price, I wanted to determinewhat portion of each month’s changes in naturalgas prices leaseholders absorbed, as shown in roy-alty payments. I analyzed data from a random sam-ple of natural gas royalties paid over a two-yearperiod (details not included). Based on this analysis,I established a goal-price metric based on my esti-mate that, on average, leaseholders absorb 15.5 per-cent of total market-price changes that occur fromthe start to the end of the month. In months withsmall overall price changes (less than 12 percent ofthe total market price), I used the average daily mar-ket price. The average daily market price is tied to theHenry Hub index, which is the principal daily marketindex for natural gas from the Gulf of Mexico. Theprincipal monthly index is the New York MercantileExchange (NYMEX) monthly settle price. In the equa-tions below, Zt is my goal price metric for month t,NYMEXt is the NYMEX index price in month t, andDaily Averaget is the average of Henry Hub index

prices in month t:

Zt =

NYMEXt − 15�5%�NYMEXt −NYMEXt+1��

�NYMEXt −NYMEXt+1�/NYMEXt > 12%

Daily Averaget� otherwise�

This goal-price metric is highly dependent upon thesource data. My sample data represent 20 percent ofall natural gas leases in the Gulf of Mexico and arederived from examining sales in 2000 and 2001. Sim-ilar efforts should draw from data that are similarin location to the leases of interest and should drawfrom the most recent data available. Natural gas mar-ket prices in 2000 and 2001 exhibited a large increasefollowed by a large decrease but started and endedthis two-year period at approximately the same value.I therefore examined the effects of market changeswithout an overall upward or downward bias.

I used the goal-price metric when examining roy-alties paid in the past (in RIV) by the leaseholders.Table 1 illustrates an analysis of one natural gas lease.For each month, I compared the goal-price metric toreported royalty values. Over a one-year period, thiscomparison shows the difference between the goal-price metric and the amount MMS received.

Prior to my research, MMS used the first-of-the-month (FOM) price as its primary goal-price met-ric. It could also use the daily average price or agoal price derived from the idea that about 70 per-cent of natural gas production sales are made atFOM prices and the remaining 30 percent are at dailyprices (70/30). I compared Zt with these other goal-price alternatives (including arithmetic means of Zt

with other metrics, Table 2) by employing a methodthat focuses on results of past conversion decisions.From November 1999 to November 2002, MMS con-verted natural gas flowing through 185 FMPs fromRIV to RIK. For 61 of these conversion decisions,data are complete and differentiable enough to war-rant comparative analysis (some conversions were toorecent to yield complete data; some were made underearlier pilot-program policies that called for differenttypes of data than current policies; others were notdifferentiable in that all of the goal-price metrics hadvirtually identical values). Those FMPs that earnedincreased royalties (relative to a goal price) followingconversion from RIV to RIK I define as successful.

Stoddard: Maximizing Federal Natural Gas RoyaltiesInterfaces 35(5), pp. 381–392, © 2005 INFORMS 385

Lease under consideration forconversion from RIV to RIK

NYMEX first Henry Hub Goal: Gulfof the average average net Net unit Royalty

month price daily price price price volume Loss/GainMonth ($/MMBtu) ($/MMBtu) ($) ($/MMBtu) ($/MMBtu) (MMBtu) ($)

Apr-01 5.442 5.199 5.199 5.184 651�902 �9�787�May-01 4.891 4.208 4.741 4.637 857�966 �88�938�Jun-01 3.922 3.728 3.841 3.671 878�988 �148�822�Jul-01 3.397 3.074 3.074 3.402 710�445 233,259Aug-01 3.128 3.008 2.999 3.184 333�083 61,570Sep-01 2.295 2.193 2.223 2.198 539�879 �13�349�Oct-01 1.830 2.425 2.043 1.422 570�057 �354�088�Nov-01 3.202 2.365 3.065 2.802 568�450 �149�563�Dec-01 2.316 2.369 2.369 2.189 772�124 �138�688�Jan-02 2.555 2.293 2.470 2.389 925�650 �75�187�Feb-02 2.006 2.272 2.065 2.106 794�569 32,543Mar-02 2.388 3.019 2.556 2.755 829�348 165,429Apr-02 3.472

Total: 8�432�461 �485�620�Goal loss/gain ($/MMBtu): (0.058)

Table 1: For one lease, goal and market prices varied month to month, but in January 2002, the NYMEX pricefell from $2.555 on January 1 to $2.006 per MMBtu on February 1 (Column 2). The goal price of $2.470 perMMBtu accounts for 15.5 percent of the market price decline during that month (Column 4). Under the lease,MMS received a net unit price of $2.389 per MMBtu (Column 5). It received $0.081 per MMBtu less than the goal(Column 4−Column 5), which is derived from an expectation of what an average Gulf of Mexico leaseholdershould receive. Dividing the total loss or gain (right-most column) by the total royalty volume shows that overthe course of one year, MMS received an average of 5.8 cents per unit below the goal price on this lease.

I define those that earn decreased royalties followingconversion as failures.

I analyzed RIV data for each FMP for the 12 monthsimmediately preceding conversion and RIK datafrom the first 12 months after conversion (Table 3).(A 12-month period allows me to account for seasonal

Goal price Description

FOM NYMEX first-of-the-month index price is the most common price MMS uses for comparison. Advantage: Because most natural gas issold at FOM, prices are readily available. Disadvantage: Because some gas sales occur over the course of the month, the price doesnot reflect changes in market price following FOM.

70/30 70% of FOM+ 30% of the average daily Henry Hub index price over the course of the month. Some believe that this price representsan accurate division of how commercial producers typically sell natural gas. Others argue that no actual contracts stipulate that gasbe sold using a 70/30 split.

Zt and 70/30 Mean of Zt and 70/30. Advantages: This price provides a reasonable goal in a variety of market conditions and has less variabilitythan Zt and 70/30 do individually. Disadvantages: It is more difficult to calculate than other goals and has the least basis in actualsales practices among the available goal prices.

Zt and FOM Mean of Zt and FOM. Advantages: This price accounts for market fluctuations over the course of the month and gives considerationto relationships between FOM and lease locations. Disadvantage: It has little basis in actual sales practices.

Table 2: This is a list of goal-price alternatives I compared to Zt . Prior to my research, MMS used FOM almostexclusively. MMS also offered 70/30 as an untested alternative. These goal prices along with Zt represent alter-natives that MMS could use to relate RIV prices to potential RIK prices.

differences that may occur as natural gas is used forheating and cooling in different regions.) After I deter-mined whether the conversion succeeded or failed,I ranked the goal prices. For successful conversions,I ranked the goal prices in order of the strengthof their evidence in support of conversion to RIK.

Stoddard: Maximizing Federal Natural Gas Royalties386 Interfaces 35(5), pp. 381–392, © 2005 INFORMS

NYMEX FOM 70/30 Zt Zt /70/30 Zt /NYMEX

RIV �0�348� �0�398� �0�429� �0�413� �0�388�RIK �0�308� �0�277� �0�262� �0�270� �0�285�Difference 0�040 0�120 0�167 0�144 0�104Rank 1 3 5 4 2

Table 3: These data come from an FMP that MMS converted from RIV toRIK in April 2001. In the row labeled RIV, the various goal price differen-tials offered values ranging from −$0.348 to −$0.429 per MMBtu. Zt sup-ported conversion most strongly and FOM weakly supported conversion.Analysis of RIK data using the five goal prices yielded net royalty valuesfrom −$0.262 to −$0.308. The difference between RIV and RIK for eachgoal price was a positive number. This indicated that RIK was more lucra-tive than RIV and this conversion was successful.

I ranked the goal prices from 5 (best) to 1 (worst).A low goal price implies a low value for RIV and thusprovides strong evidence in support of conversionto RIK. Whichever goal price was lowest providedthe lowest threshold for RIK and thus the strongestevidence in support of conversion to RIK. Therefore,I ranked the lowest goal price a 5 for a successfulconversion. Conversely, for conversions that failed,I ranked the highest goal price (which gave little sup-port for conversion) a 5.

Based on the successful conversion from RIV to RIK(Table 3), I ranked Zt as highest because it supportedconversion most strongly (it had the lowest value forRIV). I ranked FOM as lowest because it was mostcautious. If an estimate of potential royalties in kindwere −$0�37, for example, MMS would convert to RIKusing Zt as its benchmark. If MMS used FOM pricesas its standard, however, it would leave the FMP inRIV. Because this conversion was a success, I favor Zt

over FOM (and the other goals) for this FMP.To choose the best overall goal price from among

the five competing goal prices, I focused on 70/30

Criteria Highest rank Lowest rank

By FMP Zt 70/30 Zt and 70/30 Zt and FOM FOMRising market 70/30 Zt and 70/30 Zt Zt and FOM FOMFalling market Zt Zt and FOM FOM Zt and 70/30 70/30Successful conversions Zt Zt and 70/30 70/30 Zt and FOM FOMConversion failures FOM Zt and FOM 70/30 Zt and 70/30 Zt

Table 4: I compared the competing goal prices, from highest to lowest rank, using five evaluation criteria for61 FMPs. In addition to examining the results on an FMP-by-FMP basis, I compared the results from conversionsmade during rising and falling market conditions as well as for successful versus unsuccessful conversions.

and Zt , the two goals that performed well most con-sistently (Table 4).

Evaluating by FMP is the most important crite-rion because MMS makes conversion decisions on anFMP-by-FMP basis. Zt ranks highest on this criterion.

MMS never knows if it is making its conversiondecisions in rising or falling market conditions. Thus,consistent performance in both rising and falling mar-kets is important. Because 70/30 ranks lowest whenmarket prices are falling, Zt is superior over the spec-trum of market conditions.

70/30 ranks in the middle for both successful con-versions and conversion failures, where Zt rankshighest for successes and lowest for failures. MMSstrives to increase the RIK program by convertingleases from RIV whenever doing so provides thesame or better revenue (Minerals Management Ser-vice 2001). Thus, MMS prefers to err on the side ofconversion so as to increase the overall volume ofgas in RIK. Also, a relatively low number of failures(18 of 61) implies that this ranking was derived fromthe smallest sample.

Prior to this research, MMS typically used FOMprices for its RIV-to-RIK comparisons. But compar-isons of various goal prices for all previous RIV-to-RIK conversions show the inadequacy of using FOMprices. FOM prices provide a benchmark that is infe-rior to goal prices that account for price fluctuationsover the course of a month.Zt provides a goal price that I have shown to

be more accurate than other goal prices at predict-ing successful RIV-to-RIK conversions. It was moreaccurate for previous conversion decisions, on anFMP-by-FMP basis as well as over the spectrum ofmarket conditions, than any other tested benchmark.

Stoddard: Maximizing Federal Natural Gas RoyaltiesInterfaces 35(5), pp. 381–392, © 2005 INFORMS 387

Moreover, Zt provides the most appropriate balancebetween FOM and daily prices. MMS accepted thisgoal-price metric for evaluating its RIV-or-RIK deci-sions in 2003. (It did not use Zt exclusively, how-ever. MMS continues to use FOM and geographicallybased modifications of FOM in some of its analyses.)MMS also uses Zt to quantify the relative successesof its conversion decisions after leases have been con-verted from RIV to RIK.

Optimization ModelFor each FMP, MMS attempts to maximize royalties.That is, it chooses the most lucrative option fromamong several choices. One option is to continueto collect RIV on all of the natural gas that flowsthrough the FMP. If instead it chooses to collect RIK,it typically has many options. The number of optionsdepends upon the number of pipelines that are avail-able to transport the natural gas from the productionfields, the number of gas plants that are available forprocessing, and the number of market centers that areavailable for sales. Whenever MMS considers RIK foran FMP, it asks commercial companies to make sepa-rate bids to transport, process, and purchase the natu-ral gas. Once the bids are submitted, MMS has manyoptions from which to construct the one that willreturn the greatest royalties. These options involve allfeasible paths through which natural gas may flow(from FMP through pipelines and gas plants to mar-ket centers).

Prior to this research, MMS enumerated all possiblesolutions and chose that which returned the greatestroyalties (Table 5). It could keep the natural gas in

Option Net value

RIV +0�02RIK1 +0�03· · · · · ·RIKn −0�04

Table 5: Before it adopted my method, the Minerals Management Servicelisted all RIK options (1 through n) and compared their net values to thevalue associated with RIV. Each RIK option consists of a particular trans-portation option, a particular gas-processing option, and a particular salesoption. Net values are in dollars per million British thermal units (MMBtu)and as a differential from a known market basis.

RIV, expressing the net value as a differential from amarket basis, such as the NYMEX index. MMS basesthis differential on the amount the commercial lease-holder paid in the past. MMS assumes that the RIVdifferential from the market basis will not changein the future. The other options are combinations oftransportation, processing, and sales options. The netvalue for each option is the sales revenue (measuredas a differential from the same market basis as theRIV net value) less the transportation and processingcosts. (Transportation and gas processing can return anet gain in some circumstances; the gain is then addedto the sales revenue.)

My research enabled MMS to adopt an optimiza-tion methodology that took advantage of the underly-ing network of natural gas pipelines. In designing theoptimization tool, I took as given the physical con-nectivity of the elements, as well as production vol-umes, RIV prices, and transportation, gas-processing,and market price parameters. The optimization tooldetermines from which FMPs to take RIV and fromwhich to take RIK. For those FMPs for which RIKis optimal, it determines which pipelines, gas plants,and market centers to use (Figure 2).

One challenging aspect of modeling the networkflow involves conditional costs. Transportation costs(that is, the negative profit associated with transporta-tion) for each pipeline usually depend on the even-tual market destination. For example, the operator ofthe Tennessee Gas Pipeline (TGP) may offer a con-tract at a lower price for transporting gas to a TGPmarket center than it does for transporting gas to theColumbia Gas market center. To account for the possi-bility of conditional transportation costs, I expand thenetwork before solving it, adding paths to account forall possible costs. Adding paths to account for con-ditional transportation costs increases network sizes(Figures 3 and 4).

In addition to the attributes captured by the net-work structure, I must account for the binary natureof RIV-to-RIK conversion decisions. All natural gasthat flows through an FMP must either remain inRIV or be converted to RIK. I introduce binary vari-ables and constraints that enforce these conversiondecisions. To solve the optimization model, I use aformulation that is essentially a minimum-cost-flowproblem (where I maximize profit−royalties− insteadof minimizing cost) with the addition of binary vari-

Stoddard: Maximizing Federal Natural Gas Royalties388 Interfaces 35(5), pp. 381–392, © 2005 INFORMS

V = FMP volumeTC = Transport costPC = Processing cost

MC = Market center valueTL = Transport limit

PL = Plant limit

ML = Market limit

(V, V )F1

Source

F2

P4

P3

P0

RIV

(0, PL)

GP0

FMPs Pipelines Gas Plants

F0

F3

RIV P2

P1

Market Centers

GP1

GP2

GP3

GP4

GP5

M0

M1

M2

M3

M4

M5

PC

TC

(0, TL)

MC

(0, ML)

Sink

Figure 2: In this illustration of the model, I show a maximum profit network for one example system. The shadednodes and solid arcs represent the physical natural gas network from source to market. The elements are thefacility measurement points (FMPs), pipelines, gas plants, and market centers that the Minerals ManagementService is considering for use in RIK. The white nodes and dashed arcs support the decision process; they modelgas flow into the FMPs, account for the possibility of leaving gas in RIV, and model gas flow from the marketcenters to the sink.

ables and side constraints (Appendix). I implementedthis methodology within MMS’s computer systemusing What’sBest!.

MMS used this methodology in 2003 to analyzeits two most complicated conversion projects to date.

TC = Transport cost PC = Processing costMC = Market center valueTL = Transport limit

P2

Pipelines Gas Plants

P1

Market Centers

GP1

GP2

M1

M2

M3

PCTC

(0, TL)

MC

Figure 3: In this system with two pipelines, two gas plants, and three mar-ket centers, the transportation cost for pipeline P1 depends on which ofthe three market centers the natural gas is destined for. To overcome thisdifficulty, we expand the network structure (Figure 4).

These projects had dozens of options and on theorder of 200 variables. They were substantially morechallenging to analyze than any of MMS’s previ-ous projects. Although MMS still uses enumerationfor its simplest projects (some projects are so sim-ple that it has fewer than 10 options), it is workingto integrate the model into information systems thatare still in development. MMS continues to expandthe RIK program in terms of quantity of natural gasand the variety of transportation, processing, andsales options it employs (Minerals Management Ser-vice 2004). MMS will continue to use this optimizationmodel with the increasing variety of options.

First Implementation ProjectTo support the development and implementationof this research, I conducted an initial project in2002–2003. Although the project was a test of the toolsI had developed, it was a real project. That is, MMSimplemented the results of the project, converted theleases from RIV to RIK in November 2002, and actu-ally realized the increase in royalties predicted by my

Stoddard: Maximizing Federal Natural Gas RoyaltiesInterfaces 35(5), pp. 381–392, © 2005 INFORMS 389

Pipelines Gas Plants

P1

P2

Market Centers

P1G1M1PC

TC

(0,TL)

MCP1M1

P1M2

P1M3

P2M1

P2M2

P2M3

P1G1M2

P1G1M3

P2G1M1

P2G1M2

P2G2M1

P2G2M2

P2G2M3

P2G1M3

M1

M2

M3

Figure 4: After the system from Figure 3 has been expanded to account for conditional cost parameters, threearcs leave the node for each pipeline, P1 and P2, one for each of the eventual market-center destinations.

results. The project was the most complicated (that is,it had the most options) that MMS had considered forconversion from RIV to RIK up to that point.

In the project, I examined 18 leases from threeneighboring geographical areas in the Gulf of Mexicothat provide natural gas to four FMPs (Figure 5). (TwoFMPs are associated with Area 1, one for PipelineWhite I and one for Pipeline White II.) These FMPsrepresented conversion decision options for MMS.

The goal differentials associated with keeping thenatural gas from each area in RIV were below themarket index (the RIV for Areas 1, 2, and 3 were−$0�078, −$0�152, and −$0�152 per MMBtu, respec-tively). The various pipelines offered transportationthrough six gas plants to six different market centerswith different sale prices. Reaching the more lucra-tive markets, however, required greater transportationcosts. The processing offers from the six competing

gas plants ranged from $0.029 per MMBtu to $0.162per MMBtu.

The solution from the optimization showed thatconverting all 18 leases from RIV to RIK wouldprovide the maximum royalty return, an increaseof about $3.5 million per year (Figure 6, Table 6).After MMS converted these leases from RIV to RIK,I tracked the results over the first contract year(November 2002 to October 2003). The actual increasein net royalties was only marginally different fromthe increase I had projected prior to conversion. Pricevariations and dropping production volumes causedthe realized savings on the test project to be about$3.4 million.

ImpactMMS began using the products of my research in 2002when it implemented RIV Calc. It later adopted OGORCalc and incorporated the optimization model and

Stoddard: Maximizing Federal Natural Gas Royalties390 Interfaces 35(5), pp. 381–392, © 2005 INFORMS

Area 313,000 MMBtu/day

RIV = (15.2¢)

Area 230,000 MMBtu/day

RIV = (15.2¢)

Area 140,000 MMBtu/day

RIV = (7.8¢)

Aqua Gold

Green

Red(11.7¢)

Orange

Plant 2 Plant 5

Blue

Processor 54.4¢

Processor 62.9¢

Processor 411.7¢

Processor 316.2¢

Processor 25.5¢

Processor 113.6¢

Ora

nge

Ow

ner

A

Ora

nge

Ow

ner

B

Gol

dAqu

a

2.9¢

2.4¢

Ora

nge

Ow

ner

A

Ora

nge

Ow

ner

B

(4.7¢)

(Trans: 13.5¢)

(10.0¢)

0.6¢

FGT Z2(7.7¢)

(7.7¢)

(7.7¢)

0.0¢

(7.7¢)

(13.5¢)Basis: 2.9¢

2.4¢

(2.1¢) (2.1¢) (2.1¢)

(10.0¢)

0.6¢

(9.1¢)

(2.4¢)

(4.7¢)

(1.2¢)

(9.1¢)

(9.1¢)

(2.1¢)

(9.1¢)

(6.0¢)

White I – 40%

White II – 60%

Pipeline

Area

Facility meas. pt.

Market center

Gas plant

Junction

Transco Z3

Transco Z4

Transco Z3Transco Z3

Transco Z3

Plant 1 Plant 3 Plant 4

Columbia Gulf Columbia Gulf Columbia Gulf

TGP 500 TGP 500

ANR

Gre

en

Columbia Gulf

TGP 500

Plant 6

Figure 5: I conducted an initial implementation project in 2002–2003. Gas flows generally north (from bottomto top of the chart) from three production areas through combinations of facility measurement points (FMPs),pipelines, and gas plants, to several market alternatives. (The junctions allow natural gas to flow out of onepipeline and into another.) The market centers nearest the top had the highest sale prices, as indicated by theunderlined “basis” values to the right of the markets. Selling at Transco Zone 4, for example, provided a salesbasis of $0.029 per MMBtu above the market index. However, the rate to reach Transco Zone 4 on PipelineOrange was $0.135 per MMBtu.

goal-price metric that I developed. MMS has alsomodified OGOR Calc and RIV Calc for use in itsoil royalty program and is working to automate useof the optimization model within its informationsystems.

MMS now prospects for high-volume and under-valued RIV leases by examining substantial quantitiesof data using OGOR Calc and RIV Calc. MMS can nowidentify leases that were not previously under con-sideration by marketers. My development of RIV Calcallowed MMS to dramatically reduce analysis timeand make its analyses consistent and repeatable. Thenew goal-price metric removes bias from changingmarket conditions. MMS no longer has to enumer-

ate all RIK options to optimize transport, processing,and sales. Time savings from this are unknown butare most obviously felt when solutions are recalcu-lated within short time periods (for example, duringcontract negotiations). The reduced analysis time alsoenables MMS to examine more difficult projects. MMShas expanded from projects with tens of options toprojects with hundreds of options.

In the words of Milt Dial, the royalty-in-kind pro-gram director, “(The) contributions (of this research)have fundamentally changed the way MMS doesbusiness concerning its natural gas royalties. � � � (It)has had a profound impact on our operations.”

Stoddard: Maximizing Federal Natural Gas RoyaltiesInterfaces 35(5), pp. 381–392, © 2005 INFORMS 391

Area 230,000 MMBtu/day

RIV = (15.2¢)Area 140,000 MMBtu/day

RIV = (7.8¢) Area 313,000 MMBtu/day

RIV = (15.2¢)

Gold

Red(11.7¢)

Plant 3

Processor 316.2¢

Gol

d

FGT Z2(7.7¢)

1.2¢

White II–60%

White I – 40%

Gold

Pipeline

Area

Facility meas. pt.

Market center

Gas plant

Junction

Figure 6: The optimal solution to our initial implementation project was toconvert all areas from royalty in value (RIV) to royalty in kind (RIK), trans-port via Pipelines Red and Gold, process at Plant 3, and sell at FloridaZone 2. This solution would improve royalties by 11.9 cents per unit, fora projected one year net royalty increase of about $3.5 million.

Appendix

Formulation

Indicesi� j� k ∈N set of all nodes (e.g., FMPs and pipelines).�i� j� ∈A set of all arcs (e.g., path from FMP0 to

pipeline4).

Sale Total net Royalty RoyaltyTransport Processing (Market) unit value∗ volume value

Option (¢/MMBtu) (¢/MMBtu) (¢/MMBtu) (¢/MMBtu) (MMBtu/day) ($/day)

Area 1, RIV N/A∗ −7�8 40�000 −3�120Area 1, RIK 40%: −7�7 +16�2 +1�2 +9�7 16�000 +1�552

60%: −19�4 +16�2 +1�2 −2�0 24�000 −480

Area 2, RIV N/A∗ −15�2 30�000 −4�560Area 2, RIK −19�4 +16�2 +1�2 −2�0 30�000 −600

Area 3, RIV N/A∗ −15�2 13�000 −1�976Area 3, RIK −19�4 +16�2 +1�2 −2�0 13�000 −260

Total, RIV −11�63 83�000 −9�656Total, RIK +0�26 83�000 +212

Change +11�89 +9�868

Table 6: In this comparison between RIV and the optimal RIK course of action for our test project, unit pricesfor Sale and Total Net Unit Value reflect differentials from the New York Mercantile Exchange (NYMEX) marketindex. The volume from Area 1 is divided by pipeline volume constraints and thus has two different sets of valueswhen in RIK. For each area, the total value (in the right-hand column) is greater for royalty in kind (RIK) than forroyalty in value (RIV). The bottom row shows the total change from RIV to RIK in both dollars per day and centsper million British thermal units (MMBtu).

∗ I show RIV at the total net unit value only. I determined net unit values for RIK (Column 5) by summing thevalues in Columns 2 through 4.

f ∈ F set of all FMP nodes; F ⊂N .p ∈ P set of all pipeline nodes; P ⊂N .

�f � p� ∈K set of all arcs from FMP nodes topipelines; K ⊂A.

r RIV node; r ∈N .�f � r� ∈R set of all arcs from FMP nodes to RIV;

R⊂A.s source node; s ∈N .

DataPi� j royalty profit from i to j ($/MMBtu).Ui� j upper bound on arc �i� j� (MMBtu).Vf royalty volume at FMP f (MMBtu).M a large constant, used in constraints with binary

switches.

VariablesXi� j amount of natural gas flow from i to j

(MMBtu).Yf �p 1 if natural gas flows from f to p, 0 otherwise.Wf�r 1 if natural gas flows from f to RIV,

0 otherwise.

Formulation

Max� = ∑�i� j�∈A

Pi� jXi� j

Stoddard: Maximizing Federal Natural Gas Royalties392 Interfaces 35(5), pp. 381–392, © 2005 INFORMS

subject to∑

i��i� j�∈AXi� j −

∑k��j� k�∈A

Xj�k = 0 ∀ j ∈N� (1)

Xs�f = Vf ∀ f ∈ F � (2)

Xi� j ≤Ui� j ∀ �i� j� ∈A� (3)

Xf�p ≤M ∗Yf �p ∀ �f � p� ∈K� (4)

Xf�r ≤M ∗Wf�r ∀ �f � r� ∈R� (5)∑

p��f � p�∈KYf �p +

∑r��f � r�∈R

Wf�r = 1 ∀ f ∈ F � (6)

Xi� j ≥ 0 ∀ �i� j� ∈A� (7)

Yfi�p ∈ �0�1� ∀ �f � p� ∈K� (8)

Wfi� r ∈ �0�1� ∀ �f � r� ∈R� (9)

The Pi� j data refer to revenues or costs associatedwith RIV, transportation, processing, and sales. Anyof these may be positive or negative.

The formulation is to maximize profit, which issimply the sum product of royalty profits timesthe amount of flow across each arc. The constraintsaccomplish the following:

(1) ensure that any flow that enters a node willleave that node;

(2) establish the supply of natural gas that flowsthrough each FMP;

(3) ensure that flow volumes do not exceed upperbounds;

(4) activate a binary switch for flow from an FMPto a pipeline (implying RIK);

(5) activate a binary switch for flow from an FMPto RIV;

(6) ensure that all natural gas from any FMP is ineither RIV or RIK, not both;

(7) stipulate that flow amounts cannot be negative;(8) define Yf �p as binary; and(9) define Wf�r as binary.Some factors, including binary variables, condi-

tional transportation costs, and continued expansionof the RIK program at MMS, cause optimization prob-lems to increase in complexity and require longertimes for computing solutions. With that in mind,I used the underlying physical network of pipelines topartition the problem by pipeline. This process allowsme to identify dominated markets, remove nodesfrom the network, and thus to reduce the problem

size. Partitioning creates several smaller problems.The set of partitioned problems contains mutuallyexclusive and collectively exhaustive subsets of theoriginal set of pipelines. For example, a problem with200 pipelines can be partitioned into 200 smaller prob-lems with one pipeline each. Each partitioned prob-lem may then be solved individually. The solution foreach partitioned problem provides an optimal mar-ket destination (or destinations) for its pipeline. Theunion of market subsets from all partitioned problemsprovides a subset of the entire set of markets, leav-ing out markets that were nonoptimal in the solu-tions to all partitioned problems. Markets that are notchosen by any partitioned problem, then, are domi-nated by other markets and may be eliminated fromconsideration. After solving the partitioned problems,I reformulate the problem using all pipelines but dis-regarding any dominated markets. I examined theprocess by solving 10 test cases using a SunBlade1000 workstation, AMPL Version 7.100, and CPLEXVersion 7.1.0. Each test case returned optimal solu-tions to the partitioned problems while saving anaverage of 67 percent of run time.

AcknowledgmentsThis research would not have been possible withouta tremendously cooperative effort between the MineralsManagement Service and the Colorado School of Mines.In particular, I thank MMS’s Milt Dial, Greg Smith, PamRieger, Karen Bigelow, Joe Cornellisson, Mike DeBerard,and Bob Kronebusch. I also thank Gene Woolsey, DineshMehta, and Alexandra Newman of the Colorado School ofMines.

ReferencesGeneral Accounting Office. 2003. Mineral Revenues; A More Sys-

tematic Evaluation of the Royalty-in-Kind Pilots Is Needed.GAO-03-296. General Accounting Office, Washington, DC.

General Accounting Office. 2004. Mineral Revenues; Cost and RevenueInformation Needed to Compare Different Approaches for CollectingFederal Oil and Gas Royalties. GAO-04-448. General AccountingOffice, Washington, DC.

Minerals Management Service. 1997. 1997 Royalty in Kind BusinessFeasibility Study. US Department of the Interior, Washington,DC.

Minerals Management Service. 2001. Implementing Royalty in KindBusiness Processes and Support Systems; Road Map to the Future.US Department of the Interior, Washington, DC.

Minerals Management Service. 2004. Five Year Royalty in Kind Busi-ness Plan. US Department of the Interior, Washington, DC.

Price, H., S. Rawlings, C. Schaeffer, L. Shoaff. 2000. Mineral Revenues2000, Report on Receipts from Federal and American Indian Leases.US Department of the Interior, Washington, DC.