a large us retailer selects transportation carriers under diesel price uncertainty

Vol. 42, No. 4, July–August 2012, pp. 365–379ISSN 0092-2102 (print) � ISSN 1526-551X (online) http://dx.doi.org/10.1287/inte.1110.0610

© 2012 INFORMS

A Large US Retailer Selects TransportationCarriers Under Diesel Price Uncertainty

John TurnerThe Paul Merage School of Business, University of California, Irvine, California 92697,

[email protected]

Ben Peterson, Soo-Haeng Cho, Sunder Kekre, Alan Scheller-WolfTepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

{[email protected], [email protected], [email protected], [email protected]}

A large US retailer that procures transportation services from third-party carriers experienced an unexpectedjump in fuel surcharges as the price of diesel fuel skyrocketed in the summer of 2008. As a result, it soughtto limit its future exposure to diesel price risk. We collaborated with this retailer to create a lane assignmentoptimizer (LAO) that incorporates diesel price risk when selecting carriers for its transportation lanes. TheLAO tool has significantly improved the retailer’s capability to evaluate the trade-off between the two crucialcomponents of a lane’s per-shipment cost: base price and risk-adjusted fuel surcharge. The retailer can nowtake diesel price risk into account when selecting cost-effective carriers for its lanes, negotiating fuel surchargelimits to share diesel price risk with its carriers, and better aligning the fuel surcharges it pays with the truecost of diesel. We estimate that the more favorable contract terms the retailer negotiated for 2009–2011 translateto nearly $5 million in potential savings during years with unexpected diesel price hikes, such as 2008.

Key words : price uncertainty; risk aversion; service contract; transportation.History : This paper was refereed. Published online in Articles in Advance July 5, 2012.

On July 14, 2008, the price of diesel fuel inthe United States peaked at $4.76 per gallon,

representing a whopping year-over-year increase of65 percent (U.S. Energy Information Administration2009c). Consumers, and even more so, businesseswith year-long transportation services contracts expe-rienced this price shock at the pump. In particular,a large multibillion dollar US retailer that procurestransportation services from third-party full-truckloadcarriers found itself paying substantially more forfreight than expected because of fuel surcharges paidto carriers.

The retailer, like others in its industry, pays carriersdiesel price-dependent fuel surcharges in addition toper-truckload base prices; thus, as the price of dieselrose, so did its transportation costs. Most alarm-ingly, these surcharges sometimes rose faster than fuelprices! The retailer was exceeding its annual trans-portation budget by millions of dollars and neededto quickly curb its expenses. Fortunately, it was ableto renegotiate some of its contracts; however, thisrequired significant effort.

The high diesel prices did not last long: byChristmas, diesel was down to $2.34 per gallon—roughly half what it had been five months ear-lier (U.S. Energy Information Administration 2009c).Because of its renegotiated contracts, the retailer wasout of trouble for the time being. However, it hadlearned an important lesson: it must explicitly man-age diesel price risk. Up to that point, the retailer hadbeen accustomed to evaluating transportation con-tracts using a rough proxy for expected cost.

In the spring of 2009, the retailer initiated a projectwith us to improve its processes for (1) selecting trans-portation carriers, and (2) negotiating better contractterms with these carriers. Together, we developed alinear programming (LP) decision support tool, thelane assignment optimizer (LAO), to help its analystsselect transportation carriers under diesel price uncer-tainty. In addition to base prices, LAO uses carriers’fuel surcharge schedules and analysts’ estimates offuture diesel prices to select a carrier for each of theretailer’s transportation lanes. LAO can incorporatedifferent levels of the retailer’s risk aversion and also

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Turner et al.: Selecting Transportation Carriers Under Diesel Price Uncertainty366 Interfaces 42(4), pp. 365–379, © 2012 INFORMS

guarantee that the proportion of lanes won by anygiven carrier falls within a retailer-specified range.We implemented LAO in Excel using Microsoft SolverFoundation to allow the retailer’s transportation pro-fessionals to easily query it while negotiating withcarriers.

By using LAO, the retailer was able to identify andevaluate opportunities to adjust the shape of the fuelsurcharge curve it faces. When it renewed its con-tracts in October 2009, it was able to get all carriersto agree to a common fuel surcharge schedule thathas a lower slope (i.e., lower surcharge rate) and acap (a maximum surcharge rate that applies to alldiesel prices above a given threshold). As we willsee, changing the slope of the fuel surcharge curvebenefits the retailer by aligning surcharges with thetrue cost of diesel, while capping the surcharge curveallows the retailer to share some diesel price risk withits carriers. Such modifications can be crucial for con-trolling transportation costs in years when the priceof diesel rises dramatically. Had the retailer bent andcapped its surcharge curves in this manner in Octo-ber 2007, we estimate that it could have saved nearly$5 million in 2008.

LAO’s specific focus on diesel price risk distin-guishes it from other implementations of optimiza-tion-based transportation procurement. Although itsunderlying mathematical program is essentially ageneral carrier assignment model, as Caplice andSheffi (2004) describe, specific implementation-baseddetails make LAO useful in practice. In particular, ourway of modeling diesel price risk by extrapolatingtrajectories from a single baseline forecast and thenweighting the trajectories according to a risk-aversionparameter contributes to practice because it is (1) fastto calculate, (2) avoids burdensome data require-ments like distributions for each period’s diesel priceor price evolution models, and (3) is intuitive—ourrisk-aversion parameter is easily tuned because it isnot just a nebulous number: its relationship to ourmodel’s diesel price trajectories can be seen graphi-cally in LAO’s Excel interface.

Our paper also complements existing optimization-based approaches such as those by Powell et al. (1988)and Ergun et al. (2007), which focus on maximiz-ing the profitability of carriers by minimizing thenumber of empty miles driven between loaded trips.Although we do not explicitly consider the optimiza-

tion problem of pairing lanes with backhauls, we alsocare about reducing empty miles; therefore, we dis-cuss how shippers can provide incentives for carriersto solve that problem. From our perspective, fewerempty miles means less diesel used, which lowersdiesel price risk.

Finally, our paper contributes to the transportationplanning literature by discussing the concept of a fuelsurcharge cap and by showing how one retailer suc-cessfully implemented fuel surcharge caps to sharediesel price risk with its carriers.

We organized this paper as follows. We begin bydescribing how the retailer purchases transportationcontracts and how fuel surcharges are computed inpractice. We then describe the retailer’s negotiationprocess prior to our collaboration and the improvednegotiation process, which LAO aids. We next describehow LAO computes the risk-adjusted expected cost ofeach candidate carrier-lane pairing using both thesecosts and other constraints to find an optimal carrier-lane assignment. We also discuss LAO’s easy-to-useExcel interface and its principal benefits. LAO pro-vides an intuitive automated way to compute opti-mal carrier-lane assignments under diesel price uncer-tainty and empowers the retailer to negotiate bettercontractual terms. We conclude with a description ofthe benefits observed to date.

Background

Fuel Surcharge BasicsThe price of diesel fluctuates over time; in someyears—notably 2008—this fluctuation was severe (seeFigure 1). Because of these fluctuations, carriers typi-cally pass on their diesel price risk by charging a fuelsurcharge on top of the agreed-upon per-truckloadprice. That is, the price carriers charge for a full-truckload shipment is

price per shipment = base price + fuel surcharge0

The base price stays fixed over the duration of thecontract, whereas the fuel surcharge varies accordingto the price of diesel at the time of shipment. Thefunction that maps the current diesel price to the fuelsurcharge levied is called a fuel surcharge schedule.

Fuel surcharges transfer diesel price risk fromcarriers to shippers (retailers), making it safer for

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Turner et al.: Selecting Transportation Carriers Under Diesel Price UncertaintyInterfaces 42(4), pp. 365–379, © 2012 INFORMS 367

Forecast

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Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10

($)

Figure 1: A plot of the US retail diesel price (per gallon) shows the dra-matic spike that occurred in the summer of 2008. Although a modest priceincrease was forecast throughout 2009–2010, there was, of course, achance that prices could jump back up to 2008 levels (source: U.S. EnergyInformation Administration 2009a).

carriers to negotiate long-term high-volume trans-portation contracts with shippers. If fuel surchargescould be implemented perfectly, the surcharge billedto the shipper would be exactly equal to the car-rier’s cost of diesel. However, as we will see, fuelsurcharges are only rough approximations of the truecost of diesel; typically, they do not account for factorsthat affect a carrier’s fuel economy on specific routes,such as terrain, traffic patterns, speed driven, class oftruck, load weight, and proportion of time the car-rier’s trucks are empty or full. Furthermore, fuel sur-charges typically depend on the price of diesel as pub-lished in a national or regional price index, whereascarriers buy diesel at times and places other than theindex specifies; they might even buy diesel wholesaleinstead of paying the on-road retail price. Therefore,retailers have latitude to negotiate more favorable fuelsurcharge terms with carriers.

Contract NegotiationEach year, the retailer’s contracted carriers accumu-late millions of miles moving tens of thousands oftruckloads over the retailer’s transportation network.This network consists of hundreds of lanes, whereeach lane is a one-way link between a pair of cities(see Figure 2). Every two years, the retailer negoti-ates new contracts with carriers to provide service onits transportation network. This negotiation processbegins with a request-for-proposal (RFP); the retailerinvites 7 to 10 carriers that cover wide geographicareas (e.g., Schneider National, Werner Enterprises,

Los Angeles

Chicago

Detroit

New York

Dallas

Lane 6

Lane 7

Lane 8

Lane 9Lane 2

Lane 1

Lane 4

Lane 3Lane 5

Figure 2: The diagram shows a subset of a retailer’s transportation net-work. Nodes represent cities, and directed arcs represent lanes.

and J. B. Hunt) to submit bids for each lane theywould like to operate. The retailer discloses lane vol-ume forecasts; thus, carriers know approximately howmany full truckloads they will be asked to transportshould they win the contract for a given lane.

With the first round of bids in hand, the retailerwould produce a preliminary assignment of carriersto lanes such that each lane was assigned to exactlyone carrier—typically, the carrier with the lowestexpected cost, computed as the sum of the base pricebid and the carrier’s fuel surcharge, which is evalu-ated at the average price of diesel from the previousyear. However, because of secondary objectives andside constraints, the retailer would sometimes choosea different carrier to operate a lane. In particular, theretailer ensured that each carrier was allotted at leasta few lanes to keep carriers participating in the RFPyear after year. The retailer would also limit its depen-dence on any one carrier by ensuring that it did notassign too many lanes to one carrier; thus, the retailermoderated its supply chain risk and retained its bar-gaining power for future RFPs. For similar reasons,such market share constraints are typical in other auc-tions, for example, auctioning school meals in Chile(Epstein et al. 2002).

The retailer would use this preliminary assignmentas a starting point for its negotiations with carri-ers. If an incumbent carrier was reliably running alane, the retailer typically would prefer to renew theincumbent’s contract rather than switching carriers.The retailer might also give that incumbent a chanceto match the lowest bid. Similarly, the retailer mightask a carrier that it knows, for example, to be the most

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reliable or the best organized relative to paperwork tomatch the lowest bid. Several iterations of this manualprocess, in which carriers would provide the retailerwith updated bids, would take place. Once the retailerreached mutual agreements with its carriers for all ofits lanes, it would finalize the lane assignment, whichwould then become contractually binding.

In the negotiation process described above, eachbid is for a single lane. However, we should mentionthat a more sophisticated process for selecting carri-ers, a combinatorial auction, would allow carriers tobid on a group of lanes with a single package price.Combinatorial auctions can yield more efficient laneassignments because they encourage carriers to offerdiscounts on bundles of routes; they might reducetheir costs, for example, by forming complete cir-cuits in their networks. According to Sheffi (2004),many large retailers use third-party market makers torun combinatorial auctions for them; as a result, theyhave reduced their transportation costs by 3–15 per-cent. However, fewer than 10 percent of the laneswon via combinatorial auctions are bid as a group of

ITEM 201

When the index price is at least:

115 cents per gallon











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For each 5 cent increase in the U.S. National Average Fuel Index beyond 165, the FSC will increase 0.5%












But less than: Fuel surcharge will be: (%)

Except as otherwise stipulated, all line haul rates provided in Pricing Agreements and Contract Schedules governedby and subject to this publication will be subject to a Fuel Surcharge (FSC) as provided in the table below. The FSCwill apply when the U. S. National Average Fuel Index, as reported by the U. S. Department of Energy, exceeds109.9 cents per gallon. No FSC will apply when the index is below 110 cents per gallon. The surcharge will beshown as a separate entry on the freight bill and will apply as a percentage of net line haul charges. The FSC willnot apply on accessorial charges. The index will be updated every Monday. Revisions to the FSC will go into effecton the following Wednesday. The surcharge amount will be based on the following:

FUEL SURCHARGE (FSC)

Figure 3: An example of a fuel surcharge schedule shows how the fuel surcharge, computed as a percentage of the base price, changes with the price ofdiesel.

lanes (Sheffi 2004), indicating that combinatorial auc-tion cost savings result from a few substantial mod-ifications to an otherwise lane-independent biddingprocess. Because the retailer with which we collabo-rated does not currently use combinatorial auctions,we will not discuss them in this paper. However, ourapproach to valuing diesel price risk is also applicableto the combinatorial auction framework.

Fuel Surcharge DetailsEach carrier has its preferred way of implement-ing fuel surcharges; the two most common methodsare percentage of base price and surcharge per mile.Of the seven carriers that participated in the retailer’sOctober 2007 RFP, three implemented the percentage-of-base-price method, whereas the other four imple-mented the surcharge-per-mile method. Carriers thatimplement percentage of base price define fuel sur-charges as a k-percent factor of the lane’s base price,where the factor k varies with the price of diesel. Forexample, given a base price of $1,000, according tothe fuel surcharge schedule in Figure 3, if diesel is

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250

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Fue

l sur

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$)

Diesel price ($)

Figure 4: The fuel surcharge schedule from Figure 3 expressed in absolutedollar terms for a lane with a base price of $1,000. The per-truckload fuelsurcharge (in dollars) is plotted as a function of diesel price.

between $1.55 and $1.59 per gallon, the fuel surchargeis $50 (5 percent of $1,000). However, carriers thatimplement surcharge per mile define fuel surchargesas being $x per lane-mile, where x varies with theprice of diesel. For example, suppose the surcharge ofa carrier is $0.50 per mile when the price of diesel is$3.60 per gallon. On a 600-mile lane, this correspondsto a per-shipment fuel surcharge of $300 ($0050×6005.

The distinction between the percentage-of-base-price and surcharge-per-mile methods can be impor-tant, as we will show later. However, for now wenote that regardless of how a fuel surcharge is imple-mented, it can be expressed in absolute dollar terms;that is, the per-shipment fuel surcharge (in dollars)can be expressed as a function of the current dieselprice. As Figure 4 shows, fuel surcharge schedules areoften piecewise-linear: no surcharges are levied whenthe price of diesel is below a threshold called the peg($1.10 per gallon in this case), and the per-shipmentsurcharge increases linearly as the price of diesel risesabove the peg.

In general, however, fuel surcharge schedules donot need to be piecewise-linear with two segments.Prompted by the run-up in diesel prices in 2008,shippers began experimenting with different fuel sur-charge functions; as Bonney (2011) describes, someswitched to so-called zero-peg fuel surcharge sched-ules, which are purely linear and start accruing sur-charges on the first cent of diesel paid. As ChrisCaplice, executive director of the Center for Trans-portation and Logistics at the Massachusetts Instituteof Technology points out (see Bonney 2011), zero-peg surcharge schedules make fuel surcharges more

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$1.10 pegsurcharge

$0 pegsurcharge

Fuel cost hidden inthe base price

Figure 5: Using the $1.10 peg fuel surcharge schedule from Figure 3leads to some fuel costs being hidden in the base price, as the graphindicates.

transparent, making them easier to measure and man-age. In general, a fuel surcharge schedule with a $kpeg will begin accruing surcharges when the priceof diesel exceeds $k. Thus, the higher the peg, thelower are total fuel surcharges. However, the first $kof every gallon of diesel the carrier buys is hidden inthe base price; therefore, we can expect higher baseprices when higher pegs are used (see Figure 5).

The retailer with which we worked has surchargeswith pegs in the $1.10–$1.30 range. Although thismeans that some fuel costs are hidden in the baseprice, this is not a problem for quantifying diesel pricerisk because the likelihood that the price of dieselwill drop below the peg is negligible (i.e., this hiddencharge will remain constant in all future scenarios).

The Importance of Explicitly Managing DieselPrice RiskWe define diesel price risk as an unexpected priceincrease above the level forecast. This is consistentwith our claim that fuel surcharges are importantin managing diesel price risk, because if carrierscould accurately predict all price increases, then thecorresponding costs could be built into base priceswithout a need for fuel surcharges. Along this lineof reasoning, we argue that carriers can effectivelymanage basis risk (i.e., the risk that carriers facebecause fuel surcharges are computed using a pub-lished price index, which might differ from the actualprice paid at the pump) by including a risk premiumin their base prices. Because basis risk depends onthe volatility of the spread (index price minus on-roadprice) rather than a drastic upward shift in the price

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Carrier 3Carrier 5Carrier 6

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-shi

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Figure 6: We plot the cost per shipment (base price plus fuel surcharge)as a function of diesel price for three carriers (from the retailer’s October2007 RFP) that offer to operate lane 121. Whether Carrier 5 or Carrier 6 ischeaper depends on whether diesel is above or below $3.30 per gallon.

of diesel, we can view basis risk as a normal cost ofdoing business; this is not the case for diesel price risk.

It is important for retailers to take diesel pricerisk into account when choosing which carrier bidsto accept, because the carrier that is the cheapestdepends on the current diesel price; the cheapest car-rier could change as the price changes (see Figure 6).Notice that for lane 121, Carrier 5 is the lowest-costcarrier when diesel is below $3.30 per gallon; how-ever, Carrier 6 is the cheapest when diesel is above$3.30 per gallon. As we will see, the best carrier for agiven lane depends on the retailer’s diesel price fore-cast, the uncertainty of this forecast, and the retailer’stolerance for diesel price risk. Often, a risk-averseretailer may be willing to accept a transportation con-tract with a higher base price if the fuel surchargeschedule has a shallower slope.

The New Contract Negotiation ProcessTo incorporate fuel surcharges into the retailer’s RFP,we initially proposed that each bid for a lane shouldinclude both a base price and a lane-specific fuel sur-charge schedule. This would entice carriers to modifytheir fuel surcharge schedules on a lane-by-lane basisto express local comparative advantages in fuel econ-omy driven by, for example, the terrain of the routeor the number of empty miles required to pick upa subsequent load. Although the retailer agreed thatlane-specific fuel surcharge schedules would be bene-ficial, it decided, at least for the time being, to limit thenumber of variables that it negotiates with carriers by

a

b

c

Carriers

1

2

3

LanesStart

Request initialbids

Compute optimalassignment

(LAO)

Is assignmentacceptable?

Yes

Accept all bids,finalize

contracts

Stop

Negotiate withcarriers:

Get revised bidsNo

Figure 7: The retailer’s transportation professionals can use LAO to com-pute optimal lane assignments at each iteration of the contract negotia-tion process.

instead having each carrier bid a single fuel surchargeschedule to be shared across all of that carrier’s lanes.

Given this bidding structure, we used Excel andMicrosoft Solver Foundation to develop LAO to com-pute the cost of each candidate carrier-lane pairingand to subsequently solve for an optimal assignmentof carriers (see Figure 7). A crucial component ofLAO is how potential diesel price paths and thusdiesel price risk are incorporated into the objectivefunction in a computationally cheap, intuitive way.We describe the details of LAO next.

Computing Carrier-Lane CostsLAO computes the cost of each candidate carrier-lanepairing using formulas that synthesize informationfrom a monthly forecast of diesel prices, a volatilityparameter, and a risk-aversion parameter, as well asthe base prices and fuel surcharges from the carri-ers’ bids. This section elaborates on these parametersand how they affect cost. To be consistent with the

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retailer’s current practice (i.e., its forecasts for dieselprices and lane volumes are available for one yearahead only), we evaluate LAO over a one-year hori-zon, despite the contracts’ durations being two years.

The standard approach to modeling a risk-aversedecision maker (Kreps 1988) involves modeling thedecision maker’s utility function as concave increas-ing and computing his expected utility over uncertainprices. For example, for expected mean-variance util-ity, a risk-averse retailer’s expected utility for a can-didate carrier-lane pairing would be expected annualcost minus some multiple of the variance of annualcost. However, this approach is cumbersome: to com-pute the variance of annual cost, the retailer wouldneed to estimate the covariance matrix for monthlydiesel price—a task it preferred to avoid. Further-more, the retailer felt that picking a multiplier for scal-ing the variance in the expected utility calculation wasnonintuitive. Thus, in consultation with the retailer,we devised a more intuitive and simpler way of com-puting risk-adjusted expected costs.

LAO computes the risk-adjusted expected cost ofeach candidate carrier-lane pairing from a sum ofmonthly costs. Each monthly cost is the product of anestimated shipping volume times a per-shipment cost.The per-shipment cost is equal to a base price plusa risk-adjusted expected fuel surcharge, which variesby month. Finally, it computes each risk-adjustedexpected fuel surcharge by appropriately weightingand summing together the lane’s fuel surcharge eval-uated along several possible diesel price trajecto-ries. To describe the computation of a risk-adjustedexpected fuel surcharge, we must first describe howwe generate diesel price trajectories.

Generating Diesel Price TrajectoriesThe U.S. Energy Information Administration pub-lishes a downloadable report (U.S. Energy Informa-tion Administration 2007), which includes a monthlyforecast of diesel prices—a monthly diesel price timeseries that extends one year into the future. We takethis forecast as our baseline, which we call the mediantrajectory or the 50th percentile trajectory. We assumethere is an equal chance that the future price of dieselwill be above or below this baseline.

To construct additional trajectories, we model theuncertainty of the diesel price at the end of the

12-month horizon. Following the common assump-tion from the finance literature (cf. Dixit and Pindyck1994) that price changes are lognormally distributed,we assume that the price of diesel at the end of thehorizon is lognormally distributed with median equalto the baseline forecast. The retailer provides as inputto LAO the scale parameter of this lognormal randomvariable (i.e., the volatility parameter); it uses a com-bination of historical data, market conditions, and itsown beliefs about future price uncertainty to estimatethe volatility parameter. Different percentiles of thislognormally distributed random variable give differ-ent possible end-of-horizon diesel prices. For details,please refer to the appendix.

In addition to the median (50th percentile) trajec-tory, LAO uses six trajectories, that correspond toprice paths that begin at today’s price and termi-nate at the horizon at the 10th, 30th, 70th, 85th,95th, and 99th percentiles of the lognormally dis-tributed end-of-horizon price. We selected the numberof paths and the percentiles of each in consultationwith the retailer; more or different levels could eas-ily be accommodated. We interpolate the price pointsalong each trajectory such that no deviation from thebaseline occurs today, a 50 percent deviation fromthe baseline occurs halfway to the horizon, and a100 percent deviation from the baseline occurs at thehorizon (please see the appendix for details). Fig-ure 8 illustrates the seven price trajectories that LAOgenerates.

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Figure 8: The graph shows an example of the seven price trajectories.Notice that all trajectories mimic the seasonality exhibited in the base-line forecast. We generated these trajectories using a baseline forecastfrom October 2007, which we used to evaluate LAO over the 2008 run-upin diesel prices.

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Figure 9: As the risk-aversion parameter increases, LAO gives moreweight to higher-percentile trajectories.

Weighting Diesel Price TrajectoriesLAO weights and sums the fuel surcharges evalu-ated along the seven price trajectories to compute arisk-adjusted expected fuel surcharge in each monthfor each candidate carrier-lane pairing. If a retaileris risk neutral, LAO selects weights so that the risk-adjusted expected fuel surcharges are simply expectedfuel surcharges. However, because the retailer tendsto be averse to diesel price risk, risk-adjusted expectedfuel surcharges are typically higher than expected fuelsurcharges.

The retailer’s risk-aversion parameter, which LAOuses to skew the weights away from the risk-neutralcase, determines exactly how much higher. As therisk-aversion parameter increases, LAO gives moreweight to the higher-percentile trajectories, therebyshifting the emphasis of the retailer’s plan from usingexpected diesel prices to using higher-than-expectedprices. Therefore, risk aversion is not aversion to priceincreases from the current price level, but rather aver-sion to price increases above the projected future pricelevel, as modeled by the forecast (50th percentile tra-jectory). Figure 9 illustrates how the weights for eachtrajectory behave as the retailer’s risk-aversion levelincreases. The appendix provides details on how theweights are computed.

Using LAO to ComputeOptimal Lane AssignmentsWe implemented LAO in Microsoft Excel to allow theretailer’s transportation professionals to easily inter-act with it as they negotiate contracts with carri-ers. LAO contains five main spreadsheets: Settings,Model, SolverResults, Solution, and LaneView.

The user enters the main inputs—a monthly fore-cast of diesel prices, a volatility parameter, and arisk-aversion parameter—on the Settings sheet, whichincludes the charts shown in Figures 8 and 9 to guidethe user in providing these parameters. In conjunc-tion with lane volumes and the carriers’ bids for eachlane (input on the Model sheet), Excel formulas usethese parameters to calculate the total annual risk-adjusted expected cost for each carrier-lane combina-tion. The computed costs are stored in matrix form onthe Model sheet for easy reference.

LAO solves for the optimal carrier-lane assignmentusing Microsoft Solver Foundation for Excel, which

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pulls data from the relevant spreadsheets and sendsthe complete solution as output to the Solver Resultssheet. Because LAO is intended to be used interac-tively throughout the negotiation process, it must befast; it takes less than a second to find the optimalcarrier-lane assignment that minimizes risk-adjustedexpected costs, subject to lower and upper boundson the number of lanes each carrier can win. Theappendix provides the formal representation of thelinear program.

Two spreadsheets summarize the solution: the Solu-tion sheet slices the total annual cost by lane and thenby carrier. It also reports the total annual cost of theoptimal allocation evaluated along each of the sevendiesel price trajectories, thereby providing sensitivityanalysis. Base prices and fuel surcharges are sepa-rated out for all of the above.

Finally, the Lane View sheet graphically displays,for a single lane, the cost of accepting each carrier’sbid as a function of the diesel price (see Figure 6). Thisinterface is particularly useful, because the retailer’stransportation professionals can use it to understandhow awarding a lane to a carrier other than the onethat LAO selected would impact the annual cost ofrunning that lane at various diesel prices.

ImplementationIn October 2009, the retailer used LAO in negotiat-ing its new contracts. Its transportation profession-als appreciated LAO’s user-friendly interface, whichhelped determine how to (1) bend the cost curve tomore closely align surcharge rates with the true costof diesel, and (2) cap the cost curve to share dieselprice risk with the retailer’s carriers. We next dis-cuss these two important cost-curve improvementsand estimate their cost savings.

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Figure 10: By bending the cost curve, the slope of a fuel surcharge schedule is more closely aligned with the true cost of diesel.

Bending the Cost CurveCarriers use fuel surcharges to transfer the amountthey pay for diesel to their customers (i.e., retailers).In practice, this transfer is seldom perfect, leading car-riers to either overcharge or undercharge for diesel ona lane-by-lane basis. Graphically, overcharging occurswhen the upward-sloping part of the fuel surchargeschedule is too steep. Thus, the retailer would like toidentify when a carrier is likely to be overcharging,so it can negotiate to flatten the slope and bend thecost curve (see Figure 10).

Knowing exactly how fuel efficient its carriers are isdifficult for the retailer. As we mentioned previously,fuel efficiency depends on many factors, includingclass and age of truck, driving speed, traffic patterns,flatness of terrain, and load weight. As a startingpoint, however, the retailer may choose a benchmarkfuel economy to compare carriers. For our bench-mark, we will use the published national average fueleconomy of 6.0 miles per gallon (mpg) for freighttrucks, as measured by the U.S. Energy InformationAdministration (2009b).

We call a fuel surcharge schedule perfectly alignedif the rate at which fuel surcharges are billed tothe retailer is equal to the rate at which the carrierspends money on diesel to serve the contracted lane.Thus, a fuel surcharge schedule is perfectly alignedwhen its slope (as represented in gallons per mile)is equal to the carrier’s actual fuel consumption ingallons per mile. A zero-peg perfectly aligned fuelsurcharge schedule will ensure that the total fuel sur-charges billed in dollars over the life of the transporta-tion contract are equal to the carrier’s actual dieselexpenditures. Moreover, a $x-peg perfectly alignedfuel surcharge schedule will, if $x is small enoughfor the price of diesel to exceed $x for the entire life

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of the transportation contract, yield a total surchargein dollars equal to the carrier’s actual diesel expen-ditures, minus the first $x dollars of each gallon ofdiesel, which we assume to be included in the lane’sbase price.

The benchmark 6.0 mpg fuel economy implies afuel consumption rate of 1/6 gallons per mile, whichwe can quickly compare with the slopes of the fuelsurcharge schedules from the retailer’s October 2007RFP. Doing this, we notice that all carriers that imple-mented per-mile surcharges charged exactly 20 centsper mile for every dollar that a gallon of diesel waspriced above the peg (the peg was carrier specificand in the range of $1.10–$1.30). This gives each ofthese carriers an implied fuel consumption rate (fuelsurcharge slope) of 1/5 gallons per mile ($0.20 permile ÷ $1 per gallon), which is 20 percent higher thanthe 1/6 gallons-per-mile benchmark. Therefore, fromthis rough analysis, we can conclude that these car-riers are overcharging for fuel by about 20 percent(i.e., the retailer has some negotiating room to bendthe cost curve).

Of course, this simple analysis does not considerthe effect of the empty (deadhead) miles that a carriermust drive to pick up the next load after deliveringthe retailer’s shipment. Because rising diesel pricesalso increase the carrier’s costs of running emptymiles and thus decrease the profitability of a givenlane, one can argue that a properly aligned fuel sur-charge schedule should also transfer the cost of dieselfrom deadhead miles to the retailer. In this case, a bet-ter benchmark for fuel consumption is 0.2033 gallonsper mile, which we compute by inflating the old 1/6gallons-per-mile benchmark by 22 percent because,in 2008, truckload carriers reported they were driv-ing empty 22 percent of the time (American TruckingAssociation 2008). This benchmark is likely a tad high,because we have not considered that empty trucksweigh less and therefore should have an average fueleconomy higher than 6.0 mpg. Nonetheless, we notethat when the cost of diesel for running empty milesis included, carriers no longer appear to be over-charging. Thus, a normative question presents itself:Should retailers encourage carriers to use the fuel sur-charge or the base price to transfer the cost of dieselused for empty miles back to them?

Lazarus (2010) advises carriers to inflate fuel sur-charges to transfer diesel costs for empty miles backto shippers (retailers). Although this approach is pru-dent for carriers, it may undermine supply chain effi-ciency. Indeed, if a carrier is bound by a surchargeschedule with a shallower slope than its diesel con-sumption rate, that carrier will have a strong incentiveto lower its fuel consumption to curb its exposureto escalating diesel prices (i.e., carriers will spendmore effort finding backhauls to lower the number ofempty miles driven, and spend more money upgrad-ing their fleet to boost fuel economy). Therefore, aretailer that is averse to diesel price risk or perhapsone with sustainability initiatives that encourage fuelefficiency may want to accept a higher base price inreturn for a fuel surcharge schedule with a shallowerslope. For this reason, we believe it is appropriate touse 1/6 gallons per mile as a broad fuel consumptiontarget—a fuel consumption rate that will be roughlyaligned with the true cost of diesel on lanes with anefficiently chosen carrier.

Figure 11 compares our rough 1/6 gallon-per-milefuel consumption benchmark with the implied fuelconsumption rates offered in the retailer’s 2007 RFP.Each point represents the fuel surcharge for a sin-gle candidate carrier-lane pair, assuming that diesel is$4 per gallon. The upward-sloping solid line in Fig-ure 11a, which is our benchmark, represents a carrierwith a fuel surcharge schedule with a slope of 1/6gallons per mile and a peg of $1.15 (this is appro-priate because carriers had pegs in the $1.10–$1.30range). Points below the line are good, whereas pointsabove the line are bad; that is, carrier-lane pairs below(resp. above) the line have shallow (resp. steep) fuelsurcharge schedules that pay for fuel at a rate lower(resp. higher) than 1/6 gallons per mile. As we men-tioned previously, all carriers with surcharge-per-milebased schedules (indicated by x-marks) have sched-ules with a 1/5 gallon-per-mile slope; thus, they areabove our benchmark.

An interesting pattern surfaces when we look at thecarrier-lane pairs from carriers that use percentage-of-base price surcharges (cf. the solid circles in Fig-ure 11). From Figure 11a, we see that the majority ofshort-haul carrier-lane pairs are above the line andare therefore overcharging for fuel relative to our

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(a) The graph shows the fuel surcharge levied in dollars pertruckload for each (carrier, lane) bid, as compared to ourbenchmark. We assume that the price of diesel is $4 per gallon.

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(b) The graph shows the relative amount each (carrier, lane)bid is overcharging for diesel, as compared to our benchmark.The graph does not show 10 outliers (the highest is anestimated overcharge of 12,943 percent on a 1.1 mile lane).

($)

(%)

0

Figure 11: The graphs illustrate fuel surcharges for each carrier-lane pairin the retailer’s 2007 RFP, ordered by lane-miles and compared with the1/6 gallons-per-mile fuel consumption benchmark.

benchmark, whereas the majority of long-haul carrier-lane pairs are below the line and are undercharg-ing. Moreover, Figure 11b shows that the carrier-lanepairs with the lowest lane-miles tend to overchargethe most in percentage terms (computed by tak-ing the gap between fuel surcharge and benchmarkfrom Figure 11a and dividing it by the benchmark).To some extent, we expect this pattern because trucksspend a larger proportion of time in stop-and-go traf-fic on short-haul lanes than long-haul lanes, whichtranslates into a higher fuel consumption rate for

short-haul lanes. However, to a larger extent, this pat-tern manifests for a different reason.

The overcharging and undercharging pattern ofFigure 11b is predominantly a side effect of theretailer’s choice to have each percentage-of-base-pricecarrier adopt a single surcharge schedule for all ofits lanes. To see why, note that a carrier incurs bothfixed costs and variable costs for transporting a truck-load on a lane. The variable costs, which includediesel, increase with the number of lane-miles, butthe fixed costs do not. As a result, short hauls havea higher proportion of fixed costs than long hauls,and extremely short hauls (∼1 mile) have almostno variable costs (or diesel costs!) at all. When fuelsurcharges are levied directly on lane-miles, shorthauls are appropriately surcharged very little. How-ever, when fuel surcharges are levied on base prices,short hauls overcharge because the base price, whichincludes fixed costs, does not approach zero as lanemileage approaches zero. This effect is strongest forthe shortest lanes, as Figure 11b shows, where the esti-mated percentage overcharge approaches infinity aslane-miles approach zero.

When one surcharge schedule is shared across allof a carrier’s lanes, the base price is the only lever thecarrier has to express how efficient it would be operat-ing a lane, and because base price includes fixed costsand other nonfuel variable costs, it is difficult for acarrier to use base price alone to show a retailer thata specific lane has a low fuel consumption rate—animportant metric for retailers in explicitly managingtheir diesel price risk. Moreover, because base priceis not directly proportional to lane mileage, a retailercannot use a single percentage-of-base-price scheduleto perfectly align fuel surcharges to all of a carrier’slanes. The best we can hope for is that the same car-rier wins a good share of both short and long hauls,so that overcharges are roughly balanced by under-charges. In general, this outcome is hard to guaranteewithout imposing constraints on the distribution oflane lengths assigned to each carrier; however, con-straining LAO’s assignment problem in this mannerwould increase the cost of the optimal carrier-laneassignment.

Even in the case in which fuel surcharges arelevied per mile, we may benefit from lane-specific sur-charges. This is because the specific economics of each

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lane (which depend on the number of empty milesdriven to collect the next load) could motivate the useof different fuel surcharge slopes for similar-lengthlanes that have different backhaul opportunities.

Therefore, we recommend using lane-specific fuelsurcharge schedules whenever possible. However, werecognize the necessity to strike a balance betweenmore degrees of freedom with which to optimizeand fewer degrees of freedom with which to speedup the RFP’s negotiation process. Thus, although theretailer agrees that lane-specific fuel surcharge sched-ules would be beneficial, and continues to enhanceLAO and its negotiation process, the retailer decidedto use carrier-specific fuel surcharge schedules in itsOctober 2009 RFP.

Capping the Cost CurveTypical fuel surcharge schedules (see Figure 4) haveunbounded surcharges; that is, if the price of dieselcontinues to climb, the fuel surcharge assessed tothe retailer also continues to increase. As a result,the retailer exclusively bears unlimited diesel pricerisk. An upper bound to the fuel surcharge sched-ule, called a surcharge cap, causes diesel price riskto be shared between the retailer and the carrier.With a cap, the carrier bears the most extremeprice increases and the retailer bears moderate priceincreases. Using LAO, the retailer can negotiate to capthe cost curve by establishing a maximum fuel sur-charge (see Figure 12).

Certainly, the retailer prefers to lower its exposureto diesel price risk; however, instituting a surchargecap might be costly because carriers could increasetheir base prices to compensate for the burden ofhaving a cap. Therefore, the retailer must balance its

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Figure 12: A fuel surcharge cap limits the retailer’s exposure to diesel price risk by sharing some risk with itscarriers.

desire to mitigate diesel price risk with its objectiveof minimizing the expected cost of transportation; thepoint at which to strike this balance depends on theretailer’s risk-aversion level.

Ultimately, if either party—retailer or carrier—isassigned a higher level of diesel price risk than itscomfort level allows, it could engage in hedging bypurchasing call options in the diesel futures market.Then, should the price of diesel rise, higher fuel costswould be (partially) offset by revenue generated fromexercising the call option. Because diesel is more inte-gral to the carriers’ business than to the retailer’s, theretailer argued that carriers can leverage their knowl-edge of diesel prices to potentially hedge diesel pricerisk at a lower cost than the retailer, motivating theretailer’s use of surcharge caps to transfer some dieselprice risk onto carriers.

Estimated Cost SavingsIn its October 2009 RFP, the retailer began to activelymanage diesel price risk by negotiating with its car-riers to bend and cap their surcharge schedules. Theresult of these negotiations was a common fuel sur-charge schedule, which all carriers adopted, that sig-nificantly reduced the retailer’s exposure to dieselprice risk. This common surcharge schedule computessurcharges via the percentage-of-base-price method;in comparison to the surcharge schedules from 2007,it has a shallower slope and includes a surchargecap (a new feature). In response to the lower negoti-ated fuel surcharges, carriers raised their base pricesby 7.26 percent over 2007 levels. However, savingsfrom lower fuel surcharges exceed costs from higherbase prices under nearly all diesel price trajectories,

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Without LAO ($) With LAO ($)

Base Fuel Total Base Fuel TotalTrajectory charges surcharges cost charges surcharges cost

10% 7109 1303 8502 7609 806 850530% 7109 1506 8705 7609 1000 860950% 7109 1705 8904 7609 1102 880170% 7109 1905 9104 7609 1206 890485% 7109 2106 9305 7609 1308 900795% 7109 2403 9603 7609 1507 920699% 7109 2708 9908 7609 1701 9400Expected 7109 1709 8908 7609 1105 8804Actual 7109 2603 9802 7609 1608 9306

Table 1: We estimate that the retailer could have saved $4.6 million in2008. All figures are in millions of dollars.

and are most significant for the highest trajectories(i.e., cases with the largest unexpected increase indiesel price).

Table 1 describes two cases: one without LAOand one with LAO. The without-LAO case runs theOctober 2007 RFP (the last RFP for which we havecomplete data) according to the retailer’s previousevaluation criterion (the cost of a carrier-lane com-bination is its base price plus the fuel surchargeevaluated at the prior year’s average diesel price;i.e., the retailer is risk neutral and expected fuel costis based on historical data). In comparison, the with-LAO case runs the October 2007 RFP using LAOto optimally select carrier-lane assignments that min-imize base price plus risk-adjusted expected cost(with the risk-aversion parameter set at level 4). Thewith-LAO case additionally uses the common fuelsurcharge schedule introduced in October 2009 andraises the base prices of all bids by 7.26 percent. Fuelsurcharges were computed from actual 2008 prices(labeled “Actual”), and from forecasted price trajec-tories (labeled Trajectories 10%1 0 0 0 199%). Expectedcosts (labeled “Expected”) were computed by appro-priately weighting and summing the possible pricetrajectories.

From this comparison, we can see that the with-LAO case has markedly lower costs for high-percentiletrajectories, resulting in substantial savings in years inwhich diesel prices increase dramatically (e.g., 2008).Specifically, evaluating the cost along the actual pricetrajectory observed in 2008, LAO estimates the retailercould have saved $4.6 million 4$9802 − $93065 had it

used the new fuel schedule with surcharge cap in its2007 RFP. This analysis serves to illustrate the powerof a good decision support tool in helping to negotiatemore favorable contract terms.

ConclusionsThe LAO tool has improved the retailer’s capabil-ity to evaluate the trade-off between base price andrisk-adjusted fuel surcharge, allowing the retailer to(1) cap and bend its cost curves, and (2) select carriersbased on lowest risk-adjusted annual cost. LAO hasincorporated diesel price risk into the retailer’s carrierselection process, leading to transportation contractsthat are robust in the face of uncertain diesel prices.

We note that the retailer decided to convince its car-riers to use a common percentage-of-base-price fuelsurcharge schedule for all lanes in its October 2009RFP. In this special case, the common fuel surchargecan be factored out of the objective, leaving LAO tominimize the sum of the base prices from selectedcarrier-lane pairs. As a result, the optimal carrier-laneallocation under the given common fuel surchargeschedule is independent of diesel price—a strong con-dition that implies that regardless of how the price ofdiesel evolves, the retailer will not have an incentiveto switch carriers on any lane. However, the retailerpays a price for insisting on this level of homogeneity.As Figure 11 shows, aligning the slope of this com-mon surcharge schedule with all carrier-lane pairs isimpossible; thus, short hauls will overcharge. More-over, by insisting that all carriers adopt the samefuel surcharge schedule, the retailer learns less aboutindividual carriers’ fuel consumption rates, making itharder to know which slope and cap to suggest forits common fuel surcharge schedule.

Allowing carriers to competitively bid fuel sur-charge schedules on a lane-by-lane basis is the idealcase, because carriers with the best fuel economieswould be more apt to win lanes. However, strikinga balance between having more degrees of freedomwith which to optimize and fewer degrees of freedomto speed up the RFP’s negotiation process is necessary.Fortunately, LAO’s ability to manage the complexityof lane-specific fuel surcharge schedules will allow theretailer to strategically introduce heterogeneity into itsfuel surcharge schedules to capture additional savingsin future years.

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� lb (%) ub (%)

10 0 2030 20 4050 40 6070 60 770585 7705 9095 90 9799 97 100

Table 2: Each trajectory � is representative of continuous-space trajec-tories from the lower-bound percentile 4lb5 to the upper-bound per-centile 4ub5.

AppendixThis section provides supplementary material for four sec-tions of the paper: Generating Diesel Price Trajectories, Weight-ing Diesel Price Trajectories, Computing Carrier-Lane Costs, andUsing LAO to Compute Optimal Lane Assignments.

Generating Diesel Price TrajectoriesLet H be the lognormally distributed end-of-horizon dieselprice. Specifically, H ∼ Log-N4�1�25, where e� is the dieselprice specified by the baseline forecast at the end of the hori-zon and � is the scale parameter (i.e., volatility parameter)specified by the retailer. Denoting h� as the �th percentileof H and ê4 · 5 as the cumulative distribution function ofthe standard normal distribution, we have h� = e�+�ê−14�5 =

4e�54e�ê−14�55. Thus, we can think of the end-of-horizon price

h� at a given percentile � as the baseline price e� multipliedby a distortion factor e�ê

−14�5. To generate the rest of theprice points along a trajectory, we progressively attenuatethis distortion for price points closer to today’s. Thus, for aprice point on the �th percentile trajectory at month m of12, the appropriate distortion factor is dm1� = e4m/125�ê−14�5.Finally, the diesel price in month m along the �th percentiletrajectory is pm1� = pm150 × dm1�, where pm150 is the value ofthe baseline forecast (median trajectory) at month m.

Weighting Diesel Price TrajectoriesLet � be the retailer’s risk-aversion parameter, which rangesfrom 0 (risk neutral) to 5 (very risk averse). We treat eachtrajectory � as a sample path, which occurs with probabil-ity w�. In this section, we describe how the retailer’s risk-aversion parameter � determines the weights w�.

Although we have discretized our sample space to onlyseven trajectories, we can envision a continuous space oftrajectories from the 0th percentile to the 100th percentile(see Table 2).

When �= 0 (risk-neutral case), we define the weights asw� = ub − lb. However, as � increases, progressively moreweight is given to higher-percentile trajectories. The retailerchose the proprietary weighting formulas used for �≥ 1 tobe graphically intuitive. Qualitatively, as � increases, pro-gressively more weight is given to higher-percentile trajec-tories. Note that the relative weights shown in Figure 9 have

Indicesi = a carrier.j = a lane.m = a month ∈ 81 0 0 0129.�= a trajectory ∈ 8101301501701851951999.Decision Variablesxij = 1 if carrier i is assigned to lane j , 0 otherwise.Parametersai , ai = min/max # of lanes to assign to carrier i.bij = base price bid by carrier i for lane j .cij = annual risk-adjusted expected cost for lane j if carrier i is chosen

to operate the lane.pm1� = diesel price in month m on trajectory �.rijm = risk-adjusted fuel surcharge for carrier i, lane j , month m.sij 4 · 5= fuel surcharge function bid by carrier i for lane j .vjm = volume of lane j in month m (# truckloads).w� =weight of trajectory �.

Table 3: The table shows the notation used to formally define LAO’s inputsand outputs.

been normalized by dividing by the risk-neutral weightsub− lb.

Computing Carrier-Lane CostsUsing the notation of Table 3, the risk-adjusted expectedfuel surcharge for carrier i on lane j in month m is rijm =∑

�w�sij4pm1�5, the price per shipment in month m for car-rier i on lane j is bij + rijm, and the annual risk-adjusted costof lane j under carrier i is cij =

∑

m vjm4bij + rijm5.

Using LAO to Compute Optimal Lane AssignmentsLAO solves a linear program that minimizes the risk-adjusted expected cost of an assignment, subject to the con-straints that each lane is assigned to exactly one carrier, andcarrier i is assigned at least ai but no more than ai lanes.This linear program, which always produces integer solu-tions, is

min∑

i1 j

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j

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0 ≤ xij ≤ 1 ∀ i1 j0

AcknowledgmentsWe thank Senior Deputy Dean Ilker Baybars and CarolynHess Abraham for their help in organizing the collaborationbetween Carnegie Mellon University and the retailer, NicolaSecomandi for discussing commodity price modeling, andour collaborators at the retailer who must remain anony-mous to preserve confidentiality. Many thanks also to two

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anonymous referees and the editors of Interfaces for the com-ments and suggestions, which have decidedly improvedthis manuscript.

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The editor-in-chief has received a verification letter attest-ing to the impact of this work on the firm. The firm hasrequested to remain anonymous.

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a large us retailer selects transportation carriers under diesel price uncertainty

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