Improving bid efficiency for humanitarian food aid procurement

Int. J. Production Economics 134 (2011) 238–245

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Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe

Improving bid efficiency for humanitarian food aid procurement Aniruddha Bagchi a,1, Jomon Aliyas Paul a,2, Michael Maloni b,n a b

Department of Economics, Finance, & Quantitative Analysis, Kennesaw State University, 1000 Chastain Road, Kennesaw, GA 30144, USA Department of Management & Entrepreneurship, Kennesaw State University, 1000 Chastain Road, Kennesaw, GA 30144, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 26 January 2011 Accepted 8 July 2011 Available online 26 July 2011

The competitive bid process used by the US Department of Agriculture (USDA) to procure food supplies and transportation services for humanitarian food aid is subject to bidder gaming that can increase prices and deter competition. Additionally, suppliers and carriers are matched after bid submission, preventing synergies from coordinated planning. Given these concerns, we determine the optimal auction mechanism to minimize gaming then justify pre-bid planning between suppliers and carriers using properties of the cost distribution functions. We operationalize these changes with a uniform price auction. The improved mechanism should deter gaming, enhance bid participation, and increase delivered food aid volumes. & 2011 Elsevier B.V. All rights reserved.

Keywords: Auctions Procurement Humanitarian logistics

1. Introduction The catastrophic earthquake in Haiti in 2010 highlighted the urgency of global food aid. Yet, with estimates of the malnourished exceeding one billion persons worldwide (Food and Agriculture Organization, 2009), the need for food aid distribution is constant. As the world’s largest food donor (Shapouri and Rosen, 2004), the United States distributes more than $1 billion of emergency and non-emergency food aid annually, primarily via the US Public Law 480 ‘‘Food for Peace’’ Title II program. Currently, procurement of Title II food supplies and transportation services is conducted via a competitive bidding process by the US Department of Agriculture (USDA), which selects sealed food supplier and carrier bids based primarily on a linear programming transshipment model (Trestrail et al., 2009). Despite the humanitarian intentions of food aid, there is evidence from industry that the current USDA bid process is subject to gaming by bidders (Trestrail et al., 2008). The USDA ideally seeks bids that closely reflect actual bidder (food supply and transportation) costs. In gaming the bid system, however, bidders attempt to estimate clearing (i.e., winning) bid amounts then bid as high as possible (i.e., well above costs) to maximize profits (Trestrail et al., 2008). Beyond leading to higher award costs to the USDA, such gaming also complicates the bid preparation process, creates an unfair bidding environment (Cramton and Stoft, 2006), and can deter bidder participation (Rothkopf and

n

Corresponding author. Tel.: þ1 770 423 6549. E-mail addresses: [email protected] (A. Bagchi), [email protected] (J. Aliyas Paul), [email protected] (M. Maloni). 1 Tel.: þ1 770 423 6720. 2 Tel.: þ1 770 423 6086. 0925-5273/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2011.07.004

Harstad, 1994). Moreover, the USDA forms supplier–carrier pairings for lanes after food suppliers and carriers have submitted independent bids, thus restricting opportunities for these bidders to coordinate to find operational synergies. This again potentially increases bid amounts. From a humanitarian perspective, higher food aid bids ultimately reduce the volume of food aid that can be delivered to persons in need. Rising food prices and increasing emergency requests have already strained US food aid resources (American Shipper, 2008). Additionally, US food aid budgets have generally decreased over recent decades (US General Accounting Office, 2002), and current federal deficits could lead to further reductions in food aid funding. Unfortunately, high bids and low competition instigated by both gaming and the lack of pre-bid coordination will increase food aid costs, more quickly consume available budgets, and restrict the ability to respond to additional food aid requests. This implores exploration of improvements to the USDA bid process to promote more open and pure competition among bidders. In this paper, we investigate two research questions focused on enhancing USDA bid effectiveness: 1. What is the optimal mechanism for awarding bids that will minimize bidder gaming? 2. What is the most efficient approach for forming supplier– carrier pairings when using this mechanism? Our methodology proceeds as follows. We first determine the optimal auction mechanism to deter gaming. We then use the properties of the cost distribution functions of supplier–carrier pairings in terms of the likelihood ratio to justify pre-bid supplier–carrier partnership capabilities. We subsequently coordinate these recommendations by demonstrating the benefits of shifting from a discriminatory auction (in which all bidders are awarded their individual actual bid amounts) to a uniform price auction (in which all bidders are

A. Bagchi et al. / Int. J. Production Economics 134 (2011) 238–245

awarded the highest rejected bid amount). The aggregate final auction approach should deter gaming, simplify bid preparation, and lower bid prices.

2. Food aid procurement The US government donates Title II food aid to foreign countries in need but still must purchase these food supplies and transportation services from industry providers (Trestrail et al., 2009). The US Agency for International Development (USAID) manages the Title II food aid program, but the USDA conducts the procurement process. Private voluntary and non-governmental organizations submit food aid requests to the USAID, and the USDA then executes a bid every few weeks for the food supplies and transportation services. Historically, food suppliers submit sealed bids to deliver food commodities to a railhead or port, and ocean carriers independently tender sealed bids to carry the food to the foreign port or inland destination. While recent literature has addressed procurement and logistical challenges of disaster relief (Balcik et al., 2010; Gatignon, Wassenhove and Charles, 2010; Oloruntoba, 2010), efficiency analyses of food aid procurement are limited. The US Government Accountability Office (2007b, 2009) has identified existing inefficiencies with food aid procurement that increase program costs and limit delivered aid. As one example, 75% of aid must be carried on USflagged vessels, which generally retain higher costs and a more difficult regulatory environment that vessels with flags of convenience (e.g., Liberia or Panama) (US Government Accountability Office, 2007b). As another example, there is limited ability to track shipments inland to final recipients, creating difficulty in verifying actual delivery to intended parties. Below, we identify two additional concerns that have yet to be addressed by current literature: bidder gaming and the lack of appropriate paired (supplier–carrier) bidding. 2.1. Bid estimation and gaming As detailed by Trestrail et al. (2009), the linear program (LP) used by the USDA to select winning food aid bids attempts to minimize total food commodity and transportation costs subject to food aid demand as well as several self-imposed constraints addressing vessel-flagging, port preferences, and disadvantaged suppliers. A portion of the historical bid and award information is publicly accessible under the US Freedom of Information Act. Subsequently, Trestrail et al. (2009) have demonstrated that the USDA LP can be mimicked with this historical bid data, allowing bidders to accurately estimate clearing prices for future bids. By happenstance, the USDA has recently moved from a two-stage bid collection process (in which suppliers bid first then carriers bid in a second round) to one in which independent supplier and carrier sealed bids are collected in a single stage. However, the new LP can once again be mimicked (Appendix A) to successfully replicate bid estimation with the same high accuracy of Trestrail et al. (2009). Bid estimation enables gaming of the USDA award process, allowing bidders to intelligently set the highest possible bid that will still win the award rather than basing bid pricing on actual costs. Confidential feedback from bidding organizations indeed confirms gaming well above cost (Trestrail et al., 2008), thus providing empirical evidence of increased costs to the USDA. From a business perspective, the food suppliers and carriers also serve commercial markets that tend to be more consistent and profitable than food aid business. Additionally, some cost elements of food aid have been identified to unnecessarily increase costs for food suppliers and carriers (US Government Accountability Office, 2007b). So, it is reasonable to allow at least a modest level of

239

bidder profit, else the bidders might ignore food aid markets entirely. Examining rationale from an auction perspective however, a firm has to expend resources in order to estimate clearing prices. Therefore firms with greater resources (e.g., employees and technology) have an advantage over firms with fewer resources (Cramton and Stoft, 2006), thus softening competition. Less bid competition then perpetuates the ability to game higher prices. Overall, an extreme level of bidder profitability negates the anticipated efficiency of the USDA bid process. Higher costs also contradict the humanitarian intentions of food aid and decrease the USDA’s ability to address other aid requests.

2.2. Paired bidding Another concern with the current bid process is that food suppliers bid independently of carriers. Food suppliers select transshipment points (railheads, Great Lakes ports, or coastal ports) in the US as destinations of their bids. Carriers use such transshipment points as the origins of their bids though without visibility of supplier-selected transshipment points. There is limited if any coordination between suppliers and carriers when selecting their preferred transshipment points. Bidders generally independently select transshipment points based on convenience or previous experience without coordination with other bidders (Trestrail et al., 2008). After bids are submitted, the USDA must then match supplier and carrier bids to fulfill a food aid lane. Without pre-bid visibility, such pairings are arbitrary and most likely inefficient. For instance, a supplier offering a low-cost bid for a commodity may not be chosen since their self-selected transshipment points did not align with that of a reasonably lowcost carrier. Pre-bid planning among suppliers and carriers could help bidders identify operational efficiencies from mutuallybeneficial shipment routings and transshipment points. Such coordination could thus potentially reduce their operational costs, a portion of which could be passed on to the USDA in the form of lower bids.

3. Methods We use auction theory to address the above USDA bid inefficiencies. In Section 3.1, we first determine a mechanism to reduce bidder gaming and better support the USDA’s underlying objective of minimizing awarded bid prices. In Section 3.2, we then rationalize coordination between suppliers and carriers prior to bid submission through analysis of the cost distribution functions in terms of the likelihood ratio. Finally, we provide guidelines for implementation of a uniform auction approach in Section 3.3 to operationalize these recommendations. Suppose that the USDA wants to deliver food aid to a set of foreign destinations and that there are a certain number of suppliers and carriers, who could be matched to fulfill these requests. The total number of such pairings, referring to matches of suppliers and carriers that can be formed is n. Note that matching a supplier and a carrier is a necessary step in the delivery of aid to a destination. Each firm (referring to a supplier, carrier, or pairing) incurs a cost for the service: supplier l denoted by sl, carrier j by tj, and pairing i by ci (see Appendix B for a summary of notations). The cost of each firm is a random variable that is drawn independently from a probability distribution function. In particular, ci, the cost of pairing i, follows the distribution G(  ) with support ½0,c and density function g(  ). The term c represents the maximum possible cost per shipment that will ever be realized by a pair. From pairing i’s perspective,

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the costs of the competing pairings are denoted by ci  ðc1 , . . ., ci1 , ci þ 1 ,. . ., cn Þ and the joint density function of the competing pairings by g  i(c  i). n We now introduce other statistics notations. Fm ðUÞ denotes the n n distribution function of cðmÞ , where cðmÞ is the mth lowest cost realized among the n pairings while fmn ðUÞ denotes the associated density function. Suppose that the USDA wants to award a maximum of k contracts with each contract specifying the total food and delivery costs to the USDA. We now determine the minimum cost that the USDA must incur for these k contracts under the assumption that each pairing can fulfill at most one contract. We demonstrate that under the optimal auction mechanism, bidders retain the best probability of winning when the auction environment discourages gaming and encourages bidding closest to the true cost.

3.1. Optimal mechanism with a pairing We use standard auction theoretic methods to determine the optimal mechanism under a pairing. To simplify our approach, we utilize the revelation principle (Myerson, 1981), which establishes that the search for an optimal mechanism can be restricted to direct mechanisms and equilibrium of the direct mechanisms obtained under a truth-telling setup (Krishna, 2010) wherein all bidders report true costs in the case of the USDA. In a direct mechanism, each pairing is asked to report its cost, and the USDA then selects an allocation as a function of these reports. The outcome of a direct mechanism is the pair (Q,M), where Qi(c1, c2, y, cn) is the probability that pairing i wins a contract and Mi(c1, c2, y, cn) is the payment to pairing i. Analyzing the equilibrium from the perspective of pairing i, let qi(zi) be the probability that pairing i wins a contract when it reports its cost as zi, given that the others report truthfully: Z qi ðzi Þ ¼ Qi ðzi ,ci Þgi ðci Þdci : ci

Considering the interpretation of the above term in detail, suppose we fix pair i’s report of zi. Given that others report truthfully, the probability that pair i wins a contract therefore depends on the profile of costs of the other pairs, denoted by c  i with the joint density function g  i(c  i). Therefore, we obtain the probability of pair i winning a contract by calculating the marginal probability of Qi(zi,c  i). This is done by integrating Qi(zi,c  i) g  i(c  i) over the entire domain of c  i.3 Similarly, let mi(zi) be the expected payment to pairing i when it reports its cost as zi, given that the others report truthfully Z mi ðzi Þ ¼ Mi ðzi ,ci Þgi ðci Þdci : ci

Therefore, the expected payoff to pairing i is given as

Pi ðzi Þ ¼ mi ðzi Þqi ðzi Þci : In a truth-telling equilibrium, it must be suboptimal for pairing i to falsely report its cost as zi when its true cost is ci. Hence

Pi ðci Þ ¼ zi A ½0,csup

Pi ðzi Þ ¼ zi A ½0,csup

fmi ðzi Þqi ðzi Þci g:

3 Our notation for the limits of the integral is simply a shorthand for the entire domain of c  1.

It then follows from the integral form envelope theorem (Milgrom, 2004, p. 67) that Z Pi ðci Þ ¼ Pi ðcÞ þ qi ðzi Þdzi : ð1Þ ci c

By definition:

Pi ðci Þ ¼ mi ðci Þqi ðci Þci

ð2Þ

and

Pi ðcÞ ¼ mi ðcÞqi ðcÞc:

ð3Þ

By combining Eqs. (1) and (2) we obtain Z c qi ðzi Þdzi : mi ðci Þ ¼ Pi ðcÞ þ qi ðci Þci þ

ð4Þ

ci

The above result is known as the revenue equivalence theorem, implying that if the allocation rule (k lowest costs) is the same in any two mechanisms, the expected payment to a pairing is then also the same in these two mechanisms. We later use this result in Section 3.3 to recommend an appropriate real-world auction mechanism for the USDA. We now use Eq. (4) to derive the cost to the USDA (i.e., payment made to a pairing) under the optimal mechanism. The ex ante expected payment to pairing i is Z c mi ðci Þgðci Þdci : ð5Þ 0

Hence, the ex ante expected payoff to the USDA (i.e., surplus of the available budget less awarded bids) from pairing i is Z c Ui ¼ ½cmi ðci Þgðci Þdci : ð6Þ 0

By substituting Eq. (4) into Eq. (6) and simplifying, it follows that:  Z c  Gðci Þ qi ðci Þgðci Þdci : Ui ¼ Pi ðci Þ þ c ci þ ð7Þ gðci Þ 0 In this expression, the first term on the right hand side, given by  Pi ðcÞ, is the negative of the ex ante expected payoff of the worst type of pairing. In the second term, the expression Jðci Þ ¼ ci þ

Gðci Þ gðci Þ

is commonly known as the virtual cost of a pairing with cost ci (Fudenberg and Tirole, 1991, p. 278). It is the sum of the true cost (ci) of pairing i and the inverse of the reverse hazard rate g(ci)/ G(ci). This inverse of the reverse hazard rate is the information rent that pairing i enjoys because its true cost is not known to others (i.e., the bid mark-up when the USDA is unaware of bidder costs). This component specifically aids gaming and results in increased costs to the USDA. Notice that the term in the square bracket on the right hand side of Eq. (7) represents the surplus that the USDA recognizes after paying the information rent of pair i (if pair i wins a contract), which occurs with probability qi(ci) in the truthtelling equilibrium. Hence, ½cJðci Þqi ðci Þ is the expected surplus of the USDA from pair i, conditional on pair i having a cost of ci. However, in an ex ante sense, the cost of a pair is a random variable between 0 and c with the associated density function being g(  ). Thus, the second term in the right hand side of (7) is the ex ante expected value of the USDA’s surplus from pair i. The USDA has to maximize its ex ante expected payoff by selecting the function qi(ci) and the payoff of the worst bidder Pi ðcÞ subject to the constraint that it can select a maximum of k winners. To solve this maximization problem, we impose a restriction that the function J(ci), the virtual cost of pair i, is increasing in ci. The USDA can maximize its ex ante expected payoff in two steps.

A. Bagchi et al. / Int. J. Production Economics 134 (2011) 238–245

First, it must ensure that the expected payoff of a pairing that has the worst type (c) is 0. That is, Pi ðcÞ ¼ 0 in the optimal mechanism. Second, it must select the function qi(ci) as ( n 1 if ci r minfcðkÞ ,cn g, qi ðci Þ ¼ ð8Þ 0 otherwise, where cn ¼ J 1 ðcÞ:

ð9Þ

This implies that the USDA should award a contract to a pairing provided the pairing has one of the k lowest costs and that cost is not more than cn, the reserve price (i.e., the maximum price that the USDA will pay for a shipment). Hence, under the optimal mechanism, the USDA extracts a payoff of cJðci Þ from pairing i n only if ci rminfcðkÞ , cn g. Therefore, the total amount of the ex ante expected payoff that the USDA extracts from all n pairings is k Z cn X n n n ½cJðcðjÞ Þfjn ðcðjÞ ÞdcðjÞ : ð10Þ Un ¼ j¼1

0

3.2. Choosing between distributions: the role of likelihood ratios Given the optimal mechanism above, we next investigate the impact of a change in the distribution of costs on the ex ante expected payoff to the USDA. Specifically, we compare the USDA’s payoff when one distribution dominates the other in terms of a criterion known as the likelihood ratio. We then argue that this desirable distribution will generally emerge if, unlike the current USDA approach, suppliers and carriers are allowed to form pairs on their own prior to bid submission. We first define the term likelihood ratio. Consider two dis^ i Þ. By definition, the distribution tribution functions G(ci) and Gðc ^ Þ is said to dominate the distribution G(ci) in terms of the Gðc i ^ i Þ=gðci Þ likelihood ratio if the ratio of the density functions gðc ^ i Þ is is increasing in ci (Krishna, 2010, p. 276). This implies that gðc relatively small compared to g(ci) for small values of ci and is relatively large compared to g(ci) for large values of ci. In other ^ i Þ has more of its mass concenwords, the density function gðc trated towards the upper end of the domain ½0, c. Consequently, ^ i Þ as being less efficient (or at one can think of the distribution Gðc least less desirable to the USDA) than the distribution G(ci). The likelihood dominance property has the following implications: ^ i Þ dominates the distribution G(ci) 1. The distribution function Gðc in terms of the reverse hazard rate. This means that the following inequality must hold for all ci: ^ iÞ gðci Þ gðc Z : ^ Þ Gðci Þ Gðc i

This implies that the virtual cost of pair i is lower with the ^ Þ: distribution G(ci) than with Gðc i ^ Þ Gðc i ^ Jðci Þ r Jðci Þ  ci þ for all ci : ð11Þ ^ iÞ gðc Since the virtual cost of each pair is lower when the distribution function is G(ci), the USDA therefore prefers the distribu^ i Þ. tion G(ci) over the distribution Gðc ^ 2. The distribution function Gðci Þ stochastically dominates the distribution G(ci) in the first order, meaning that the following inequality must hold for all ci:

241

^ Þ. Note that the desirable distribution of G(ci) compared to Gðc i need not always have the lower costs. Rather we are only requiring that the desirable distribution has a higher probability of obtaining a lower cost. Once more, the USDA therefore prefers ^ i Þ. the distribution G(ci) over the distribution Gðc 3. Let ci denote the cost of pair i when the distribution is G(ci) and ^ i Þ. Further, c^ i denote the cost of pair i when the distribution is Gðc let the surplus of the USDA be si ¼ cci and s^ i ¼ cc^ i , respec^  ). By tively, with associated distribution functions H(  ) and H( ^ i Þ. Note ^ i)¼1 Hðs ^ i Þ ¼ 12Gðc definition, H(si)¼1G(ci) and H(s ^ i Þ dominates G(ci) in terms of the likelihood ratio, that since Gðc ^ therefore, H(s) stochastically dominates H(s) in the first order ^ HðsÞ r HðsÞ

Z

s

for all s A ½0,c. This also implies that Z s ^ HðxÞdxr HðxÞdx:

0

0

^ That is, H(s) also stochastically dominates H(s) in the second order (Shaked and Shanthikumar, 1994, p. 357). It follows as an implication of the Rothschild–Stiglitz Theorem (Gollier, 2001, p. 44; Huang and Litzenberger, 1988, p. 50; Sydsaeter et al., 2005, p. 182)   that there exists a random variable e with the property E e9s r 0 such that s^ is distributed as ðs þ eÞ. This means that the surplus of the USDA is more ‘‘spread out’’ if the costs ^ follow the distribution GðUÞ rather than G(  ) and may have a lower ^ mean, signifying higher uncertainty and risk if costs follow GðUÞ. Consequently, one can argue using the Rothschild–Stiglitz Theorem that if the USDA is risk averse, it would then prefer the distribution G(  ). Based on the above discussion, we next show that the USDA’s payoff is higher when the underlying distribution is G(ci) rather ^ i Þ . Let F^ n ðUÞ denote the distribution function of cn when than Gðc m ðmÞ ^ costs are drawn from the distribution function GðUÞ. Following the same steps above, the total ex ante expected USDA payoff from all ^ n pairings given the distribution function GðUÞ is n Z k c^ X n n ^ n n ^n ¼ U ½c^JðcðjÞ Þf j ðcðjÞ ÞdcðjÞ : ð12Þ j¼1

0

where 1 n c^ ¼ ^J ðcÞ:

ð13Þ

^ iÞ Proposition 1. Consider the distribution functions G(ci) and Gðc ^ such that Gðci Þ dominates G(ci) in terms of the likelihood ratio. Then the ex ante expected payoff to the USDA is higher when the under^ iÞ lying distribution is G(ci) rather than Gðc n

^ : Un 4 U n

To prove this proposition, we first compare cn and c^ , noting that Eqs. (9) and (13) imply n Jðcn Þ ¼ c ¼ ^Jðc^ Þ:

It also follows from Eq. (11) that JðUÞ r ^JðUÞ. Further, J(ci) and ^Jðci Þ are both increasing functions of ci. It then follows that: n

cn 4 c^ :

^ Þ: Gðci Þ 4 Gðc i The USDA’s probability of obtaining lower costs is higher under the distribution G(ci), again demonstrating the relative desirability

Given the distribution G(ci), the term cn represents the threshold level of cost beyond which the USDA would not award a contract to a pairing (an actual USDA practice). Similarly, the

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A. Bagchi et al. / Int. J. Production Economics 134 (2011) 238–245 n

term c^ represents the threshold level when the distribution is ^ i Þ. The USDA should, and generally currently does, impose Gðc threshold levels to restrain the amount of information rents that bidders may enjoy. However, the cost of imposing this threshold level is that it reduces the number of contracts that will eventually be awarded. When the distribution is given by G(ci), the information rents of the bidders are low. The USDA can then afford to slacken the threshold level and thereby increase the n number of contracts. So, c* is higher than c^ . n

ˆ given in Eqs. (10) Considering the expressions for U* and U and (12), respectively, note that: k Z cn k Z c^ n X X n n n n n n ^n ¼ U n U ½cJðcðjÞ Þfjn ðcðjÞ ÞdcðjÞ  ½cf^ j ðcðjÞ ÞdcðjÞ 0

j¼1

¼

k X j¼1



Z 0

k Z X j¼1

0

n n n ½cJðcðjÞ Þfjn ðcðjÞ ÞdcðjÞ þ

k X j¼1

k Z X j¼1

¼

j¼1 n c^

n c^

0 n c^

0

Z

cn

n c^

n n n ½cJðcðjÞ Þfjn ðcðjÞ ÞdcðjÞ

n n ^ n n ½c^JðcðjÞ Þf j ðcðjÞ ÞdcðjÞ

n n n n ½^JðcðjÞ ÞJðcðjÞ Þfjn ðcðjÞ ÞdcðjÞ þ

n n fjn ðcðjÞ ÞdcðjÞ 4 0:

k Z X j¼1

cn n c^

n ½cJðcðjÞ Þ

ð14Þ

The expression in Eq. (14) is positive because JðUÞ r ^JðUÞ and JðcÞ rc for c rcn. Proposition 1 demonstrates that the ex ante expected USDA ^ payoff increases if the distribution function is G(  ) rather than GðUÞ. Eq. (14) retains two components that make G(  ) more attractive to R c^ n P n n n n the USDA. The first term, kj ¼ 1 0 ½^JðcðjÞ ÞJðcðjÞ Þfjn ðcðjÞ ÞdcðjÞ , indicates that inefficient pairings soften competition, leading to higher information rents to the pairings. Hence, a higher likelihood of inefficient pairings will increase virtual costs and decrease the R P n n n USDA’s payoff. The second term, kj ¼ 1 cn c^ n ½cJðcðjÞ Þfjn ðcðjÞ ÞdcðjÞ , can be called the ‘‘quantity effect,’’ the consequence of a lower number of pairs with costs less than the reserve price under the distribu^ tion GðUÞ (i.e., no ex ante pairings and a higher likelihood of inefficient pairings). Proposition 1 expresses that G(  ) is more desirable to the USDA since it would prefer a distribution that is dominated by other distributions in terms of the likelihood ratio. This insight can be used in determining whether or not the USDA should allow the suppliers and the carriers to form pairs on their own. Consider the two pairing strategies: (a) the USDA forms supplier–carrier pairings based on independent bids (the as-is process) (b) the USDA allows the suppliers and carriers to form pairings among themselves prior to bidding. Notice that each ‘‘pair’’ refers to a match between a supplier and a carrier. Thus, we are not suggesting that under policy (b) the USDA should allow the suppliers (or carriers) to collude amongst other suppliers (carriers). The USDA will be better off using (a) only if there is reason to believe that the resulting distribution will be dominated in terms of the likelihood ratio by the distribution that results from (b). In other words, the USDA will benefit from the first option only if it believes that it can form more efficient pairings in terms of the likelihood ratio than what firms can do on their own. We argue, however, that it is more plausible that the USDA will be better off with (b). First, suppliers and carriers retain superior information to the USDA about their industries and are thus better capable of finding operational synergies (e.g., compatible transshipment points). This implies a higher probability of achieving lower costs when firms are allowed to form pairs. Per the earlier discussion on first order stochastic dominance, this is equivalent to the distribution under (b) being G(  ) and the

^ distribution from policy (a) being GðUÞ. The distribution G(  ) would be more preferable to the USDA if it is risk neutral. Second, the USDA would also prefer the distribution G(  ) if it is risk averse. From the discussion of second order stochastic dominance, the spread of the surplus associated with G(  ) is lower in ^ comparison to that associated with GðUÞ. As additional evidence that G(  ) is more likely associated with policy (b), note that under policy (a), the USDA must accurately estimate the true cost of each firm by correctly inverting the bids. This is likely to result in estimation errors that would be captured by the random variable e defined in the discussion of second order stochastic dominance. Estimation errors would mean that under policy (a), the surplus of the USDA would be more ‘‘spread out’’ and hence less appealing if the USDA is risk averse. A concern might be that policy (b), in which suppliers and carriers pair before the bids, can have a negative effect on the USDA’s surplus by reducing the number of bids. Notice that a pair is simply a match between a supplier and a carrier. Thus, formation of a pair simply integrates firms vertically and not horizontally and thus does not harm competition. Further, a pair has to be formed anyway for the delivery of aid to a destination, and the number of independent pairs that can be formed is the same, irrespective of who forms them. We can then apply Eq. (14) to argue two reasons that ex ante pair formation actually raises the USDA’s surplus. One, allowing carriers and suppliers to achieve operational synergies increases the intensity of competition and thus reduces information rents as given by the first term on the right hand side of Eq. (14). More intuitively from the perspective of the current discussion, the second reason is the ‘‘quantity effect,’’ which simply says that the optimal reserve price under ex ante pairing (b) is higher than the optimal reserve price under ex post pairing (a) assuming that ex ante pairing results in the distribution G(  ). Thus, under ex ante pairing, the number of admissible bids (that is, the number of bids lower than the reserve price) will in fact be higher because there will be some pairs whose costs of delivering aid will lie between the two reserve prices. This second factor will therefore have a positive effect on the USDA’s surplus. In practice, it might happen that some suppliers or carriers may not be able to find partners. This could happen primarily if the negotiation costs are too high. The USDA can take steps to reduce the negotiation costs by supporting an information exchange to allow suppliers and carriers to easily identify and contact one another. In any case, the firms that might have difficulties in forming a pair will usually be inefficient with costs likely exceeding the reserve price anyway. Thus, as long as the negotiation costs are not too high, the negative effect of the absence of a few inefficient firms is likely to be outweighed by the positive effect of the synergies that can be achieved. Further, one could also consider a third policy in which ex post (that is, after observing the bids), the USDA would form pairs between firms that were unable to find a partner. Such a policy would achieve results that lie between (a) and (b) and would still be an improvement over the current design.

3.3. Auction implementation The discussions above provide guidelines for the optimal food aid auction mechanism for the USDA. First, the USDA extracts a n payoff of cJðci Þ from pairing i if ci r minfcðkÞ , cn g. Second, the USDA should use the supplier–carrier pairing formation rule that yields the dominated distribution in terms of the likelihood ratio. We still require a method, however, to actually implement the optimal auction mechanism. To accomplish this, we first determine the expected payment of pairing i under the optimal mechanism. Note that the allocation rule in the optimal mechanism is given by Eq. (8),

A. Bagchi et al. / Int. J. Production Economics 134 (2011) 238–245

implying that the following holds true for this mechanism: ( Z c n n minfcðkÞ , cn gci if ci rminfcðkÞ , cn g, qi ðzi Þdzi ¼ 0 otherwise : ci

ð15Þ

In the optimal mechanism, Pi ðcÞ ¼ 0. Hence, substituting Eq. (15) into Eq. (4) yields ( n n minfcðkÞ , cn g if ci rminfcðkÞ , cn g, ð16Þ mi ðci Þ ¼ 0 otherwise : We use Eqs. (8) and (16) as guidelines for determining the optimal real-world auction implementation for the USDA, which we show below to be a uniform price auction in which suppliers form pairs with carriers before the auction. Consider a uniform price auction with a reserve price of cn wherein each pairing can win at most one contract. Also note that in such an auction, the reserve price specifies the maximum USDA payment for any contract (i.e., a ceiling on admissible bids). In the symmetric equilibrium of the uniform price auction with k winners, the lowest k pairings each win a contract and are paid the minimum of the (kþ1)th lowest bid (the lowest rejected bid) and the reserve price. Although some winners may receive higher prices than their actual bids, the dominant strategy of each firm in a uniform price auction is to bid truthfully (Krishna, 2010, p. 192). Hence, the bid of pair i that has cost ci is given by bU ðci Þ ¼ ci : In equilibrium, pair i therefore wins a contract only if n ci rminfcðkÞ , cn g. Hence, the allocation rule in the uniform price auction is given by Eq. (8). Furthermore, each winner is paid the minimum of the lowest rejected bid and the reserve price. Consequently, the expected USDA payment to a pair is given by Eq. (16). Since the allocation and payment rules in the uniform price auction are identical to those for the optimal mechanism, the uniform price auction therefore implements the optimal mechanism. To summarize, the USDA’s current auction approach is similar to a discriminatory auction. The USDA also pairs suppliers and carriers after observing the bids (i.e., ex post pairings). Our proposed mechanism differs from the USDA’s approach in two ways. First, the proposed approach is similar to a uniform price auction, and second, suppliers and carriers form pairs before the bid submission (i.e., ex ante pairing). This generates several changes to the USDA’s surplus. First, the surplus of the USDA will be higher when one moves from a discriminatory auction with the current ex post pairings between suppliers and carriers to a discriminatory auction with ex ante pairings. This occurs since ex ante pairings allows the suppliers and the carriers to capture operational synergies. Second, consider the change from a discriminatory auction with ex ante pairings to a uniform price auction with ex ante pairings. If costs are independently distributed, as assumed in this paper, one might argue that the discriminatory auction would yield the same ex ante expected payoff to the USDA as the uniform price auction. However, we assert that the uniform price auction retains additional advantages: 1. Discriminatory auctions require bidder estimation of the cost distributions of all bidders. Bid preparation is thus more difficult and likely to deter bidders. Bid preparation under the uniform price auction requires less effort since each bidder only requires its own cost. With lower preparation costs, the USDA is likely to attract more bidders, which would subsequently promote greater bid competition. The revenue equivalence result holds when bid preparations costs are the same between the two auction formats. With differences in these

243

auction formats stated above, the uniform price auction represents a more desirable format. 2. If the USDA opts to retain policy (a) of pairing suppliers and carriers itself, it must accurately estimate the cost of each firm, and estimation errors may lead to the formation of inefficient pairings. Under the uniform price auction, the cost of a firm is simply its bid, thus reducing or eliminating estimation errors. 4. Conclusion The US Government Accountability Office (2007b) reports that US food aid programs retain high, inefficient costs, especially in comparison to the United Nations World Food Programme. Given constrained US food aid budgets, higher costs mean less delivered food for needy persons. In fact, the US Government Accountability Office (2007b, p. 10) estimates that ‘‘at current US food aid budget levels, every $10 per metric ton reduction in freight rates could feed about 1.2 million more people during a typical hungry season.’’ With the US providing more than half of all total global food aid (Shapouri and Rosen, 2004), the USDA must explore procurement best practices of both the private sector (US Government Accountability Office, 2007a) and other major food donors, including the European Union, Japan, Canada, and Australia (Shapouri and Rosen, 2004), to lower costs, improve efficiency, and increase transparency (Panayiotou et al., 2004). However, private procurement practices do not necessarily translate well to public applications (Panayiotou et al., 2004). In the instance of US food aid, the current bid process encourages bidder gaming and does not capture potential synergies between suppliers and carriers. As a result, bids are most likely much higher than actual costs in some cases, contradicting the cost minimization intentions of the bid system. In response, we have presented two recommendations for optimal food aid award allocation. First, we propose a switch to a uniform price auction approach to both promote bidding closer to actual costs and encourage greater levels of bid participation. Second, we advise paired bidding in which suppliers and carriers can submit joint bids before USDA awards in order to pass along lower costs from operational synergies. The two changes reduce bid preparation uncertainty and would subsequently likely lead to lower bid prices.

4.1. Limitations and considerations Challenges still remain, however, with implementation of the proposed auction approach. As one, joint bidding by suppliers and carriers would increase the award solution complexity similar to that of combinatorial auctions (Lee et al., 2007; McKelvey et al., 2009; Pekec and Rothkopf, 2003). As another, behavioral nuances of auctions are difficult to model and might lead to unanticipated outcomes. For instance, Pekec and Tsetlin (2008) found that a discriminatory auction approach can be more efficient when there is uncertainty surrounding the number of bidders. Also, increased competition and decreased bidder profits could eventually discourage bid participation (Rothkopf and Harstad, 1994), especially considering that food suppliers and carriers are forprofit organizations that also serve more profitable commercial markets. As another challenge, bidders may become complacent in pairing with partners and not continually work to find new partners or efficiency opportunities. Similarly, efficient formation of bidder pairings adds complexity to auction preparation (Jin and Wu, 2006), so some bidders may decline to bid due to difficulties of identifying and working with partners. These factors could potentially decrease competition. We again highlight the need for

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the USDA to actively support an information exchange for interested bidders. This exchange could reduce pairing negotiation costs by publishing bidder contact information, preferences (e.g., commodities, geographical regions, and ports), and even historical win percentages to help other bidders discover efficient partners. Accordingly, we recommend long-term pilot trials with a subset of food aid volumes to assess actual bidder behaviors. The pilot approach has been effectively used to evaluate changes with other government procurement mechanisms such as Medicare (Katzman and McGeary, 2008). In conjunction with the pilot, it may also be helpful to explore other options to encourage bidder truth-telling such as open instead of sealed bids (i.e., akin to an English out-cry auction) or USDA use of historical bid data to identify non-competitive bids (Skitmore, 2002). As another opportunity, the business rules currently required for US food aid (e.g., vessel-flagging) might be best accommodated by a multi-attribute auction format (Chen and Tseng, 2010; Perrone et al., 2009) rather than as the current hard constraints. With the above limitations and considerations, developing an actual auction mechanism would require significant investment of resources by the USDA. As such, there is a clear opportunity for the USDA to partner with academia and industry to explore the proposed changes.

Appendix A. Single Stage Model for USDA Food Aid Procurement (to adapt to USDA bid process changes since Trestrail et al. (2009)) Indices I j k l m n o FF

food commodity food commodity supplier transshipment location of transfer from supplier to ocean carrier ocean carrier final destination demand point levels of different product quantities offered by suppliers supplier origin location foreign flag

QSijok

quantity of product i transported to location k by supplier j from supplier origin o y_ijokn proportion of total quantity of product i transported by supplier j to location k from supplier origin o that is associated with level n of product quantity Da_ijokn total quantity of product i that could be supplied by supplier j to location k from supplier origin o if level n of product quantity is used ba_ijokn upper bound on the quantity of product i that supplier j could supply to location k from origin o if level n of product quantity is selected bcijokn cost of product quantity baijokn Dcijokn cost of product quantity Daijokn xilkmfn proportion of total quantity of product i transported by carrier l from location k to destination m with flag f that is associated with level n of product quantity Doailkmfn total quantity of product i that could be transported by carrier l from location k to destination m with flag f if level n of product quantity is selected boailkmfn upper bound on the quantity of product i that carrier i could transport from location k to destination m with flag f if level n of product quantity is selected bocilkmfn cost of product quantity boailkmfn Docilkmfn cost of product quantity Doailkmfn Vk variable cost of using location k Fk fixed cost of using location k LBlk lower bound on quantity that can be transported by carrier l from location k UBlk upper bound on quantity that can be transported by carrier l from location k LBl lower bound on quantity that can be transported by carrier l irrespective of location UBl upper bound on quantity that can be transported by carrier l irrespective of locat XX X X X ½COilkmf þQOilkmf ðVk þ Vm Þ Minimize i A I l A L k A K m A Mf A F

þ

XX X X

X X XX

X

Dim ¼ QOilkmf ,

tlkmf ðFk þ Fm Þ

l A L k A K mM f A F

i A I j A J o A Ok A K

8i, l, k, f

ðaÞ

mAM

X XX X

QOilkmf r0:25

m A M l A L k A K f ¼ FF

QSijok r

Domains

CSijok þ

X

XX

Dim ,

ðbÞ

iAI mAM

yijokn Daijokn ,

8i, j, o, k

ðcÞ

yijokn Dcijokn ,

8i, j, o, k

ðdÞ

nAN

I J K L M N O

set set set set set set set

of of of of of of of

food commodities suppliers transshipment locations ocean carriers final destinations product quantity levels supplier origin locations

CSijok Z

X nAN

yijokn rzijokn

n A fn9n A N, n 40g

zijokn r yijokðn1Þ ,

n A fn9n A N, n 40g

Daijokn ¼ baijokn baijokðn1Þ , Decision Variables and Parameters Dim Piklmf COiklmf COiklmf QOiklmf

demand of product i at destination m proportion of demand for product i at destination m allocated to carrier l with flag f at transshipment point k cost of procuring and transporting product i to location k by supplier j from supplier origin o cost of transporting product i to location k by supplier j from supplier origin o quantity of product i transported by carrier l with flag f to final destination m

Daijokn ¼ baijokn ,

n A fn9n A N, n ¼ 1gÞ

Dcijokn ¼ bcijokn bcijokðn1Þ , Dcijokn ¼ bcijokn , QOilkmf r

X

n A fn9n A N, n 41g

n A fn9n A N, n 4 1g

n A fn9n A N, n ¼ 1gÞ

ðeÞ ðfÞ ðgÞ ðhÞ ðiÞ ðjÞ

xilkmfn Doailkmfn ,

8i, l, k, m, f

ðkÞ

xilkmfn Docilkmfn ,

8i, l, k, m, f

ðlÞ

nAN

COilkmf Z

X nAN

A. Bagchi et al. / Int. J. Production Economics 134 (2011) 238–245

xilkmfn r wilkmfn ,

n A fn9n A N, n 4 0gÞ

wilkmfn r xilkmf ðn1Þ ,

n A fn9n A N,

Doailkmfn ¼ boailkmfn boailkmf ðn1Þ , Doailkmfn ¼ boailkmfn ,

Docilkmfn ¼ bocilkmfn , Elk r

XXX

n 40g

ðnÞ

n A fn9n A N, n 41g

ðoÞ

n A fn9n A N, n ¼ 1g

Docilkmfn ¼ bocilkmfn bocilkmf ðn1Þ ,

n A fn9n A N, n 4 1g

n A fn9n A N, n ¼ 1g

QOilkmf r UBlk ,

ðmÞ

8l, k

ðpÞ ðqÞ ðrÞ ðsÞ

i A I m A Mf A F

LBlm r

XXX

QOilkmf rUBlm ,

8l, m

ðtÞ

8l

ðuÞ

i A I k A Kf A F

LBl r

XX X X

QOilkmf rUBl ,

i A I k A K m A Mf A F

zijokn , wilkmfn , tlkmf A f0,1g

ðvÞ

Appendix B. Summary of Notations bu(ci) ci c ci n cðmÞ c* n Fm ðUÞ n fm ðUÞ G(  ) g(  ) g  i(c  i)

bid of pair i under the uniform price auction total cost of pair i to deliver aid, ranging between 0 and c maximum possible cost per shipment realized by a pair costs of the competing pairings that pair i faces mth lowest cost among n pairs reserve (ceiling) price of the USDA n probability distribution function of cðmÞ n probability density function of cðmÞ probability distribution function of ci probability density function of ci joint density function of the costs of the competing pairings that pair i faces H(  ) probability distribution function of the USDA surplus J(ci) virtual cost of pair i k maximum number of contracts the USDA wants to award Mi(c1, c2, y, cn) amount that the USDA pays to pair i as a function of the costs of all pairs mi(zi) expected amount that the USDA pays to pair i when pair i reports its cost as zi and other pairs report truthfully n total number of independent pairs that can be formed (where a pair is a match between a supplier and a carrier) Qi(c1, c2,y,cn) probability that pair i wins a contract as a function of the costs of all pairs qi(zi) probability of pair i winning a contract with a reported cost of zi given that the others report truthfully si USDA surplus when selecting pair i Ui expected payoff to the USDA zi report of cost (i.e., bid) by pair i Q expected payoff to pair i with a reported cost of zi i(zi)

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