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Enhancing strategic supply decisions by estimating suppliers' marginal costs.


Electronic reverse auctions (e-RAs), in which competing suppliers place bids through an online platform to win a contract with a purchaser, are being used with growing popularity. e-RAs have been adopted as a strategic tool in the purchasing function and are becoming a standard for many procurement activities. In particular, this strategy has become prevalent in the industrial sector (Rosenthal, Zydiak and Chaudhry 1995). Over the last decade, nearly every Fortune 500 company has implemented a plan for reducing supply chain costs, and e-RAs have been one of the most common tools in that regard (Pearcy, Giunipero and Wilson 2007). However, the utility of e-RAs is complicated by the fact that suppliers who obtain contracts as a result of low bids might not be able to deliver on their promises (Garvin and Kagel 1994; Harbour 2000). Therefore, the purchaser must carefully examine the supplier's costs to be able to identify underbidding situations and to ensure that bid prices are realistic (Emiliani 2000; Mullane, Peters and Bullington 2001).

Came-theoretic approaches have been proposed for predicting the bids of an ongoing auction, although they do not address the bidder's ability to deliver on his promise. Research on the game theory of auctions has focused primarily on two models: the independent private value (IPV) model (Vickrey 1961; Tombak and Wang 2005) and the common value (CV) model (Wilson 1967, 1969). In IPV auctions, an indivisible item has a value to each of the participating bidders that is an independent draw from a known probability distribution. The bids are submitted simultaneously, where each bidder knows only his own valuation of the item with certainty. This model corresponds to the first-price sealed-bid auction we focus on in this study. In a first-price sealed-bid procurement auction, each supplier independently submits a single bid without seeing the bids of others. Usually, each participant is allowed to submit only one bid ("one shot"). The name "first-price" comes from the fact that when a single contract is up for auction, the bidder who submits the lowest price (or the most economically advantageous bid) wins the auction and is awarded the contract for the price bid (Soudry 2004).

The buyer can adopt one of three approaches in making a purchasing decision: using only the e-RA (bidding) process to make a decision, using an e-RA to initiate the process (like traditional bids were before the technology existed), and then following up with a traditional negotiation to achieve an outcome, or entering a traditional negotiation with a potential supplier without using an e-RA or bidding to initiate the process. This research can facilitate the purchasing decision in the first situation, and it seeks to better understand the purchaser's ability to further negotiate with the supplier in the second situation. The goal of this study was to assist in supplier selection by providing an estimate of the supplier's marginal costs. This is accomplished with a model that incorporates the relationship between common selection criteria, the auction rate of savings (the reduction of the catalog price expected with the auction), and a game-theoretic approach to the competition between suppliers in an auction.

The supplier selection process has been the focus of writings dating as far back as 1832 (Das and Buddress 2007). In particular, as Dickson's (1966) publication of 23 different suggested criteria for vendor selection, many studies have focused on the analysis of such criteria. Weber, Current and Benton (1991) reviewed and classified 74 articles that addressed vendor selection criteria in manufacturing and retail environments. In general, it should be noted that the relative importance of the various criteria is not straightforward, even in the case of traditional criteria such as price. Some studies have found price to be one of the most important decision criteria used by purchasers in the process of supplier selection (Deng and Wortzel 1995; Ghymn, Liesch and Mattsson 1999), whereas others have found it to be unimportant or the least important criterion (Choi and Hartley 1996; Sonmez and Moorhouse 2010).

In auction-based supplier selection, the criteria of past experience (in terms of purchases that the buyer made from a specific supplier) and quality are viewed as important (Choy, Lee and Lo 2004). In addition, service has been identified to be a significant parameter in situations in which the product has procedural or performance issues (Lehmann and O'Shaughnessy 1974). Losch and Lambert (2007) and Hackney, Jones and Losch (2007) also find that price is a favorite criterion, particularly among e-RA users. This may be due to the fact that buyers tend to ensure in advance that their potential suppliers are qualified in terms of other selection criteria, leaving price as the most important selection criterion to negotiate in price-only e-RA events. In selecting variables for the regression analysis, our goal was to study whether supplier characteristics that are commonly available to buyers, can be sufficient to reliably reveal the supplier's bidding policy and eventually the marginal cost.

Whatever set of criteria is chosen, the traditional approach to supplier selection is then to assign priorities (weights) to each criterion, on the basis of which a single criterion for each supplier can be derived. A stream of research suggests advanced mathematical programming-based methods for carrying out this process. One such method is data envelopment analysis (DEA), a linear programming-based technique developed to evaluate relative efficiency of nonprofit and public sector decision-making units (DMUs) that use multiple inputs to produce multiple outputs. Weber and Desai (1996) and Weber, Current and Desai (1998) have demonstrated the use of DEA in evaluating supplier efficiency by maximizing weighted outputs for a given supplier.

Sherman (1981, 1982) illustrated that econometric regression techniques are less powerful than DEA in identifying efficient production relationships. The data generated by Sherman were later used for regression analysis (RA) and DEA by Bowlin, Chames, Cooper and Sherman (1985) and Giokas (1997). Specifically, Bowlin et al. (1985) extended the study of Sherman (1984) by comparing DEA, RA and ratio analysis. Sherman (1984) developed a DEA model for providing a managerial audit tool to identify and measure relative inefficiencies among several hospitals. In that model, each hospital used three inputs (xi: full-time-equivalent staff employed per year; x2: number of hospital bed days available per year and x3: supplies in terms of dollars cost per year) to produce three outputs (TU: the number of teaching units; RP: regular patients; and SP: severe patients). The DEA model identified all efficient hospitals. Bowlin et al. (1985) summed up all inputs into one total cost, as a dependent variable, and then performed RA to determine the weights of all independent variables (RP, SP and TU). They found that ratio analysis was the worst performer in evaluating efficiency, and that DEA outperformed RA. They noted that the three techniques are not mutually exclusive; it is not necessary to select solely one option for a given case, and a combination of the two approaches can be used. Giokas (1997) utilized DEA to generate efficient costs and then carried out RA to determine new weights (marginal costs) for the independent (output) variables. Giokas showed that the marginal costs of the outputs derived from the combination of DEA at the first stage and either goal-programming or regression at the second appeared to be more accurate than those based on DEA or RA alone. Talluri (2002) used DEA to further extend Giokas's (1997) model by allowing managerial preference for various suppliers to be incorporated into the evaluation process. Talluri's study presented a set of multicriteria models for estimating suppliers' efficient marginal costs.

Our goal was to estimate the suppliers' marginal costs rather than their relative inefficiencies as in the studies discussed above. Therefore, the methodological concepts of our study are different. Specifically, the supplier's bid tends to the marginal cost as the number of suppliers participating in the auction increases. This is a fundamental result of the game-theoretic approach to modeling competition under auctioning, which has also been supported by real-life observations (Jap 2002). Carter, Kaufmann, Beall, Carter, Hendrick and Petersen (2004) have further shown that bid prices are influenced not only by the number of suppliers but also by the degree of competition among those suppliers. Yeniyurt, Watson, Carter and Stevens (2011) examine the pattern of bids submitted by suppliers across different auctions to find the factors that influence suppliers to submit bids. They find that buyers can use information regarding suppliers' historical bidding activities to recognize suppliers who, because of the "allure of fierce competition," bid lower prices to win at all costs. In the current research, the integration of empirical results (regression analysis) and game-theoretical results (with a finite number of competing bidders) enables us to account for suppliers' characteristics and gaming policies in estimating their underlying marginal costs. We believe this approach constitutes a unique contribution that is important to both management theory and practice. Moreover, we show that (i) these estimates are superior compared with the DEA estimates of the corresponding efficient marginal costs; and (ii) supplier characteristics that are commonly available to buyers can be sufficient to derive these estimates.

Similarly to Giokas (1997), we also employ a combination of two models (stages) to determine a supplier's marginal cost. As mentioned above, our approach is based on the fact that e-RA bids reveal some information about the suppliers' marginal costs (Zhang and Jin 2007), which may enhance the knowledge base of marginal costs beyond that introduced in previous research. In contrast with previous studies, we first use RA to predict the supplier's final bid, measuring the supplier's efficiency by contrasting its final bid to its initial bid. Then the forecasted final bid is refined with the aid of the theoretical, Nash-equilibrium bid (symmetric IPV auction model) to estimate the marginal cost. Note that DEA is a comparative analysis intended to assist in determining specific relative inefficiencies among the suppliers. The RA, on the other hand, is based on actual auction results. We thus reveal the efficient marginal cost for the winning bid supplier at the first stage (RA), regardless of the efficiency of the other bidders. Moreover, in contrast to Sherman (1981, 1982) internal organization analysis, the goal of the RA here was to provide an initial estimate of the supplier's marginal cost based only on the limited information that is externally available about the supplier. This information includes such commonly used controls as price, quality, service level and past experience.

Our regression analysis indicates that although all considered traditional outputs may affect the supplier's marginal cost, the supplier's experience rating on its own encompasses, all necessary information and therefore may be sufficient to determine the supplier's efficiency. However, new suppliers--i.e., suppliers who have no experience with the buyer--sometimes make attractive offers; in these cases, such factors as quality and service become important for determining the supplier's efficiency.

We apply our model to a real-life e-RA from the food and beverage industry. Most studies on the performance of e-RAs are based on data that consist of participants' perceptions, which are inherently subjective (Losch and Lambert 2007). Similarly, the data generated by Sherman (1984), which were later used for RA and DEA by Bowfin et al. (1985), Thanassoulis (1993), and Giokas (1997), are hypothetical, whereas our results are based on an analysis of 84 contracts concluded with e-RAs. Our case applications show that the first-stage (RA-based) estimates of suppliers' marginal costs are already closer to those made by the suppliers than the corresponding estimates based on DEA. We illustrate how the suggested estimates can be employed for supplier selection with either bargaining or auctioning.


We propose a model for estimating suppliers' marginal costs based on the combination of RA and a symmetric IPV auction model. Specifically, we first design a regression model to estimate the final bid for a supplier. Then, the forecasted final bid is substituted for the winning Nash-equilibrium bid of the IPV auction model to assess the supplier's marginal cost. We then test the suggested model with a case application.

For the first stage, RA, we construct a linear regression model for assessing the supplier's efficiency according to the auction's rate of savings, typically used as a measure of an auction's success (Millet, Parente, Fizel and Venkataraman 2004; Amelinckx, Muylle and Lievens 2008). The dependent variable, y, the savings for a supplier in our regression model, is defined, according to the supplier's final bid, B, and his initial price, P, defined as the catalogprice (Aydin and Ziya 2008):

Y = (P-B) / P (1)

Note, that in terms of DEA, 1-y is the supplier's efficiency score.

Our independent variables are summarized in Table 1.


Independent Variables

Variable Name        Notation  Equation

Quality rating       QR        Number of defects produced total
                               number products

Experience rating    PER       Purchases from a specific supplier
                               total number of purchases from all

Service rating (a)   SR        [W.sub.1] x responsiveness to change
                               + [w.sub.2] x lead time to order +
                               [w.sub.3] x response to inquiries

Number of competing  N         Number of bidders

Initial price        P         Catalog price in dollars

(a) [w.sub.1], [w.sub.2], [w.sub.3] are weights set by the
purchasing manager.

We consider the independent variables as analogous to those employed by Bowlin et al. (1985) and Giokas (1997). Specifically, the different patient types referred to their studies (denoted RP and SP) require different treatments and therefore can be viewed as special cases of the supplier's output variable "service rating" in our model. Similarly, the variable TU (teaching units) in Bowlin et al. (1985) and in Giokas (1997) can be seen as a special case of the output variable "quality rating" in our model, as the medical qualifications of personnel in a hospital affect the quality of treatment. Our model considers these two variables as well as two other commonly used parameters (see the above literature review on selection criteria): price (analogous to the "input" variable in DEA) and past experience (measured as the percentage of purchases that the buyer made from a specific supplier relative to the total number of purchases from all suppliers (Wind 1970)). In what follows we show that these commonly available supplier characteristics can be sufficient to reliably reveal the supplier's bidding policy and eventually the underlying marginal cost.

Similarly to Ting and Cho (2008), we measure quality rating according to the defect and scrap ratios taken from defective item reports. Similarly to Wind (1970), we measure experience rating as the percentage of the buyer's purchases from a specific supplier relative to the buyer's total number of purchases from all suppliers. Service rating is measured by three factors, as in Ting and Cho (2008): responsiveness to change as perceived by the purchasing department, lead time to order taken from historical delivery data or defined in the supply contracts and response to inquiries as perceived by the purchasing department. All rating scores are converted on a 1-10 scale. The number of competing suppliers and initial price are extracted from the contract files repository.

Given a regression equation, one can substitute the data outlined in Table 1 for a specific supplier to predict possible savings if the supplier participates in the auction. The supplier's final bid (price), B, is then calculated as

B = (1-y )P (2)

At the second stage, we employ Tombak and Wang's (2005) auction model. The model's assumptions match those of the general setting of the IPV auction described in the introduction and are as follows (to distinguish between the suppliers, we next use the index i).

1. Seller i's marginal cost of production, [C.sub.i], is privately known only by seller i. Costs are independently and continuously distributed in 10, Mi and are drawn from a common distribution F([C.sub.i]).

2. The bidding function B-([C.sub.i]): [0, M] [right arrow] [R.sup.+] is a monotonic increasing continuous function of [C.sub.i] and bids made are statistically independent.

3. The selling firms are rational, are risk neutral and try to maximize the expected value of their profits.

The equilibrium bidding strategy is solved by maximizing the following objective function for each bidder:

[Max.sub.Bi]([B.sub.i] - [C.sub.i])[(1 - F([B.sup.-1]([B.sub.i]))).sup.N - 1] (3)

where [(1 - F([B.sup.-1]([B.sub.i]))).sup.N - 1] is the probability that the bidder wins the auction with a bid of [B.sub.i], and N is the number of competing suppliers. Assuming F(*) is a uniform distribution, the Nash-equilibrium bid (wholesale price) of a supplier is then straightforwardly found with the first-order optimality condition (see Tombak and Wang (2005)):

[B*.sub.i] = [C.sub.i] + 1 / (N(M-[C.sub.i])) (4)

where B7 is the optimal bid for supplier i. The optimal bid of a supplier is defined as the wholesale price that the rational supplier should bid to win. Therefore, we equate the RA-predicted final bid B of a supplier and the equilibrium bid for this supplier, B = [B*.sub.i]. Then from equation (4) we find the marginal cost of the supplier,

[C.sub.i] = (N * ((1-y) * P)) - M) / (N - 1) (5)


Our results are based on an analysis of 84 contracts concluded with e-RAs, initiated by seven local companies and one international company (buyers) operating in six different industries: food and beverages (56 percent of the contracts), security (28.6 percent), aviation (4.8 percent), insurance (4.8 percent), health (3.6 percent) and high-tech (2.4 percent). Furthermore, 61.9 percent of the contracts are related to small companies (up to 5,000 employees), 20.2 percent to medium-size companies (5,000-10,000 employees) and 15 percent to large companies (10,000 + employees). In all 84 contracts, the suppliers did deliver on their promises and sustained the offered prices.

The linear regression equation obtained based on the independent variables given in Table 1 is as follows:

y = 1.653 - 0.080 * PER - 0.046 * QR - 0.047 * SR +0.016*N + 5.363 * P (6)

This equation is characterized by a coefficient of determination (R2) of 0.935, and it includes all the independent variables. From this regression, we observe that the savings grow as the number of competing suppliers and initial price increase, which is quite intuitive and agrees with the literature (Carter et al. 2004) as well as with the auction model presented in the previous section. This result also agrees with the findings of Millet et al. (2004), who observed that the savings grow linearly when the number of suppliers does not exceed six, as is the case in most contracts we studied. Specifically, as N grows, the final bid decreases (see equation (4)), which implies a higher rate of savings to the purchaser. On the other hand, SR, QR and PER negatively impact the rate of savings, which corresponds to the basic properties of DEA. Indeed, in terms of DEA, SR, QR and PER are typical outputs, whereas P is the standard input. DEA implies that the greater the outputs of a supplier the higher its efficiency and therefore the lower the price reduction (savings) that can be negotiated with the supplier, whereas the effect of the supplier's inputs is opposite.

The regression results are summarized in Table 2. From this table we observe that all variables are highly statistically significant. Among the suppliers' outputs, experience rating (PER) has the highest absolute coefficient value of 0.08, which implies that a one-unit increase in the experience rating would improve savings by 8 percent. PER also has the largest 13 coefficient, the coefficient that would be obtained if the outcome and predictor variables were all transformed into standard z-scores. That is, one standard deviation increase in PER leads to a 0.364 standard deviation decrease in the predicted savings rate.

TABLE 2 Regression Results

     Coefficients  Statistical     Weight  [R.sup.2]    [DELTA]
              (8)    Error (SE   ([beta])             [R.sup.2]

QR         -0.046         .022   -0.229 *

PER         -0.80         .023  -0.364 **

SR         -0.047        0.018   -0.244 *

N            .016         .005   0.142 **

P           5.363        0.997  0.213 ***      0.935   .929 ***

* Significant at p < 0.05.

** Significant at p < 0.01.

*** Significant at p < 0.001.

We also observe that PER is significantly correlated with supplier outputs QR (Spearman's p (63) = 0.919, [rho] < 0.001) and SR ([rho](63) = 0.916, [rho] < 0.001). To show that the experience rating encompasses most quality and service-related information, we perform a linear regression, where PER is the dependent variable and QR and SR are the independent variables. The regression equation obtained,

PER = 1.157 + 0.484 * QR + 0.388 * SR (7)

is characterized by a coefficient of determination of 0.87. Accordingly, equation (7) enables estimation of the potential experience rating PER for a new supplier to a company.

Finally, to avoid colinearity, we extract QR and SR from regression (6) and perform a linear regression in which the only independent variables are N, P and PER. The regression equation is then

[gamma] = 1.665 - 0.172 * PER + 0.011 * N + 6.803 * P (8)

with a very similar percent of explained variation (R2 = 0.91) to that for the initial equation (6). The regression results are summarized in Table 3. All variables are highly statistically significant. Furthermore, PER also has the largest [beta] coefficient, i.e., in terms of standard scores, the effect of the supplier's experience on the buyer's savings is the highest one.


Results of Regression with No Multicollinearity

     Coefficients   Statistical     Weight  [R.sup.2]    [DELTA]
              (8)  Error (SE B)   ([beta])             [R.sup.2]

PER        -0.172         0.010     -0.788

N           0.011         0.005     0.099*

P           6.803         1.084  0.270 ***      0.909  0.904 ***

* Significant at p < 0.05.

** Significant at p < 0.01.

*** Significant at p < 0.001.


In May 2007, one of the largest local companies in the food and beverages industry decided to continue with its outsourcing strategy regarding maintenance services for its facilities. The contract with the current supplier was about to end, and the company did not want to extend it. The company had recently begun using e-RA for procurement only, a strategy that had proved highly successful in terms of cost reduction. Accordingly, the company decided to use e-RA to contract with a new maintenance service supplier. Industrial maintenance services in food and beverage facilities must meet stringent quality and regulatory standards. Maintenance procedures must be customized and comply with environmental/safety regulations, including those of the Food and Drug Administration (FDA). Among the suppliers who applied to participate, five met a basic criterion with respect to the regulations and were chosen to compete for the contract. The suppliers were not new to the company; hence, there was adequate information available to determine the suppliers' scores.

In this section, we use the scaled data from the e-RA event in which the five suppliers who offered identical services competed. We evaluate each supplier's marginal cost using the model described above, hereafter referred to as RA-Nash. We then compare our results with marginal-cost estimates obtained using RA only (i.e., the RA estimates generated in the first stage of the model), with DEA, and with the marginal costs as evaluated by these service providers.

DEA Procedure

We adapt the DEA linear programming model see, for example, Talluri 2002):


where p is the index of the supplier being evaluated; s represents the number of supplier outputs; m represents the number of supplier inputs; [] is the amount of output h provided by supplier i; [x.sub.ji]; is the amount of input j used by supplier i; decision variables [v.sub.k] and [u.sub.j] are the weights assigned to output h and input j, respectively. The above model is run separately for each supplier N times (where N represents the number of suppliers). In our model, similarly to Talluri (2002), price is the only input, whereas the outputs are service, quality and experience ratings, which were analyzed in the RA. A supplier with a score of 1 is considered to be efficient, and therefore no further savings (offered price reductions) are expected when contracting with this supplier. A score of less than 1 indicates that the evaluated supplier is inefficient and that the initial price might be cut.

The supplier's evaluation criteria (the "outputs", in DEA terminology) are presented in Table 4. The initial prices, auction results and mean absolute deviations (MAD) for the marginal cost assessments are shown in Table 5 (suppliers are ordered, according to final bid). According to DEA, although supplier 5 is efficient, supplier 1 has the lowest efficient marginal cost estimate, whereas both RA and RA-Nash predict that supplier 5 has the lowest marginal costs. Supplier 1 is also the one to submit the lowest bid in the auction. The MAD comparison shows the superiority of Nash-RA, followed by RA, over DEA. Specifically, the MAD score obtained with DEA is about 138 percent higher than that obtained with RA, and about 210 percent higher than that obtained with RA-Nash.


Suppliers Evaluation Ratings

Supplier No.   Quality   Experience   Service
1                    7          7.5         7
2                    8            8         8
3                    8            8       7.5
4                    9            7         7
5                    9            8         8

Sensitivity Analysis

The goal of the sensitivity analysis was to highlight the accuracy of our RA-Nash approach for estimating marginal costs as compared with RA- and DEA-based methods, thereby validating the main contribution of our study compared with the extensive existing literature on efficient marginal costs. Incrementing the experience rating of efficient supplier 5, we find that RA-Nash outperforms DEA for the whole range (0), (10) of the experience rating. When supplier 5's experience rating is varied in the range of 6.1-10, RA-Nash is the best model, producing estimates that are closest to those made by the suppliers.

Figure 1 shows the MAD from the suppliers' estimates for each of the three models, for different values of supplier 5's experience rating within the range [6.1, 10]. This figure highlights the clear advantage of the RA-Nash model over RA and DEA. For example, when supplier 5's experience rating is 9, the marginal costs obtained by RA-Nash are 34.72 percent closer to the estimates made by the suppliers compared with those obtained by RA, and are 151.75 percent closer than those obtained by DEA. Overall, even when the supplier's experience (or the effect of the supplier's experience on the efficient marginal cost) is estimated with an error of up to 100*(10-6.1)/8 = 48.75 percent, the RA-Nash model still remains superior over the RA and DEA models. Moreover, the RA and RA-Nash models retain their advantage over DEA even if we utilize an interval rather than the point estimate of the marginal cost. Specifically, RA is advantageous over the DEA for the entire experience range 1[0, 10], which corresponds to the efficiency score (1-[gamma]) interval [0, 0.95]. On the other hand, the 95 percent confidence interval of the efficiency score of supplier 5 is much narrower [0.47, 0.73]. Therefore, for any value adopted from the former interval, RA will yield an estimate of the marginal cost that is closer to that made by the supplier compared with the DEA estimate.


In this section, we contrast final auction bids with likely negotiation results derived with the aid of DEA. Weber and Desai (1996) and Weber et al. (1998) demonstrated how DEA evaluations of vendor efficiency can be used in strategies for negotiating efficient prices with inefficient suppliers. In DEA, the efficient price of a supplier is defined as the supplier's efficiency score (determined using DEA) multiplied by the supplier's initial price. Bowlin et al. (1985) pointed out that DEA generally assumes that corrective action is possible for the inefficiencies that are detected. Under this assumption, negotiation can be used to reduce the delta between the supplier's price offer and its efficient price.

On the basis of the data presented in the case applications, we compare the real final auction bid [B.sub.real], the estimated final auction bid [B.sub.estimated] based on the RA-Nasli marginal cost [C.sub.RA-Nash],

[B.sub.estimated] = [C.sub.RA-Nash] + (N(M-[C.sub.(RA-Nash)] (10)

and the final bid (the efficient price) [B.sub.DEA] that would be obtained through negotiations based on the DEA efficiency score S and the initial price P.

[B.sub.DEA] = P * S (11)

Recall that the suppliers' estimates of the marginal costs, the RA-Nash marginal costs and the DEA efficiency scores are presented in Table 5. We next apply the developed estimate of marginal cost to operational decision making. In particular, we investigate whether the buyer can use the estimate to decide which method for supplier selection, i.e., negotiations or an auction, is advantageous under specific conditions. To make this decision, the buyer uses each method to identify the lowest bid that he is likely to obtain from the eligible suppliers.


Auction Final Bids and Marginal Cost Estimates

Supplier        1       2       4       5       3  MAD (a)

Price      0.0113  0.0100  0.0138  0.0080  0.0163

Final bid  0.0075  0.0076  0.0076  0.0078  0.0081

Rate of    0.5065  0.4120  0.6095  0.3984  0.4545

DEA score  0.6667  0.8000  0.5818  1.0000  0.4923

DEA cost   0.0075  0.0080  0.0080  0.0080  0.0080   0.0031

RA cost    0.0056  0.0059  0.0054  0.0048  0.0089   0.0013

RA-Nash    0.0049  0.0053  0.0047  0.0040  0.0091   0.0010

Estimated  0.0050  0.0047  0.0045  0.0045  0.0055

(a) Calculated with respect to Estimated Cost (last row) i.e.
RA-Nash MAD = [SIGMA] [RA-Nash cost-Estimated cost] / 5

Comparisons between the final estimates of the RA-Nash and of the DEA models and each model's MAD score with respect to the real final bids are shown in Figure 2 (suppliers are ordered by the final bid). From Figure 2 we observe that compared with DEA, RA-Nash yields estimated final bids with a lower MAD. Specifically, RA-Nash's MAD score with respect to the real final bids is 244 percent lower than that of DEA. From Figure 2 we also observe that supplier 5 is the preferred supplier both according to the real final bid and according to the RA-Nash estimate. These bids are lower than that of supplier 1, which is the lowest bid estimated using DEA and thus the bid likely to be obtained through negotiations. Note that supplier 5 is the most efficient in terms of both the RA-based efficiency score and the DEA efficiency score. Thus, we find that the auction may lead to a lower final bid compared to negotiations, and that a decision can be made according to the RA-Nash estimate.

Sensitivity analysis

In the previous section, we showed that an auction may be the preferred supplier selection method for a specific real-life case. We next demonstrate that under some conditions, bargaining may be the preferred method to select a supplier with the lowest bid. In the previous sections we found that experience played a key role in determining auction results for the industry contracts we processed. As a result, the DEA-based estimate was less sensitive to experience than the RA-Nash estimate. This, however, is not always the case. For example, suppliers that specialize in production of basic products are frequently characterized by limited learning by doing (Ades and Glaeser 1999). Consequently, the regression-based bid of such a supplier will have low sensitivity to experience. As a result, bargaining with an inefficient supplier may result in a lower final bid than that obtainable with an auction. To sustain this claim, we modify the regression result as follows.

1. We significantly reduce the effect of experience in the regression equation (8) by multiplying the coefficient of the experience variable by 0.05 and subtracting a constant, 1.3, from the intercept of (8) to normalize the outcome within the feasible region of the efficiency values.

2. We reduce the efficiency of supplier 5 by decreasing each of his output values to the same level of 3, thereby making this supplier inefficient.

The rationale for the presented modifications is as follows: (i) if the effect of experience significantly decreases while the other factors retain their impact, then the rate of savings y increases above the maximum level of 100 percent, which can only be corrected by reducing the intercept of the regression line; (ii) the lower a supplier's efficiency, the lower the final bid that can be negotiated with that supplier; we make supplier 5, the least efficient by reducing his outputs.

The resultant bid comparisons and the MAD scores of the two models with respect to the real final bid are shown in Figure 3. From Figure 3 we observe that in negotiations, supplier 5 submits the lowest bid, and this bid is lower than any auction-based bid among all competing suppliers. Furthermore, the DEA-based negotiation bid of supplier 5 is 14.99 percent lower than the estimated auction bid and 16.67 percent lower than the real auction bid. Thus, in this case, negotiations may be preferred over an auction, and the correct method can be selected by comparing the DEA estimate to the RA-Nash estimate. This result also implies that the efficient marginal cost defined by DEA tends to both the real auction bid and the RA-Nash estimate when the supplier is characterized by inefficient output parameters relative to the other suppliers, and when the supplier's experience rating has an insignificant impact on the final auction bid.


This study may provide a potential solution to one of the fears purchasers face when conducting procurement deals: the inability of the supplier to live up to the agreement and deliver on its promise. The significant increase in popularity and usage of electronic tools to aid in procurement, such as the e-RA, has strengthened this fear, as some suppliers tend to bid less than their marginal value.

We suggested a multi-factor, two-stage model for estimating the supplier's marginal cost and demonstrated its application to real-life purchasing contracts. For the purpose of the study, we collected data from 84 contracts, initiated by eight companies operating in six different industries that concluded through an e-RA. At the first stage, based on externally available information about the suppliers, regression analysis was used to predict each supplier's best bid, thereby determining each supplier's efficient marginal cost. In selecting variables for the regression analysis, our goal was to study whether supplier characteristics that are commonly available to buyers can be sufficient to reliably reveal the supplier's bidding policy (at the first stage) and eventually the marginal cost (at the second stage). We found that the coefficient of determination in the regression analysis based on these basic characteristics was very high, and thus the approach, we suggested would be potentially both reliable and easy to implement in practice. We also found that although all the controls we considered may affect the supplier's marginal cost, experience rating on its own could be used to encompass all necessary information. In the case of a first-time supplier, however, service, quality and initial price could be used to estimate the marginal cost. The second stage of the model refined the estimated marginal cost, using game theory's Nash equilibrium.

We validated the model by applying it to data from an e-RA process in which a food and beverage company selected suppliers for industrial maintenance services. The results, the final marginal cost assessments of the model, were compared with marginal-cost estimates based on RA alone (i.e., the estimates from the first stage of the model) and to the efficient marginal costs obtained with the widely used approach of DEA. Our estimates were very close to those made by the suppliers, and even the estimates based on RA alone were closer to the suppliers' estimates compared with those based on DEA. The latter outcome was due to the fact that whereas the DEA calculates efficient marginal costs relative to the other suppliers, RA uses actual bids. For the case we studied, we found that RA-Nash estimates were consistently closer (30 percent) to the suppliers' estimates of their marginal costs compared with the RA estimates. This gap became enormous (210 percent) when we compared the RA-Nash estimates to the DEA estimates. Moreover, the sensitivity analysis showed that the regression-based estimates (both RA and RA-Nash) retained their advantage even if a 95 percent confidence interval was used rather than the RA point estimate of the marginal cost.

Finally, using a case application, we showed how supply decisions can be enhanced on the basis of estimates obtained from the RA-Nash model we developed. We also demonstrated that the DEA-based bids obtained in negotiations may be lower compared with those obtained through auctions in cases, where a supplier is characterized by inefficient output parameters relative to the other suppliersand the supplier's experience rating has no significant effect on the final auction bid.


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Bar-Ilan University

Eyal Eckhaus (Ph.D., Bar-Ilan University, Israel) is a researcher in the department of management at Bar-Ilan University in Ramat-Gan, Israel. His research interests include e-commerce, e-business and e-reverse auctions with a particular focus on e-marketing and the internet economy culture. Dr. Eckhaus' current research projects include data mining electronic communication, and the formation of a global language. Prior to his current academic appointment, he worked as a senior technology consultant for a high-tech industry and was involved in the formation of numerous software development projects.

Konstantin Kogan (Ph.D., Central Research Institute of Mechanization and Power Engineering, Moscow) is a professor in and head of the department of management at Bar-Ilan University in Ramat-Gan, Israel. His research interests focus on the optimal control of dynamic systems, specifically in production control, scheduling and supply chain management. Dr. Kogan has published more than 80 papers and three books on operations management in supply chains and industrial systems. His current research projects include the effect of risk aversion on supply chains with postponed pricing; supply chain games with design and conformance quality under wholesale price and revenue-sharing contracts; trans-shipments in hazardous environments with cooperative and non-cooperative quality control; and heuristics for coordinated production and pricing under uncertainty and finite production horizons.

Yael Perlman (Ph.D. Ben-Gurion University, Israel) is a lecturer in the department of management at Bar-Ilan University in Ramat-Gan, Israel. Her research interests primarily are in the areas of game theory for supply chain management, production and operations management, and multi-echelon inventory models. Dr. Perlman has published her research in a variety of outlets including the International Journal of Production Research, the International Journal of Production Economics, the Journal of the Operational Research Society, and the IMA Journal of Management Mathematics.
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Author:Eckhaus, Eyal; Kogan, Konstantin; Perlman, Yael
Publication:Journal of Supply Chain Management
Geographic Code:1USA
Date:Oct 1, 2013
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