Optimal Procurement Mechanism Research Articles

Note on Optimal Procurement Mechanisms for Assembly

Problem definition: We consider contract confidentiality in a decentralized supply chain, in which a single principal orders different components from different agents, each of which has private cost information. The principal may commit to publicly observed bilateral contracts or offer secretly observed contracts to each agent simultaneously. We also consider the problem of sequential contracting. Methodology/results: By correcting the main analysis in Hu and Qi [Hu B, Qi A (2018) Optimal procurement mechanisms for assembly. Manufacturing Service Oper. Management 20(4):655–666], we employ passive beliefs to study secret contracting. We show that there is a unique configuration of two-part tariffs under secret offers in both simultaneous and sequential contracting. We also extend the analysis to take into account ex post individual rationality (IR), which is arguably more relevant in this assembly setting. With ex post IR, we show that the traditional two-part tariffs should be augmented with payment adjustments. Managerial implications: We find that the efficiency achieved through public offers can be maintained with secret offers in this assembly setting contrary to conventional wisdom. Our analysis, thus, offers an explanation for why nondisclosure agreements are important and common in practice. Funding: This work was supported by the National Natural Science Foundation of China [Grant 72192805]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2024.0907 .

Optimal Procurement with Quality Concerns

Adverse selection in procurement arises when low-cost bidders are also low-quality suppliers. We propose a mechanism called LoLA (lowball lottery auction) which, under some conditions, maximizes any combination of buyer’s and social surplus, subject to incentive compatibility, in the presence of adverse selection. The LoLA features a floor price, and a reserve price. The LoLA has a dominant strategy equilibrium that, under mild conditions, is unique. In a counterfactual analysis of Italian government auctions, we compute the gain that the government could have made, had it used the optimal procurement mechanism (a LoLA), relative to a first-price auction (the adopted format). (JEL D44, D82, H57, L14)

Robust mechanism design and production structure for assembly systems with asymmetric cost information

We consider the design of a robust procurement mechanism for an assembler who must procure multiple complementary components under limited information regarding the unit production costs of the potential suppliers. We abandon the standard assumption that there exists a common prior distribution for the suppliers’ costs and we employ the max-min criterion in which we design a mechanism to maximize the assembler’s worst-case expected profit when only the means of the suppliers’ costs are known. We formulate this problem using a linear semi-infinite programming model and we apply a primal-dual approach to reduce the problem to a single joint optimization model. We characterize the optimal procurement mechanism (payments and ordering quantities) under the assumption of balanced ordering and uncertain end-customer demand. We use these results to compare the performance of component production, under which the components are sourced from separate suppliers, and integrated production, under which the components are sourced from the same supplier. We find that component production is preferred when the production costs of the components are heterogeneous. We also propose two heuristic mechanisms which are easier to compute and implement in practice, particularly when the number of components is large. Finally, we extend our analysis to the case in which the average and variance of the suppliers’ costs are known.

Sourcing Innovation: Integrated System or Individual Components?

Problem definition: Most industrial innovations consist of multiple interacting components that must be combined into a final product to form an integrated system. When procuring such complex innovations from their suppliers, buyers face a substantial challenge: Should they tender the integrated system as a whole or, instead, procure the system’s components individually from (possibly) different suppliers? Academic/practical relevance: Suppliers have become a major source of innovation for many firms, so buyers ponder how best to structure their procurement efforts. This paper offers guidance on how complex industrial products can be optimally sourced when the buyer’s primary goal is to identify and incentivize innovation. In contrast, most previous research on procurement has concentrated on cost-reduction efforts. Methodology: We use a game-theoretic model to design and compare different procurement mechanisms that allow a buying firm to tap into the innovation potential of its supplier base. Results: Three factors largely determine whether a buyer should procure an integrated system or individual components—namely, the novelty of the innovation to be sourced, the size of the supplier base, and the extent and distribution of component integration costs. We demonstrate how buyers can improve the effectiveness of procurement mechanisms via active supplier management. Managerial implications: Our study provides clear guidelines for managers seeking to source complex industrial innovation. The recommendations presented here reveal how the optimal procurement mechanism changes with the characteristics of the desired product and of the buyer’s supplier base.

A demand partitioning framework to reserve production for small enterprises

Abstract The reservation of goods to be produced in the micro, small, and medium enterprises (MSME) sector, in the early years after India's independence, addressed the dual needs of development of the industrial sector and production of goods. However, these industrial policies created an incentive for firms to remain small so that they can continue to avail of the benefits provided by the Government. On the positive side, the MSMEs typically employ more labor intensive production processes and consequently contribute significantly to the provision of employment opportunities, generation of income, and poverty reduction. But, on the negative side, the policies have also partly facilitated the creation of a divide in terms of productivity between the MSMEs and large sized firms. In particular the policy raises important questions for a firm auctioning supply contracts among suppliers with a significant cost differential. In this paper we propose an idea to allocate supply contracts wherein a manufacturing firm partitions the stochastic demand into mutually exclusive portions and awards each portion to a different supplier. We characterize such an optimal procurement mechanism when there are two types of suppliers and an arbitrary number of demand portions. We show that the optimal procurement may require the manufacturer to intentionally withhold some demand portion, and this arises when one type of supplier is considerably inefficient in serving a demand portion. We extend our analysis to the cases with multiple types with two suppliers and two types with multiple suppliers. The optimal partition is composed of at most six contiguous demand portions, and it may include a detrimental demand portion that only generates a negative expected payoff to both supplier types. Our demand partitioning mechanism leads to a strictly higher manufacturer's expected payoff than the conventional winner-take-all case unless one supplier type completely dominates the other. We present numerical experiments that indicate when such a mechanism holds the greatest advantage for the buyer.

Supplier Competition and Cost Reduction with Endogenous Information Asymmetry

Problem definition: We consider a buyer sourcing from multiple competing suppliers who exert cost-reduction efforts before procurement contracts are awarded. Academic/practical relevance: The supply chain is subject to the classic hold-up problem—as the lack of a contract commitment hinders suppliers’ incentives to make investment upfront—complicated with supplier competition. Methodology: With deterministic cost-reduction outcomes, suppliers will not exert any effort if this effort is observable, and a pure-strategy equilibrium does not exist if the effort is unobservable. We analyze the mixed-strategy equilibrium with unobservable supplier effort, in which suppliers randomize their efforts and the buyer designs an optimal procurement mechanism. Results: We show that the optimal procurement mechanism can be implemented by a conventional single-price reverse auction with a random reserve price. The mixed strategy of supplier effort generates endogenous information asymmetry on supplier costs that provides suppliers with information rent, which sustains their efforts. The endogenous information asymmetry improves effort efficiency (by inducing positive supplier effort), yet introduces trade inefficiency (by causing the possible failure of trade between the parties). Although increasing supplier competition (measured by the number of suppliers) hurts the effort efficiency, it improves trade efficiency. As a result, the buyer is always better off introducing supplier competition by including more than one supplier in the supply base. However, the desired supply base size (number of suppliers) depends on the product revenue: For high-margin goods, the optimal size is achieved with two suppliers, whereas for low-margin goods, a larger supply base is better for the buyer. We show that the result based on deterministic cost reduction can be established as a limit of the case when uncertainty in cost reduction exists and shrinks to null. Managerial implications: Our study helps to understand the impact of supplier competition when supply-chain parties deliberately make their actions unpredictable to avoid being held up. The findings provide managerial guidance on procurement auction and supply base designs.

Sourcing Innovation: Integrated System or Individual Components?

Problem Definition. Most industrial innovations consist of multiple interacting components that must be combined into a final product to form an integrated system. When procuring such complex innovations from their suppliers, buyers face a substantial challenge: Should they tender the integrated system as a whole or, instead, procure the system’s components individually from (possibly) different suppliers? Academic/Practical Relevance. Suppliers have become a major source of innovation for many firms, so buyers ponder how best to structure their procurement efforts. This paper offers guidance on how complex industrial products can be optimally sourced when the buyer’s primary goal is to identify and incentivize innovation. In contrast, most previous research on procurement has concentrated on cost reduction efforts. Methodology. We use a game-theoretic model to design and compare different procurement mechanisms that allow a buying firm to tap into the innovation potential of its supplier base. Results. Three factors largely determine whether a buyer should procure an integrated system or individual components—namely, the novelty of the innovation to be sourced, the size of the supplier base, and the extent and distribution of component integration costs. We demonstrate how buyers can improve the effectiveness of procurement mechanisms via active supplier management. Managerial Implications. Our study provides clear guidelines for managers seeking to source complex indus- trial innovation. The recommendations presented here reveal how the optimal procurement mechanism changes with the characteristics of the desired product and of the buyer’s supplier base.

Optimal Procurement Mechanisms for Assembly

This paper investigates mechanisms by which a powerful original equipment manufacturers procures multiple inputs for assembly from suppliers with privately informed costs, either simultaneously or sequentially. The optimal mechanisms always lead to matching purchase quantities of the inputs. Thus, quantity–payment contracts that implement the optimal mechanisms are contingent across suppliers (i.e., each supplier’s contract terms contain other suppliers’ private costs as variables), making the implementation impractical. To address this issue, we propose alternative implementations of the optimal mechanisms by menus of two-part tariff contracts that are noncontingent. In addition, optimal simultaneous and sequential procurement mechanisms for assembly are shown to be revenue-equivalent for all parties despite their different asymmetric information structures. Our findings suggest that procurement managers need not strategize contracting sequences for assembly, but should rather focus on achieving the best pricing with each supplier and coordinating purchase quantities.

Procurement mechanism for dual sourcing and emergency production under capacity constraint

Abstract This study investigates the optimal procurement mechanism of a buyer who faces two potential suppliers with capacity constraint and private information on costs. The buyer places regular orders to the capacitated suppliers before demand realization and has the option to place an expensive emergency order depending on remaining capacity after that. We observe that the buyer solely exercises emergency option when the virtual cost of the first supplier (with low cost) is greater than emergency production cost. When this virtual cost is not too large, the buyer chooses dual sourcing solely, dual sourcing with emergency option, and single sourcing with emergency option when the capacity is small, moderate, and large, respectively. Compared with symmetric information, information asymmetry weakens capacity constraint for the buyer in terms of order quantity in regular sourcing. However, in terms of order quantity in emergency sourcing, information asymmetry either strengthens capacity constraint when total capacity is greater than expected demand, or weakens capacity constraint when the opposite is the case. Furthermore, the capacity constraint of the first supplier causes a greater buyer’s profit loss than the second supplier (with high cost) does under symmetric information, and information asymmetry further amplifies this asymmetric effect. We also show that the dual sourcing mechanism can be extended to the case of multiple sourcing without loss of the main properties.

Supplier Competition and Cost Reduction with Endogenous Information Asymmetry

We consider a buyer sourcing from multiple competing suppliers who exert cost reduction efforts before procurement contracts are awarded. The supply chain is subject to the classic hold-up problem--as the lack of a contract commitment hinders suppliers' incentives to make investment upfront--complicated with supplier competition. With deterministic cost-reduction outcomes, suppliers will not exert any effort if this effort is observable, and a pure strategy equilibrium does not exist if the effort is unobservable. We analyze the mixed strategy equilibrium with unobservable supplier effort, in which suppliers randomize their efforts and the buyer designs an optimal procurement mechanism. We show that the optimal procurement mechanism can be implemented by a conventional single-price reverse auction with a random reserve price. The mixed strategy of supplier effort generates endogenous information asymmetry on supplier costs that provides suppliers with information rent, which sustains their efforts. The endogenous information asymmetry improves effort efficiency (by inducing positive supplier effort) yet introduces trade inefficiency (by causing the possible failure of trade between the parties). While increasing supplier competition (measured by the number of suppliers) hurts the effort efficiency, it improves the trade efficiency. As a result, the buyer is always better off introducing supplier competition by including more than one supplier in the supply base. However, the desired supply base size (number of suppliers) depends on the product revenue: for high-margin goods, the optimal size is achieved with two suppliers, whereas for low-margin goods, a larger supply base is better for the buyer. We show that the result based on deterministic cost reduction can be established as a limit of the case when uncertainty in cost reduction exists and shrinks to null. Our study helps to understand the impact of supplier competition when supply chain parties deliberately make their actions unpredictable to avoid being held up. The findings provide managerial guidance on procurement auction and supply base designs.

Procurement Design with Corruption

I investigate the design of optimal procurement mechanisms in the presence of corruption. After contracting with the sponsor, the contractor may bribe the inspector to misrepresent quality. The mechanism affects whether bribery occurs. I discuss the cases of both fixed and variable (with the size of misrepresentation) bribes, and also uncertainty about the bribe amount. In all cases, the optimal contract curtails quality for low efficiency contractors but also for the most efficient contractors. I also present models of bribe negotiations whose reduced form coincide with the model analyzed in the paper, and discuss implementation and the effect of competition. (JEL D73, D82, D86, H57, L15)

Procurement with specialized firms

We analyze optimal procurement mechanisms when firms are specialized. The procurement agency has incomplete information concerning the firms' cost functions and values high quality as well as low price. Lower type firms are cheaper (more expensive) than higher type firms when providing low (high) quality. With specialized firms, distortion is limited and a mass of types earns zero profits. The optimal mechanism can be inefficient: types providing lower second‐best welfare win against types providing higher second‐best welfare. As standard scoring rule auctions cannot always implement the optimal mechanism, we introduce a new auction format implementing the optimal mechanism.

Optimal Procurement in an Assembly Supply Chain: Contracting Timing and Supplier Merger

We consider an OEM’s contracting mechanism to procure multiple inputs from different suppliers to be assembled into its product under simultaneous and sequential contracting. We derive optimal mechanisms under both contracting scenarios, and show that they can be implemented by simple tiered-pricing contracts which are widely used in industry assembly settings. We find that optimal simultaneous and sequential procurement mechanisms for assembly are revenue-equivalent for all parties, despite them having different asymmetric information structures. All results are extended to general convex costs and concave revenues, confirming that the results capture fundamental properties of optimal procurement mechanisms for assembly.

Hotspot Economics: Procurement of Third-Party WiFi Capacity for Smart Mobile Data Offloading

The unprecedented growth of cellular traffic driven by web surfing, video streaming, and cloud-based services is creating challenges for cellular service providers to fulfill the unmet demand. To minimize congestion costs for under-served demand (e.g., dissatisfied customers, or churn), the service provider is willing to pay WiFi hotspots to serve the demand that exceeds capacity. In the present study, we propose an optimal procurement mechanism with contingent contracts for service providers to leverage the advantages of both cellular and WiFi resources. As compared with conventional cellular communication technologies, WiFi hotspots provide data rates with a limited coverage. Our present work contributes to the existing literature by developing an analytical model, which considers this unique challenge of integrating the longer range cellular resource and shorter range WiFi hotspots. We show the procedure of computing the optimal procurement mechanism with a tight integration of economics and computational technology. The model is validated using cellular network data from a large U.S. service provider. The simulation results show that the proposed procurement mechanism significantly outperforms the standard Vickrey-Clarke-Groves (VCG) auction in terms of the service provider's expected payoff.

Simple Auctions for Supply Contracts

This paper studies an optimal procurement mechanism for a newsvendor-like problem where the buyer's (newsvendor's) purchase price of the supplies is not fixed, but determined through interaction with candidate suppliers. The buyer has priors on the suppliers' costs but does not know their costs exactly. Recent literature has shown how the buyer can implement the optimal procurement mechanism by announcing a revenue function (specifying a payment for each quantity the buyer may purchase), then auctioning off the supply contract with the specified revenue function. In this paper, we show that a simple modified version of the standard open-descending auction for a fixed quantity is also an optimal mechanism for obtaining supplies. What distinguishes this mechanism is its simplicity and familiarity for the suppliers—open-descending auctions are very easy to run and ubiquitous in practice, whereas auctioning supply contracts with a specified revenue function is much less observed and more difficult to explain to suppliers. Furthermore, we show that this simple mechanism can be easily generalized to ex ante asymmetric suppliers and a class of nonlinear production costs. This paper was accepted by Yossi Aviv, operations management.

Management Insights

Management Insights

Optimal procurement mechanisms: bidding on price and damages for breach

We study the optimal procurement mechanism when contract breach and abandoning a project may be efficient, either because of completion costs higher than anticipated or because of new and more lucrative opportunities for the contractor. When contractors have private information about their costs, the procurer finds it optimal to set damages above expectation damages. There is a lock-in effect, or status quo bias; the agent that has won the award will complete the project even in situations when it would be efficient to abandon it. If the cost types of all agents are above a threshold, the optimal bidding procedure assigns the project by lottery. The optimal mechanism cannot be implemented by standard auction formats. However, the larger the number of agents bidding for the project, the closer auctions with a liquidated damage clause approximate the optimal mechanism.

Procurement with Specialized Firms

This paper analyzes optimal procurement mechanisms in a setting where the procurement agency has incomplete information concerning the firms' cost functions and cares about quality as well as price. Low type firms are cheaper than high type firms in providing low quality but more expensive when providing high quality. Hence, each type is specialized in a certain quality level. We show that this specialization leads to a bunching of types on profits, i.e. a range of firms with different cost functions receives zero profits and therefore no informational rents. If first best welfare is monotone in the efficiency parameter, the optimal mechanism can be implemented by a simple auction. If first best welfare is U-shaped in type, the optimal mechanism is not efficient in the sense that types providing a lower second best welfare win against types providing a higher second best welfare.

Optimal auctions for multi-unit procurement with volume discount bids

In this paper, we design an optimal procurement mechanism for procuring multiple units of a single homogeneous item based on volume discount bids submitted by rational and intelligent suppliers. We develop an elegant auction mechanism, VD-OPT, that minimises the cost to the buyer, satisfying at the same time: Bayesian Incentive Compatibility (BIC); interim individual rationality.

Procurement Mechanism Design in a Two-Echelon Inventory System with Price-Sensitive Demand

This paper studies a buyer's procurement strategies in a two-stage supply chain with price-sensitive demand. The buyer procures a product from a supplier and then sells to the marketplace. Market demand is stochastic and depends on the buyer's selling price. The supplier's production cost is private information, and the buyer only knows the distribution of the cost. Both the buyer and the supplier can hold inventories to improve service, and a periodic review inventory system is considered. The buyer takes two attributes into consideration when designing the procurement mechanism: quantity attribute (i.e., the total purchase quantity) and service-level attribute (i.e., the supplier's delivery performance). We first identify the optimal procurement mechanism for the buyer, which consists of a nonlinear menu of contracts for each of the two attributes. It can be shown that the optimal mechanism induces both a lower market demand and a lower service level compared to the supply chain optimum. In view of the complexity of the optimal mechanism, we proceed to search for simpler mechanisms that perform well for the buyer. We find that the above two attributes have different implications for procurement mechanism design: The value of using complex contract terms is generally negligible for the service-level attribute, while it can be highly valuable for the quantity attribute. In particular, we demonstrate that a fixed service-level contract, which consists of a target service level and a price-quantity menu, yields nearly optimal profit for the buyer. Additionally, the price-quantity menu is essentially a quantity discount scheme widely observed in practice.