Using Linear Programming in a Business-to-Business Auction Mechanism

Business to business interactions are largely centered around contracts for procurement or for distribution. Negotiations and sealed bid tendering are the most common techniques used for price discovery and generating the terms and conditions for contracts. Sealed bid tenders collect bids (that is private information between the two companies) and then pick a winning bid/s from among the submitted bids. The outcome of such interactions can be analyzed based on the theory of sealed bid auctions and have been studied extensively [7]. In contrast, negotiations tend to be more dynamic where a buyer (supplier) might be interacting with several suppliers (buyers) simultaneously and the contractual terms being negotiated with one supplier might directly impact the negotiations with another.An approach that is often used for this setting is to design an interactive mechanism where based on a "market signal" such as price for each item, the agents can propose bids based on a decentralized private cost model. A general setting for decentralized allocation is one where there are multiple agents with a utility function for the different resources and the allocation problem is to distribute the resources in an optimal way. A key difference from classical optimization is that the utility functions of the agents are private information and are not explicitly known to the decision maker. The key requirements for such a design to be practical are: (i) convergence to an "equilibrium solution" in a finite number of steps, and (ii) the "equilibrium solution" is optimal for each of the agents, given the market signal. One approach for implementing such mechanisms is the use of primal-dual approaches where the resource allocation problem is formulated as a linear program and the dual prices are used as market signals |2, 3, 8, 1, 4, 6|. Each agent can then use the dual price vector to propose a profit maximizing bid, for the next round, based on her private cost model. Here, the assumption is that the agents attempt to maximize their profits in each round. This assumption is referred to as the myopic best response |5|. In a procurement setting with a single buyer and multiple suppliers, the buyer uses a linear program to allocate her demand by choosing a set of cost minimizing bids and then use the dual price variables to signal the suppliers. In order to guarantee convergence a large enough price decrement is used on all non-zero dual prices in each iteration.In this paper we explore an alternate design where, the market signal provided to each supplier is based on the current cost of procurement for the buyer. Each supplier is then required to submit new bid proposals that reduce the procurement cost (assuming other suppliers keep their bids unchanged) by some large enough decrement d > a. We show that, for each supplier, generating a profit maximizing bid that decreases the procurement cost for the buyer by at least d can be done in polynomial time. This implies that in designs where the bids are not common knowledge, each supplier and the buyer can engage in an "algorithmic conversation" to identify such proposals in a polynomial number of steps. In addition, we show that such a mechanism converges to an "equilibrium solution" where all the suppliers are at their profit maximizing solution given the cost and the required decrement d. At the heart of this design lies a fundamental sensitivity analysis problem of linear programming - given a linear program and its optimal solution, identify the set of new columns such that any one of these columns when introduced in the linear program reduces the optimum solution by at least d.

Can data cooperatives sustain themselves?

Data cooperatives are emerging to empower consumers amidst a fast-changing data governance landscape. But they are not alone, and IT-enabled data marketplaces can be effective competitors. Sameer Mehta, Milind Dawande, and Vijay Mookerjee write that data cooperatives are not indispensable. They suggest four steps for data cooperatives to sustain themselves and thrive in this competitive market

Optimal Bidding for Mobile-Ad Campaigns

Self-service advertising platforms such as Cidewalk enable advertisers to directly launch their individual mobile advertising campaigns. These platforms contract with advertisers to provide a certain number of impressions on mobile apps in a specific geographic location (usually a town or a zip code) within a fixed time period (usually a day); this is referred to as a campaign. To meet the commitment for a campaign, the platform bids on an ad-exchange to win the required number of impressions from the desired area within the time period of the campaign. We address the platform’s problem of deciding its bidding policy to minimize the expected cost in fulfilling the campaign

Robin Hood to the Rescue: Sustainable Revenue-Allocation Schemes for Data Cooperatives

The promise of consumer data along with advances in information technology has spurred innovation not only in the way firms conduct their business operations but also in the manner in which data is collected. A prominent institutional structure that has recently emerged is a data cooperative — an organization that collects data from its members, and processes and monetizes the pooled data. A characteristic of consumer data is the externality it generates: data shared by an individual reveals information about other similar individuals; thus, the marginal value of pooled data increases in both the quantity and quality of the data. A key challenge faced by a data cooperative is the design of a revenue-allocation scheme for sharing revenue with its members. An effective scheme generates a beneficial cycle: It incentivizes members to share high-quality data, which in turn results in high-quality pooled data — this increases the attractiveness of the data for buyers and hence the cooperative's revenue, ultimately resulting in improved compensation for the members. While the cooperative naturally wishes to maximize its total surplus, two other important desirable properties of an allocation scheme are individual rationality and coalitional stability. We first examine a natural proportional allocation scheme — which pays members based on their individual contribution — and show that it simultaneously achieves individual rationality, the first-best outcome, and coalitional stability, when members' privacy costs are homogeneous. Under heterogeneity in privacy costs, we analyze a novel hybrid allocation scheme and show that it achieves both individual rationality and the first-best outcome, but may not satisfy coalitional stability. Finally, our RobinHood allocation scheme — which uses a fraction of the revenue to ensure coalitional stability and allocates the remaining based on the hybrid scheme — achieves all the desirable properties

Effective Heuristics for Multi-product Shipment Models

We consider two shipment models (motivated by a real application) where multiple customers asking for sets of products are to be satisfied from inventory in the best manner possible. The restrictions posed by the customers include that the first shipment be at least a minimum fraction of the total demand, and that the second shipment (if any) should not be too small nor be further split. We first show that solving these problems to optimality requires considerable computational effort. Thus, the performance of commercially available packages, applied directly on these problems, is unsatisfactory. Adapting the latest developments in computational integer programming, we are able to solve several instances to optimality. However, this can also require considerable computational effort with some instances not solvable within 10 hours. So we develop and analyze two heuristics: these are easy to implement, run very quickly and provide good solutions. In a test bed of 50 problems of industri..