Kemal Guler

An Experimental Comparison of Linear and Nonlinear Price Combinatorial Auctions

Combinatorial auctions are used for the efficient allocation of heterogeneous goods and services. They require appropriate software platforms that provide automated winner determination and decision support for bidders. Several promising ascending combinatorial auction formats have been developed throughout the past few years based on primal-dual algorithms and linear programming theory. The ascending proxy auction and iBundle result in Vickrey payoffs when the coalitional value function satisfies buyer submodularity conditions and bidders bid their best responses. These auction formats are based on nonlinear and personalized ask prices. In addition, there are a number of designs with linear prices that have performed well in experiments, the approximate linear prices auction, and the combinatorial clock auction. In this paper, we provide the results of lab experiments that tested these different auction formats in the same setting. We analyze aggregate metrics such as efficiency and auctioneer revenue for small-and medium-sized value models. In addition, we provide a detailed analysis not only of aggregate performance metrics but also of individual bidding behaviour under alternative combinatorial auction formats.

Compact Bidding Languages and Supplier Selection for Markets with Economies of Scale and Scope

Combinatorial auctions have been used in procurement markets with economies of scope. Preference elicitation is already a problem in single-unit combinatorial auctions, but it becomes prohibitive even for small instances of multi-unit combinatorial auctions, as suppliers cannot be expected to enumerate a sufficient number of bids that would allow an auctioneer to find the efficient allocation. Auction design for markets with economies of scale and scope are much less well understood. They require more compact and yet expressive bidding languages, and the supplier selection typically is a hard computational problem. In this paper, we propose a compact bidding language to express the characteristics of a suppliers cost function in markets with economies of scale and scope. Bidders in these auctions can specify various discounts and markups on overall spend on all items or selected item sets, and specify complex conditions for these pricing rules. We propose an optimization formulation to solve the resulting supplier selection problem and provide an extensive experimental evaluation. We also discuss the impact of different language features on the computational effort, on total spend, and the knowledge representation of the bids. Interestingly, while in most settings volume discount bids can lead to significant cost savings, some types of volume discount bids can be worse than split-award auctions in simple settings.

Multi-Period Supplier Selection Under Price Uncertainty

We consider a problem faced by a procurement manager who needs to purchase a large volume of multiple items over multiple periods from multiple suppliers that provide base prices and discounts. Discounts are contingent on meeting various conditions on total volume or spend, and some are tied to future realizations of random events that can be mutually verified. We formulate a scenario-based multi-stage stochastic optimization model that allows us to consider random events such as a drop in price because of the most favoured customer clauses, a price change in the spot market or a new discount offer. We propose certainty-equivalent heuristics and evaluate the regret of using them. We use our model for three bidding events of a large manufacturing company. The results show that considering most favored customer clauses in supplier offers may create substantial savings that may surpass the savings from regular discount offers.

A private contributions game for joint replenishment

We study a non-cooperative game for joint replenishment by n firms that operate under an EOQ-like setting. Each firm decides whether to replenish independently or to participate in joint replenishment, and how much to contribute to joint ordering costs in case of participation. Joint replenishment cycle time is set by an intermediary as the lowest cycle time that can be financed with the private contributions of participating firms. We characterize the behavior and outcomes under undominated Nash equilibria.

A Copula Approach to Inventory Pooling Problems with Newsvendor Products

This study focuses on the inventory pooling problem under the newsvendor framework. The specific focus is the change in inventory levels when product inventories are pooled. We provide analytical conditions under which an increase (or decrease) in the total inventory levels should be expected. We introduce the copula framework to model a wide range of dependence structures between pooled demands, and provide a numerical study that gives valuable insights into the effects of marginal demand distributions and dependence structure on inventory pooling decisions.

Non-Cooperative Joint Replenishment Under Asymmetric Information

We consider jointly replenishing n ex-ante identical firms that operate under an EOQ like setting using a non-cooperative game under asymmetric information. In this game, each firm, upon being privately informed about its demand rate (or inventory cost rate), submits a private contribution to an intermediary that specifies how much it is willing to pay for its replenishment per unit of time and the intermediary determines the maximum feasible frequency for the joint orders that would finance the fixed replenishment cost. We show that a Bayesian Nash equilibrium exists and characterize the equilibrium in this game. We also show that the contributions are monotone increasing in each firm’s type. We finally conduct a numerical study to compare the equilibrium to solutions obtained under independent and cooperative ordering, and under full information. The results show that while information asymmetry eliminates free-riding in the contributions game, the resulting aggregate contributions are not as high as under full information, leading to higher aggregate costs.

Optimization-based decision support for scenario analysis in electronic sourcing markets with volume discounts

Abstract E-Sourcing software has become an integral part of electronic commerce. Beyond the use of single-lot auction formats, there has been an emerging interest in using e-sourcing software for complex negotiations. Procurement markets typically exhibit scale economies leading to various types of volume discounts which are in wide-spread use in practice. The analysis of bids in such negotiations typically leads to computationally hard optimization problems. Scenario analysis describes a process, in which procurement managers compute different award allocations as a result of different allocation constraints and parameters that they put in place. This paper discusses an optimization model and computational methods which allow for effective scenario analysis with allocation problems in the presence of different types of discount policies and allocation constraints. The model reduces the number of parameter settings to explore considerably. The models are such that they can often not be solved exactly for realistic problem sizes in practically acceptable time frames. Therefore, we provide results of numerical experiments using exact algorithms and heuristics to solve the problem. We find that RINS and Variable Neighborhood Search can be effectively used in traditional branch-and-cut algorithms for this problem. Overall, new computational approaches allow procurement managers to evaluate offers even in markets with a complex set of volume discounts and multiple allocation constraints.

Design and analysis of mechanisms for decentralized joint replenishment

We consider jointly replenishing multiple firms that operate under an EOQ like environment in a decentralized, non-cooperative setting. Each firm’s demand rate and inventory holding cost rate are private information. We are interested in finding a mechanism that would determine the joint replenishment frequency and allocate the joint ordering costs to these firms based on their reported stand-alone replenishment frequencies (if they were to order independently). We first provide an impossibility result showing that there is no direct mechanism that simultaneously achieves efficiency, incentive compatibility, individual rationality and budget-balance. We then propose a general, two-parameter mechanism in which one parameter is used to determine the joint replenishment frequency, another is used to allocate the order costs based on firms’ reports. We show that efficiency cannot be achieved in this two-parameter mechanism unless the parameter governing the cost allocation is zero. When the two parameters are same (a single parameter mechanism), we find the equilibrium share levels and corresponding total cost. We finally investigate the effect of this parameter on equilibrium behavior. We show that properly adjusting this parameter leads to mechanisms that are better than other mechanisms suggested earlier in the literature in terms of fairness and efficiency.

Can Risk Aversion Mitigate Inefficiencies in Core-Selecting Combinatorial Auctions?

Core-selecting combinatorial auctions are being used in an increasing number of spectrum sales worldwide. It was shown that equilibrium strategies can lead to outcomes that are further from the core than the Vickrey outcome in sealed-bid auctions. Ascending core-selecting auctions can even lead to inefficient non-bidding equilibria. Risk aversion is arguably a significant driver of bidding behavior in high-stakes auctions. We analyze the impact of risk aversion on equilibrium bidding strategies and efficiency of core-selecting auctions in a threshold problem with one global and several local bidders. First, we characterize the necessary and sufficient conditions for the perfect Bayesian equilibria of the ascending core-selecting auction mechanism to have the small bidders to drop at the reserve price. In spite of the free-riding opportunities of local bidders, risk-aversion reduces the scope of the non-bidding equilibrium. Second, we derive equilibrium bidding strategies and revenue for sealed-bid core selecting auctions. Third, we show that in spite of the non-bidding equilibrium in the ascending auction, setting optimal reserve prices in each format leads to higher efficiency and revenue in the ascending than in the sealed-bid auction.

Newsvendor competition under asymmetric cost information

Abstract We study the newsboy duopoly problem under asymmetric cost information. We extend the Lippman and McCardle (1997) of competitive newsboy to the case where the two firms are privately informed about their unit costs. The market demand is initially split between two firms and the excess demand for each firm is reallocated to the rival firm. We show the existence and uniqueness of a pure strategy equilibrium and characterize its structure. The equilibrium conditions have an interesting recursive structure that enables an easy computation of the equilibrium order quantities. Presence of strategic interactions creates incentives to increase order quantities for all firm types except the type that has the highest possible unit cost. Consequently, competition leads to higher total inventory in the industry. However, contrary to intuition, this is only true when the firms are non-identical. A firm’s equilibrium order quantity increases with a stochastic increase in the total industry demand or with an increase in his initial allocation of the total industry demand. We demonstrate our model and results in an application in a dual-sourcing procurement setting using data that obtained from a large manufacturing company. Finally, we provide a full characterization of the equilibrium of the game for the special case of uniform demand and linear market shares.