The goal of this dissertation is to understand the market-based mechanisms that enable shippers to allocate lanes in an efficient way for truckload (TL) transportation procurement despite the self-interest of carriers. To understand the market-based mechanisms, we focus on proposing some novel models and mechanisms to enhance the use of combinatorial auction for TL transportation procurement. In this dissertation, our approach to gaining the understanding consists of three parts: 1. We develop a carrier optimal bid generation model for carriers (bidders) to discover the best sets of lanes to bid for at a given round. The optimal bid generation model simultaneously generates alternative tours and selects the most profitable package bid for the carrier under a myopic strategy, which has never been considered before. The simultaneous tour generation and selection significantly lessen the computational complexities of a carrier's optimization problem since it is unnecessary for the carrier to calculate the values for all possible packages. 2. We present an iterative combinatorial auction design that integrates the optimization problems for both the shipper and the bidders where the approximate dual prices derived from the result of a winner determination solution are used by the bidders in identifying profitable lanes. The auctions also allow the bidders to submit exclusive-OR (XOR) bids and are able to deal with some common business considerations. The extension of the concept of active bids enables this mechanism to effectively mitigate the exposure problem, the threshold problem, and the free-riding problem. Furthermore, both the shippers and the carriers are better off compared to multi-round auctions that do not integrate the shippers' and carriers' optimizations. 3. We extend a deterministic winner determination model to a two-stage stochastic winner determination model for TL transportation procurement under shipment volume uncertainty. We demonstrate that the value of the stochastic solution is always at least as good as one obtained by a deterministic model based on using expected shipment volumes. The sWDP model is to the best of our knowledge the first winner determination formulation of any kind that explicitly incorporates demand uncertainty.

The goal of this dissertation is to understand the market-based mechanisms that enable shippers to allocate lanes in an efficient way for truckload (TL) transportation procurement despite the self-interest of carriers. To understand the market-based mechanisms, we focus on proposing some novel models and mechanisms to enhance the use of combinatorial auction for TL transportation procurement. In this dissertation, our approach to gaining the understanding consists of three parts: 1. We develop a carrier optimal bid generation model for carriers (bidders) to discover the best sets of lanes to bid for at a given round. The optimal bid generation model simultaneously generates alternative tours and selects the most profitable package bid for the carrier under a myopic strategy, which has never been considered before. The simultaneous tour generation and selection significantly lessen the computational complexities of a carrier's optimization problem since it is unnecessary for the carrier to calculate the values for all possible packages. 2. We present an iterative combinatorial auction design that integrates the optimization problems for both the shipper and the bidders where the approximate dual prices derived from the result of a winner determination solution are used by the bidders in identifying profitable lanes. The auctions also allow the bidders to submit exclusive-OR (XOR) bids and are able to deal with some common business considerations. The extension of the concept of active bids enables this mechanism to effectively mitigate the exposure problem, the threshold problem, and the free-riding problem. Furthermore, both the shippers and the carriers are better off compared to multi-round auctions that do not integrate the shippers' and carriers' optimizations. 3. We extend a deterministic winner determination model to a two-stage stochastic winner determination model for TL transportation procurement under shipment volume uncertainty. We demonstrate that the value of the stochastic solution is always at least as good as one obtained by a deterministic model based on using expected shipment volumes. The sWDP model is to the best of our knowledge the first winner determination formulation of any kind that explicitly incorporates demand uncertainty.

<p>The thesis consists of four papers on combinatorial auctions and a summary. The first part is more of a practical nature and contains two papers. In the first paper, we study the performance of a caching technique in an optimal algorithm for a multi-unit combinatorial auction.</p><p>In the second paper, we compare the revenues from a second-price combinatorial auction against a second-price one-shot simultaneous auction. In particular, we show that when the synergy parameter is small, the combinatorial auction gives a higher expected revenue than the one-shot. This is in contrast to an earliear result by Krishna and Rosenthal. We also compare the two mechanisms under the assumption that bidders are risk-averse. Such bidders are more sensitive to financial loss (winner's curse) that they tend to bid less aggressively, which leads to lower revenues. Since a direct analytical approach turns out to be difficult, we present numerical results that show which auction mechanism maximizes the seller's revenue depending on the values of synergy and aversion parameter.</p><p>The second part is more theoretical. Here, we analyze the asymptotic performance of a greedy algorithm for a problem inspired by combinatorial auctions. In particular, we consider a special case in which every bid contains exactly 3 items, and use a Poisson process to model an auction with a random (Poisson) No. of bids. For this restricted case, winner determination problem is equivalent to a maximal 3-set packing on a weighted hypergraph, and hence NP-complete. However, the greedy algorithm approximates this special case within a factor of 3.</p><p>In the third paper, we compute the asymptotic expected size of the partial allocation and its corresponding expected total revenue from the greedy algorithm, for some distribution of bid prices.</p><p>In the final paper, we study the case of a deterministic number of bids, which is proportional to the number of distinguishable items in the auction, say M. Then, we prove that the number of bids allocated, suitably normalized, converges to a Normal random variable as M goes to infinity. As a prelude, we also prove that, both the number of bids allocated and those submitted, again suitably normalized, jointly converge in distribution to a continuous 2-dimensional Gaussian process as M goes to infinity.</p>

The thesis consists of four papers on combinatorial auctions and a summary. The first part is more of a practical nature and contains two papers. In the first paper, we study the performance of a caching technique in an optimal algorithm for a multi-unit combinatorial auction. In the second paper, we compare the revenues from a second-price combinatorial auction against a second-price one-shot simultaneous auction. In particular, we show that when the synergy parameter is small, the combinatorial auction gives a higher expected revenue than the one-shot. This is in contrast to an earliear result by Krishna and Rosenthal. We also compare the two mechanisms under the assumption that bidders are risk-averse. Such bidders are more sensitive to financial loss (winner's curse) that they tend to bid less aggressively, which leads to lower revenues. Since a direct analytical approach turns out to be difficult, we present numerical results that show which auction mechanism maximizes the seller's revenue depending on the values of synergy and aversion parameter. The second part is more theoretical. Here, we analyze the asymptotic performance of a greedy algorithm for a problem inspired by combinatorial auctions. In particular, we consider a special case in which every bid contains exactly 3 items, and use a Poisson process to model an auction with a random (Poisson) No. of bids. For this restricted case, winner determination problem is equivalent to a maximal 3-set packing on a weighted hypergraph, and hence NP-complete. However, the greedy algorithm approximates this special case within a factor of 3. In the third paper, we compute the asymptotic expected size of the partial allocation and its corresponding expected total revenue from the greedy algorithm, for some distribution of bid prices. In the final paper, we study the case of a deterministic number of bids, which is proportional to the number of distinguishable items in the auction, say M. Then, we prove that the number of bids allocated, suitably normalized, converges to a Normal random variable as M goes to infinity. As a prelude, we also prove that, both the number of bids allocated and those submitted, again suitably normalized, jointly converge in distribution to a continuous 2-dimensional Gaussian process as M goes to infinity.

Combinatorial auctions (CAs) are an important mechanism for allocating multiple items while allowing agents to specify preferences over bundles of items. In order to communicate these preferences, agents submit bids, which consist of one or more items and a value indicating the agent’s preference for these items. The process of determining the allocation of items is known as the winner determination problem (WDP). WDP for CAs is known to be NP-complete in the general case. We consider two distinct graph representations of a CA; the bid graph and the item graph. In a bid graph, vertices represent bids, and two vertices are adjacent if and only if the bids share items in common. In an item graph, each vertex represents a unique item, there is a vertex for each item, and any bid submitted by any agent must induce a connected subgraph of the item graph. We introduce a new definition of combinatorial auction equivalence by declaring two CAs equivalent if and only if their bid graphs are isomorphic. Parameterized complexity theory can be used to further distinguish between NP-hard problems. In order to make use of parameterized complexity theory in the investigation of a problem, we aim to find one or more parameters that describe some aspect of the problem such that if we fix these parameters, then either the problem is still hard (fixed-parameter intractable), or the problem can be solved in polynomial time (fixed-parameter tractable). We analyze WDP using bid graphs from within the formal scope of parameterized complexity theory. This approach has not previously been used to analyze WDP for CAs, although it has been used to solve set packing, which is related to WDP for CAs and is discussed in detail. We investigate a few parameterizations of WDP; some of the parameterizations are shown to be fixed-parameter intractable, while others are fixed-parameter tractable. We also analyze WDP when the graph class of a bid graph is restricted. We also discuss relationships between item graphs and bid graphs. Although both graphs can represent the same problem, there is little previous work analyzing direct relationships between them. Our discussion on these relationships begins with a result by Conitzer et al. [7], which focuses on the item graph representation and its treewidth, a property of a graph that measures how close the graph is to a tree. From a result by Gavril, if an item graph has treewidth one, then the bid graph must be chordal [16]. To apply the other direction of Gavril’s theorem, we use our new definition of CA equivalence. With this new definition, Gavril’s result shows that if a bid graph of a CA is chordal, then we can construct an item graph that has treewidth one for some equivalent CA.

Combinatorial auctions (CAs) are an important mechanism for allocating multiple items while allowing agents to specify preferences over bundles of items. In order to communicate these preferences, agents submit bids, which consist of one or more items and a value indicating the agent’s preference for these items. The process of determining the allocation of items is known as the winner determination problem (WDP). WDP for CAs is known to be NP-complete in the general case. We consider two distinct graph representations of a CA; the bid graph and the item graph. In a bid graph, vertices represent bids, and two vertices are adjacent if and only if the bids share items in common. In an item graph, each vertex represents a unique item, there is a vertex for each item, and any bid submitted by any agent must induce a connected subgraph of the item graph. We introduce a new definition of combinatorial auction equivalence by declaring two CAs equivalent if and only if their bid graphs are isomorphic. Parameterized complexity theory can be used to further distinguish between NP-hard problems. In order to make use of parameterized complexity theory in the investigation of a problem, we aim to find one or more parameters that describe some aspect of the problem such that if we fix these parameters, then either the problem is still hard (fixed-parameter intractable), or the problem can be solved in polynomial time (fixed-parameter tractable). We analyze WDP using bid graphs from within the formal scope of parameterized complexity theory. This approach has not previously been used to analyze WDP for CAs, although it has been used to solve set packing, which is related to WDP for CAs and is discussed in detail. We investigate a few parameterizations of WDP; some of the parameterizations are shown to be fixed-parameter intractable, while others are fixed-parameter tractable. We also analyze WDP when the graph class of a bid graph is restricted. We also discuss relationships between item graphs and bid graphs. Although both graphs can represent the same problem, there is little previous work analyzing direct relationships between them. Our discussion on these relationships begins with a result by Conitzer et al. [7], which focuses on the item graph representation and its treewidth, a property of a graph that measures how close the graph is to a tree. From a result by Gavril, if an item graph has treewidth one, then the bid graph must be chordal [16]. To apply the other direction of Gavril’s theorem, we use our new definition of CA equivalence. With this new definition, Gavril’s result shows that if a bid graph of a CA is chordal, then we can construct an item graph that has treewidth one for some equivalent CA.

Electronic commerce is becoming more important day by day. Many transactions and business are done electronically and many people do not want paper work anymore. When a firm wants to buy raw materials or components, it announces its need to related websites or in the newspapers. Similar demands and announcements can be seen almost everywhere nowadays. In this way, it needs to perform fast and reliable auctions as much as possible. On the other hand, buyers not only consider cost but also consider a lot of different aspects like quality, warranty period, lead time etc when they want to purchase something. This situation leads to more complex problems in the purchasing process. As a consequence, some researchers started to consider auction mechanisms that support bids characterized by several attributes in addition to the price (quality of the product, quantity, terms of delivery, quality of the supplier etc.). These are referred to as multi-attribute combinatorial auctions. In this thesis, Combinatorial Auctions are analyzed. Single-attribute multi-unit, multi-attribute multi-unit combinatorial auction models are studied and an interactive method is applied for solving the multi-attribute multi-unit combinatorial auction problem.

A key problem in designing marketplaces is how to efficiently allocate a collection of goods among multiple people. Auctions have emerged as a powerful tool with the promise to increase market efficiency by allocating goods to those who value them the most. Nevertheless, traditional auctions are unable to handle real-world market complexities. Over the past decade, there has been a trend towards allowing for package bids and other types of multidimensional bidding techniques that enable suppliers to take advantage of their unique abilities and put forth their best offers. In particular the application of iterative combinatorial auctions in procurement saves negotiation costs and time. Conceptually these auctions show a potential for improving the overall market efficiency. However, in practice they host several new challenges and difficulties. One challenge facing the auctioneer in an iterative combinatorial auction environment is to quickly find an acceptable solution for each round of the auction. Bidders require time to precisely evaluate, price, and communicate different possible combinations based on their current information of item prices. The auctioneer requires time to solve the underlying mathematical problem formulation based on the bids received, report back the feedback information and initiate a new round of the auction. In Chapter 3, we propose a Lagrangian-based heuristic to solve the auctioneer's winner determination problem. After generating the Lagrange multipliers from the solution of a linear relaxation, the heuristic applies several procedures to fix any potentially infeasible optimal Lagrange solutions. In addition to providing an efficient way of solving the winner determination problem, as compared with the leading commercial solver CPLEX, our approach provides Lagrange multipliers. The latter are used as proxies for prices in the auction feedback mechanism. In Chapter 4 we develop a model for the bidders pricing problem, an issue that has received much less attention in the literature. Using the auctioneer feedback, that includes the Lagrange multipliers, the pricing model maximizes the bidders' profit while at the same time keeping their bids competitive. We derive several optimality results for the underlying optimization problem. Interestingly, we analytically show that the auction converges to a point where no bidder is able to submit a bid that yields strictly better profit for him and is not less competitive than his previous bids submitted. We experimentally observe that this approach converges in an early stage. We also find that this iterative auction allows the bidders to improve their profit while providing lower and competitive prices to the auctioneer. In Chapter 5, we introduce a flexible auction model that allows for partial bids. Rather than the regular all-or-nothing indivisible package bids, divisible bids provide flexibility for the auctioneer with the possibility to accept parts of the bids and yet allow the suppliers to capture synergies among the items and provide quantity discounts. We show numerically that this approach improves the overall efficiency of the auction by increasing the suppliers' profit while decreasing the auctioneer's total price of procurement. In addition, we find that computationally the flexible auction outperforms the regular auction. / Thesis / Doctor of Philosophy (PhD)

One of the major planning problems faced by medium and large manufacturing enterprises is the distribution of production over various (production) facilities. The need for cross-facility capacity management is most evident in the high-tech industries having capital-intensive equipment and short technology life cycle. There have been solutions proposed in the literature that are based on the lagragian decomposition method which separate the overall multiple product problem into a number of single product problems. We believe that multi-agent systems, given their distributed problem solving approach can be used to solve this problem, in its entirety, more effectively. According to other researchers who have worked in this field, auction theoretic mechanisms are a good way to solve complex production planning problems. This research study develops a multi-agent system and negotiation protocol based on combinatorial auction framework to solve the given multi-facility planning problem. The output of this research is a software library, which can be used as a multi-agent system model of the multi-product, multi-facility capacity allocation problem. The negotiation protocol for the agents is based on an iterative combinatorial auction framework which can be used for making allocation decisions in this environment in real-time. A simulator based on this library is created to validate the multi-agent model as well as the auction theoretic framework for different scenarios in the problem domain. The planning software library is created using open source standards so that it can be seamlessly integrated with scheduling library being developed as a part of the Advanced Planning and Scheduling (APS) system project or any other software suite which might require this functionality. The research contribution of this study is in terms of a new multi-agent architecture for an Advanced Planning and Control (APS) system as well as a novel iterative combinatorial auction mechanism which can be used as an agent negotiation protocol within this architecture. The theoretical concepts introduced by this research are implemented in the MultiPlanner production planning tool which can be used for generating master production plans for manufacturing enterprises. The validation process carried out on both the iterative combinatorial framework and the agent-based production planning methodology demonstrate that the proposed solution strategies can be used for integrated decision making in the multi-product, multi-facility production planning domain. Also, the software tool developed as part of this research is a robust, platform independent tool which can be used by manufacturing enterprises to make relevant production planning decisions. / Master of Science

Allocation of objects or resources to competing agents is a ubiquitous problem in the real world. For example, a federal government may wish to allocate different types of spectrum licenses to telecom service providers; a search engine has to assign different sponsored slots to the ads of advertisers; etc. The agents involved in such situations have private preferences over the allocations. The agents, being strategic, may manipulate the allocation procedure to get a favourable allocation. If the objects to be allocated are heterogeneous (rather than homogeneous), the problem becomes quite complex. The allocation problem becomes even more formidable in the presence of a dynamic supply and/or demand. This doctoral work is motivated by such problems involving strategic agents, heterogeneous objects, and dynamic supply and/or demand. In this thesis, we model such problems in a standard game theoretic setting and use mechanism design to propose novel solutions to the problems. We extend the current state-of-the-art in a non-trivial way by solving the following problems: Optimal combinatorial auctions with single minded bidders, generalizing the existing methods to take into account multiple units of heterogeneous objects Multi-armed bandit mechanisms for sponsored search auctions with multiple slots, generalizing the current methods that only consider a single slot. Strategyproof redistribution mechanisms for heterogeneous objects, expanding the scope of the current state of practice beyond homogeneous objects Online allocation mechanisms without money for one-sided and two-sided matching markets, extending the existing methods for static settings.