Using Feedback to Mitigate Coordination and Threshold Problems in Iterative Combinatorial Auctions

Package bids, i.e., bids on sets of items, are an essential aspect of combinatorial auctions. They can allow bidders to accurately express their preferences. However, bidders on packages consisting of few items are often unable to outbid provisionally winning bids on large packages. To resolve this, both coordination as well as cooperation are needed. Coordination, since smaller bidders need to bid on packages that are disjoint; cooperation, since typically bid increases from more than one bidder are required to overcome the threshold to outbid a larger package bid. The authors design an information system that supports the implementation of an iterative combinatorial auction; this system is specifically aimed at helping bidders overcome coordination and threshold problems. They study the effect of information feedback on the behavior of bidders in different auction settings. The authors test this in an experimental setting using human bidders, varying feedback from very basic information about provisionally winning bids/prices, to providing more advanced concepts such as winning and deadness levels, and coalitional feedback. The experiment indicates that coalitional feedback has a positive impact on economic efficiency in cases where difficult threshold problems arise; however, it appears to have an adverse effect when threshold problems are easy

Scheduling a non-professional indoor football league : a tabu search based approach

This paper deals with a real-life scheduling problem of a non-professional indoor football league. The goal is to develop a schedule for a time-relaxed, double round-robin tournament which avoids close successions of games involving the same team in a limited period of time. This scheduling problem is interesting, because games are not planned in rounds. Instead, each team provides time slots in which they can play a home game, and time slots in which they cannot play at all. We present an integer programming formulation and a heuristic based on tabu search. The core component of this algorithm consists of solving a transportation problem, which schedules (or reschedules) all home games of a team. Our heuristic generates schedules with a quality comparable to those found with IP solvers, however with considerably less computational effort. These schedules were approved by the league organizers, and used in practice for the seasons 2009-2010 till 2016-2017

Fast separation for the three-index assignment problem

A critical step in a cutting plane algorithm is separation, i.e., establishing whether a given vector x violates an inequality belonging to a specific class. It is customary to express the time complexity of a separation algorithm in the number of variables n. Here, we argue that a separation algorithm may instead process the vector containing the positive components of x, denoted as supp(x), which offers a more compact representation, especially if x is sparse; we also propose to express the time complexity in terms of |supp(x)|. Although several well-known separation algorithms exploit the sparsity of x, we revisit this idea in order to take sparsity explicitly into account in the time-complexity of separation and also design faster algorithms. We apply this approach to two classes of facet-defining inequalities for the three-index assignment problem, and obtain separation algorithms whose time complexity is linear in |supp(x)| instead of n. We indicate that this can be generalized to the axial k-index assignment problem and we show empirically how the separation algorithms exploiting sparsity improve on existing ones by running them on the largest instances reported in the literature

Selecting Telecommunication Carriers to Obtain Volume Discounts

During 2001 many European markets for mobile phones reached saturation. Hence, mobile phone operators have shifted their focus from growth and market share to cutting costs. One way of doing so is to reduce spending on international calls, which are routed via network operating companies (carriers). These carriers charge per call-minute for each destination and may use a discount on total business volume to price their services. We developed a software system that supports decisions on allocating destinations to carriers. The core of this system is a min-cost flow routine that is embedded in a branch-and-bound framework. Our system solves the operational problem to optimality and performs what-if analyses and sensitivity analyses. A major telecommunication services provider implemented the system, realizing two benefits: it has structured the business process of allocating carriers to destinations and cut the costs of routing international calls