Emerging Multiple e-Auctions

We review the emerging field of multiple issue e-auctions and discuss their design features and performance criteria. We primarily consider B2B transactions in a reverse auction, that is, a procurement setting. In traditional auctions, the matching of buyers and sellers is typically based just on price. However, when there are quality and other differences in the merchandize and differences in the terms of the transaction, which are common in Request for Quotes (RFQs), additional issues besides price should be considered. Such multiple issue, multiple unit e-auctions/ negotiations, and their characteristics are the focus of our paper. We also discuss the role that OR has played and undoubtedly will play in the design and implementation of such e-auctions

On rational behavior in multi-attribute riskless choice

We theoretically compare and contrast two commonly used types of choice strategies in a riskless, multi-attribute setting: (1) the win-win (or Pareto improving) strategy, and (2) the tradeoff strategy. Both strategies can be used and are used in Multiple Criteria Decision Making theory and practice. In the win-win strategy, consumers (or decision-makers) consider, which goods they want to add to their basket. In the tradeoff strategy consumers make pairwise choices between different (efficient) baskets, where they have to give up in some goods to gain in other goods. We postulate a choice model based on standard assumptions in economics/behavioral decision theory. The key underlying theoretical assumptions in our choice model are increasing and concave single dimensional value functions with decreasing marginal values (win-win setting) and the Tversky–Kahneman reference-dependent model of choice with loss aversion (tradeoff setting). The multi-attribute value function is assumed additive and separable. We study the decision-maker's consistency with our theory in both strategies. The perspective is that of an outside observer (an analyst). The basket is filled either with different or identical goods. We compare and contrast the win-win and tradeoff strategies and draw conclusions for the development of our field. We use an empirical experiment to motivate our considerations

An interactive approximation algorithm for multi-objective integer programs

We develop an interactive algorithm that approximates the most preferred solution for any multi-objective integer program with a desired level of accuracy, provided that the decision maker's (DM's) preferences are consistent with a nondecreasing quasiconcave value function. Using pairwise comparisons of the DM, we construct convex cones and eliminate the inferior regions that are close to being dominated by the cones in addition to the regions dominated by the cones. The algorithm allows the DM to change the desired level of accuracy during the solution process. We test the performance of the algorithm on a set of multi-objective combinatorial optimization problems. It performs very well in terms of the quality of the solution found, the solution time, and the required preference information

Ratio-based RTS determination in weight-restricted DEA models

This paper provides computationally efficient approaches for determining to which returns to scale (RTS) class a unit belongs in weight-restricted Data Envelopment Analysis (DEA) models. A non-traditional computational algorithm is introduced. The suggested approach is based on the calculation of certain ratios within the data set and offers obvious computational advantages over the traditional approaches involving the solution of standard DEA models. Some theorems and algorithms are given. Computational advantages of the provided results are discussed and one of the algorithms is illustrated using real world data.Data Envelopment Analysis (DEA) Returns to scale (RTS) Weight restrictions TIMSS study

An interactive approximation algorithm for multi-objective integer programs

We develop an interactive algorithm that approximates the most preferred solution for any multi-objective integer program with a desired level of accuracy, provided that the decision maker's (DM's) preferences are consistent with a nondecreasing quasiconcave value function. Using pairwise comparisons of the DM, we construct convex cones and eliminate the inferior regions that are close to being dominated by the cones in addition to the regions dominated by the cones. The algorithm allows the DM to change the desired level of accuracy during the solution process. We test the performance of the algorithm on a set of multi-objective combinatorial optimization problems. It performs very well in terms of the quality of the solution found, the solution time, and the required preference information

An interactive algorithm to find the most preferred solution of multi-objective integer programs

In this paper, we develop an interactive algorithm that finds the most preferred solution of a decision maker (DM) for multi-objective integer programming problems. We assume that the DM's preferences are consistent with a quasiconcave value function unknown to us. Based on the properties of quasiconcave value functions and pairwise preference information obtained from the DM, we generate constraints to restrict the implied inferior regions. The algorithm continues iteratively and guarantees to find the most preferred solution for integer programs. We test the performance of the algorithm on multi-objective assignment, knapsack, and shortest path problems and show that it works well

Convex cone-based partial order for multiple criteria alternatives

In this paper, we consider the problem of finding a preference-based strict partial order for a finite set of multiple criteria alternatives. We develop an approach based on information provided by the decision maker in the form of pairwise comparisons. We assume that the decision maker's value function is not explicitly known, but it has a quasi-concave form. Based on this assumption, we construct convex cones providing additional preference information to partially order the set of alternatives. We also extend the information obtained from the quasi-concavity of the value function to derive heuristic information that enriches the strict partial order. This approach can as such be used to partially rank multiple criteria alternatives and as a supplementary method to incorporate preference information in, e.g. Data Envelopment Analysis and Evolutionary Multi-Objective Optimization