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In the Fermat-Weber problem, the location of a source point in ℝ N is sought which minimizes the sum of weighted Euclidean distances to a set of destinations. A classical iterative algorithm known as the Weiszfeld procedure is used to find the optimal location. Kuhn proves global convergence except for a denumerable set of starting points, while Katz provides local convergence results for this algorithm. In this paper, we consider a generalized version of the Fermat-Weber problem, where distances are measured by anl p norm and the parameterp takes on a value in the closed interval [1, 2]. This permits the choice of a continuum of distance measures from rectangular (p=1) to Euclidean (p=2). An extended version of the Weiszfeld procedure is presented and local convergence results obtained for the generalized problem. Linear asymptotic convergence rates are typically observed. However, in special cases where the optimal solution occurs at a singular point of the iteration functions, this rate can vary from sublinear to quadratic. It is also shown that for sufficiently large values ofp exceeding 2, convergence of the Weiszfeld algorithm will not occur in general.

Time-relaxed sports timetables use more time slots than strictly needed, and are particularly popular in amateur (indoor) leagues. However, due to unexpected events, a considerable number of games may not be played as initially planned before the start of the tournament, leading to a potentially very different realized timetable. This study focuses on dealing with these uncertain events in time-relaxed round-robin sports timetabling, and how to mitigate their effect on the quality of the timetable. We use three quality measures to evaluate the time-relaxed timetables, namely, the games played difference index, the rest difference index and the number of cancelled games. We present several combined proactive and reactive approaches taking into account venue and team availability. Proactive strategies determine the position of time slots that are used as a buffer, while reactive strategies reschedule matches to these buffers in terms of the quality measures.

This paper presents a stochastic mixed integer programming model for a comprehensive hybrid power system design problem, including renewable energy generation, storage device, transmission network, and thermal generators, for remote areas. Given the complexity of the model, we developed a Benders’ decomposition algorithm with two additional types of cutting planes: Pareto-optimal cuts generated using a modified Magnanti-Wong method and cuts generated from a maximum feasible subsystem. Computational results show significant improvement in our ability to solve this type of problem in comparison to a state-of-the-art professional solver. This model and the solution algorithm provide an analytical decision support tool for the hybrid power system design problem.

We deal with the primal–dual Newton method for linear optimization (LO). Nowadays, this method is the working horse in all efficient interior point algorithms for LO, and its analysis is the basic element in all polynomiality proofs of such algorithms. At present there is still a gap between the practical behavior of the algorithms and the theoretical performance results, in favor of the practical behavior. This is especially true for so-called large-update methods. We present some new analysis tools, based on a proximity measure introduced by Jansen et al., in 1994, that may help to close this gap. This proximity measure has not been used in the analysis of large-update methods before. The new analysis does not improve the known complexity results but provides a unified way for the analysis of both large-update and small-update methods.

We present two solution algorithms for a large-scale integrated assessment model of climate change mitigation: the well known Negishi algorithm and a newly developed Nash algorithm. The algorithms are used to calculate the Pareto-optimum and competitive equilibrium, respectively, for the global model that includes trade in a number of goods as an interaction between regions. We demonstrate that in the absence of externalities both algorithms deliver the same solution. The Nash algorithm is computationally much more effective, and scales more favorably with the number of regions. In the presence of externalities between regions the two solutions differ, which we demonstrate by the inclusion of global spillovers from learning-by-doing in the energy sector. The non-cooperative treatment of the spillover externality in the Nash algorithm leads to a delay in the expansion of renewable energy installations compared to the cooperative solution derived using the Negishi algorithm.

We analyse systemic risk in the core global banking system using a new network-based spectral eigen-pair method, which treats network failure as a dynamical system stability problem. This is compared with market price-based Systemic Risk Indexes (SRIs), viz. Marginal Expected Shortfall (MES), Delta Conditional Value-at-Risk (Delta-CoVaR), and Conditional Capital Shortfall Measure of Systemic Risk (SRISK) in a cross-border setting. Unlike paradoxical market price based risk measures, which underestimate risk during periods of asset price booms, the eigen-pair method based on bilateral balance sheet data gives early-warning of instability in terms of the tipping point that is analogous to the R number in epidemic models. For this regulatory capital thresholds are used. Furthermore, network centrality measures identify systemically important and vulnerable banking systems. Market price-based SRIs are contemporaneous with the crisis and they are found to covary with risk measures like VaR and betas.

This paper studies a simple process of demand adjustment in cooperative games. In the process, a randomly chosen player makes the highest possible demand subject to the demands of other coalition members being satisfied. This process converges to the aspiration set; in convex games, this implies convergence to the core. We further introduce perturbations into the process, where players sometimes make a higher demand than feasible. These perturbations make the set of separating aspirations, i.e., demand vectors in which no player is indispensable in order for other players to achieve their demands, the one most resistant to mutations. We fully analyze this process for 3-player games. We further look at weighted majority games with two types of players. In these games, if the coalition of all small players is winning, the process converges to the unique separating aspiration; otherwise, there are many separating aspirations and the process reaches a neighbourhood of a separating aspiration.

We conduct an international analysis of the cross-sectional risk premiums of uncertainty risk factors in addition to traditional risk factors. We consider international stock markets in five regions separately. We measure uncertainty by the local and US economic policy uncertainty indices. Economic policy uncertainty risk has negative risk premiums. This implies that investors get lower returns for assets with high uncertainty betas. We further analyze a nonlinear relationship between excess returns and uncertainty risk by adding the downside economic policy uncertainty risk factor which captures high levels of uncertainty, similar to downside market risk. The downside uncertainty risk factor has negative risk premiums.

Due to tremendous losses of resources in modern food supply chains, higher priority should be given to reducing food waste and environmental impacts of food production. In practice, multiple production options are available, but must be quantitatively assessed with respect to economic and environmental performances before they are adopted in food supply chains. The objective of this paper is to develop a mathematical model that can be used for such a quantitative assessment of alternative production options that are associated with different ways to deal with waste in food supply chains, i.e. prevention, recycling, and disposal of food waste. We develop a multi-objective mixed integer linear programming model to derive the set of eco-efficient solutions corresponding to production planning decisions. Environmental performance of the chain is expressed with an indicator based on exergy analysis, which has the potential to capture other commonly used indicators, such as energy consumption, fuel consumption, and waste generation, and express them in a single value. This simplifies the calculation of the eco-efficient frontier, and enables its intuitive graphical representation, which is much easier to communicate to the involved decision makers. The applicability of the developed model is demonstrated on a real-life industrial bread supply chain in the Netherlands. Results confirm the findings from literature that prevention is the best waste management strategy from environmental perspective. The advantages of using exergy as an indicator to capture the environmental performance is demonstrated by comparing the outcomes to other commonly used indicators of environmental performance. We illustrate the potential of studying food production planning decision problems in a multi-objective context, and demonstrate the applicability of the model in the assessment of alternative production options.

This paper argues for a careful consideration of the methodological underpinnings ofpositive decision theory. Two state-of-the-art papers published in Econometrica, whichsupport a variety of often contradictory conclusions about the empirical validity of theexpected utility model, are used to motivate a discussion of what models might be for, andtherefore what criteria should be used to determine their acceptance or rejection. It issuggested that progress in positive decision theory would be advanced if greater attentionwere given to causal structures and that this may, in turn, merit the use of simultaneousequation techniques.