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Spatial seemingly unrelated regression (spatial SUR) models are a useful multiequational econometric specification to simultaneously incorporate spatial effects and correlated error terms across equations. The purpose of the spsur R package is to supply a complete set of functions to test for spatial structures in the residual of a SUR model; to estimate the most popular specifications by applying different methods and test for linear restrictions on the parameters. The package also facilitates the estimation of socalled spatial impacts, conveniently adapted to a SUR framework. The package includes functions to simulate datasets with the features decided by the user, which may be useful in teaching activities or in more general research projects. The article concludes with a real data application showing the potential that spsur has to examine the relation of individual mobility over geographic areas and the incidence of COVID-19 in Spain during the first lockdown.

In this article we analyze firms investment incentives in liberalized electricity markets. Since electricity is economically non storable, it is optimal for firms to invest in a differentiated portfolio of technologies in order to serve strongly fluctuating demand. Prior to the Liberalization of electricity markets, for regulated monopolists, optimal investment and pricing strategies haven been analyzed in the peak load pricing literature (compare Crew and Kleindorder (1986)). In restructured electricity markets regulated monopolistic generators have often been replaced by competing and potentially strategic firms. This article aims to respond to the changed reality and model investment decisions of strategic firms in those markets. We derive equilibrium investment for strategic firms and compare to the benchmark cases of perfect competition and monopoly outcomes. We find that strategic firms have an incentive to overinvest in base-load technologies but choose total capacities too low from a welfare point of view. By fitting the framework to a specific electricity market (Germany) we are able to empirically analyze Investment choices of strategic firms, and quantify the potential for market power and its impact on generation portfolios in restructured electricity markets in the long run.

In this paper we address the issue of finding efficient partial equilibria in markets with nonconvexities. This is a problem that has intrigued generation of economists. Beside its theoretical importance this issue is fundamental in energy markets which do not give the right price signals and incentives to maintain existing and invest in new generating capacity. By considering a competitive environment in which consumers maximize utility independently of other agents actions while suppliers are profit maximizers given other market agents actions, we are able to find efficient prices in markets with non-convexities. Based on this result we propose a design for an energy-only market able to give investors the correct price signals.

In this paper, we present a bounding methodology that allows to compute a tight lower bound on the cycle time of fork--join queueing networks with blocking and with general service time distributions. The methodology relies on two ideas. First, probability masses fitting (PMF) discretizes the service time distributions so that the evolution of the modified network can be modelled by a Markov chain. The PMF discretization is simple: the probability masses on regular intervals are computed and aggregated on a single value in the corresponding interval. Second, we take advantage of the concept of critical path, i.e. the sequence of jobs that covers a sample run. We show that the critical path can be computed with the discretized distributions and that the same sequence of jobs offers a lower bound on the original cycle time. The tightness of the bound is shown on computational experiments. Finally, we discuss the extension to split--and--merge networks and approximate estimations of the cycle time.

In this note, we present a simple geometric argument to determine a lower bound on the split rank of intersection cuts. As a first step of this argument, a polyhedral subset of the latticefree convex set that is used to generate the intersection cut is constructed. We call this subset the restricted lattice-free set. It is then shown that [log2(l)] is a lower bound on the split rank of the intersection cut, where l is the number of integer points lying on the boundary of the restricted lattice-free set satisfying the condition that no two points lie on the same facet of the restricted lattice-free set. The use of this result is illustrated to obtain a lower bound of [log2(n +1)] on the split rank of n-row mixing inequalities.

We propose a tactical model which integrates the replenishment decision in inventory management, the allocation of products to warehousing systems and the assignment of products to storage locations in warehousing management. The purpose of this article is to analyse the value of integrating warehouse and inventory decisions. This is achieved by proposing two methods for solving this tactical integrated model which differ in the level of integration of the inventory and warehousing decisions. A computational analysis is performed on a real world database and using multiple scenarios differing by the warehouse capacity limits. Our observation is that the total cost of the inventory and warehousing systems can be reduced drastically by taking into account the warehouse capacity restrictions in the inventory planning decisions, in an aggregate way. Moreover additional inventory and warehouse savings can be achieved by using more sophisticated integration methods for inventory and warehousing decisions.

The progressive relocation of part of the Energy Intensive Industries (EIIs) out of Europe is one of the possible consequences of the combination of emission charges and higher electricity prices entailed by the EU-Emission Trading Scheme (EU-ETS). In order to mitigate this effect, EIIs have asked for special power contracts whereby they would be supplied from dedicated power capacities at average (capacity, fuel, transmission and emission allowance) costs. We model this situation on a prototype power system calibrated on four countries of Central Western Europe. In order to capture the main feature of EIIs' demand, we separate the consumer market in two segments: EIIs and the rest. EIIs buy electricity at average cost price while the rest pays marginal cost. We consider two different types of EIIs' contractual arrangements: a single region wide and zonal average cost prices. We also analyze the cases where generators only rely on existing capacities or can invest in new ones. We find that these average cost contracts can indeed partially mitigate the incentive to relocate activities but with quite diverse regional impacts depending on different national power policies. Models are formulated as a non-monotone complementarity problems with endogenous energy, transmission and allowance prices and are implemented in GAMS.

In this paper we develop a new primal-dual subgradient method for nonsmooth convex optimization problems. This scheme is based on a self-concordant barrier for the basic feasible set. It is suitable for finding approximate solutions with certain relative accuracy. We discuss some applications of this technique including fractional covering problem, maximal concurrent flow problem, semidefinite relaxations and nonlinear online optimization.

Competition, security of supply and sustainability are at the core of EU energy policy. The Commission argues that making the European gas market more competitive (completing the internal gas market) will be instrumental in the pursuit of these objectives. We examine the question through the eyes of existing models of the European gas market. Can model tell us anything on this problem? Do they confirm or infirm the analysis of the Commission appearing in fundamental documents such the Green Paper, the Sector Inquiry or the new legislation package? We argue that results of existing models contradict a fundamental finding (paragraph 77) of the Sector Inquiry. We further elaborate on the basis of the economic assumption underlying the models, that changing the assumptions implicitly contained in paragraph 77 cast doubts on a large part of the reasoning justifying the completion of the internal gas market. We also explain that models could help arriving at a better definition of the relevant market, which is so important in the reasoning of the Commission. Last we also find model results that question the effectiveness of ownership unbundling. As to security of supply, we explain that models can also contribute to assess the value of additional infrastructure in the context of security of supply, but this potential seems largely untapped. Last we note that sustainability has not yet penetrated models of gas markets. We conclude by suggesting other area of immediate concern, possibly of higher technical difficulty, that modellers could address in future research.

A new alternative in the analysis of manufacturing systems with finite buffers is presented. We propose and study a new approach in order to build tractable phase-type distributions, which are required by state-of the- art analytical models. Called "probability masses fitting" (PMF), the approach is quite simple: the probability masses on regular intervals are computed and aggregated on a single value in the corresponding interval, leading to a discrete distribution. PMF shows some interesting properties: it is bounding, monotonic and it conserves the shape of the distribution. After PMF, from the discrete phase-type distributions, state-of-the-art analytical models can be applied. Here, we choose the exactly model the evolution of the system by a Markov chain, and we focus on flow lines. The properties of the global modelling method can be discovered by extending the PMF properties, mainly leading to bounds on the throughput. Finally, the method is shown, by numerical experiments, to compute accurate estimations of the throughput and of various performance measures, reaching accuracy levels of a few tenths of percent.

We propose two simple upper bounds for the joint spectral radius of sets of nonnegative matrices. These bounds, the joint column radius and the joint row radius, can be computed in polynomial time as solutions of convex optimization problems. We show that for general matrices these bounds are within a factor 1/n of the exact value, where n is the size of the matrices. Moreover, for sets of matrices with independent column uncertainties of with independent row uncertainties, the corresponding bounds coincide with the joint spectral radius. In these cases, the joint spectral radius is also given by the largest spectral radius of the matrices in the set. As a byproduct of these results, we propose a polynomial-time technique for solving Boolean optimization problems related to the spectral radius. We also consider economics and engineering applications of our results which were never considered practice due to their intrinsic computational complexity.

In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant principal component of a data matrix, or more components at once, respectively. While the initial formulations involve nonconvex functions, and are therefore computationally intractable, we rewrite them into the form of an optimization program involving maximization of a convex function on a compact set. The dimension of the search space is decreased enormously if the data matrix has many more columns (variables) than rows. We then propose and analyze a simple gradient method suited for the task. It appears that our algorithm has best convergence properties in the case when either the objective function of the feasible set are strongly convex, which is the case with our single-unit formulations and can be enforced in the block case. Finally, we demonstrate numerically on a set of random and gene expression test problems that our approach outperforms existing algorithms both in quality of the obtained solution and in computational speed.

Nonnegative Matrix Factorization (NMF) is a data analysis technique which allows compression and interpretation of nonnegative data. NMF became widely studied after the publication of the seminal paper by Lee and Seung (Learning the Parts of Objects by Nonnegative Matrix Factorization, Nature, 1999, vol. 401, pp. 788--791), which introduced an algorithm based on Multiplicative Updates (MU). More recently, another class of methods called Hierarchical Alternating Least Squares (HALS) was introduced that seems to be much more efficient in practice. In this paper, we consider the problem of approximating a not necessarily nonnegative matrix with the product of two nonnegative matrices, which we refer to as Nonnegative Factorization~(NF)~; this is the subproblem that HALS methods implicitly try to solve at each iteration. We prove that NF is NP-hard for any fixed factorization rank, using a reduction to the maximum edge biclique problem. We also generalize the multiplicative updates to NF, which allows us to shed some light on the differences between the MU and HALS algorithms for NMF and give an explanation for the better performance of HALS. Finally, we link stationary points of NF with feasible solutions of the biclique problem to obtain a new type of biclique finding algorithm (based on MU) whose iterations have an algorithmic complexity proportional to the number of edges in the graph, and show that it performs better than comparable existing methods.

In this paper we develop several polynomial-time interior-point methods (IPM) for solving nonlinear primal-dual conic optimization problem. We assume that the barriers for the primal and the dual cone are not conjugate. This broken symmetry does not allow to apply the standard primal-dual IPM. However, we show that in this situation it is also possible to develop very efficient optimization methods, which satisfy all desired qualities, including the infeasible-start features. Our technique is based on asymmetric primal-dual barrier augmented by squared residual of the primal-dual linear system.

Former generation capacity expansion models were formulated as optimization problems. These included a reliability criterion and hence guaranteed security of supply. The situation is different in restructured markets where investments need to be incentivised by the margin resulting from electricity sales after accounting for fuel costs. The situation is further complicated by the payments and charges on the carbon market. We formulate an equilibrium model of the electricity sector with both investments and operations. Electricity prices are set at the fuel cost of the last operating unit when there is no curtailment, and at some regulated price cap when there is curtailment. There is a CO2 market and different policies for allocating allowances. Todays situation is quite risky for investors. Fuel prices are more volatile than ever; the total amount of CO2 allowances and the allocation method will only be known after investments has been decided. The equilibrium model is thus one under uncertainty. Agents can be risk neutral or risk averse. We model risk aversion through a CVaR of the net margin of the industry. The CvaR induces a risk neutral probability according to which investors value their plants. The model is formulated as a complementarity problem (including the CVaR valuation of investment). An illustration is provided on a small problem that captures the essence of today electricity world: a choice restricted to coal and gas, a peaky load curve because of wind penetration, uncertain fuel prices and an evolving carbon market (EU-ETS). We show that we might have problem of security of supply if we do not implement a capacity market.