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An attractive feature of standard data envelopment analysis (DEA) is that decision-making units (DMUs) are put in their best possible light. This is accomplished by not imposing any restrictions on how the inputs and outputs can be weighted together. Unfortunately, this flexibility also has drawbacks. The underlying best practice production structure is typically very complex, which can make it difficult to understand efficiency evaluations. This flexibility may also motivate DMUs to pick specialized input‒output combinations simply to appear more efficient, particularly in applications where they are rewarded based on their DEA performance. In this paper, we therefore propose an approach that retains the fundamental principles of DEA while reducing flexibility in the evaluations. Our approach entails performing ex post k-centroid clustering of DMUs according to their input‒output mix patterns. The resulting mixed-integer programming problem seeks to put the centroids (as prototypes of their generated clusters) in their best possible light. This clustering enables us to work with a less complex underlying technology, which simplifies the evaluations and enhances their interpretability. Furthermore, it limits the possibility of DMUs inflating their performance by selecting extreme input‒output combinations. We demonstrate our approach with a simple numerical example and a complex data set involving Brazilian electricity distribution companies, providing clear and realistic illustrations of its application., An attractive feature of standard data envelopment analysis (DEA) is that decision-making units (DMUs) are put in their best possible light. This is accomplished by not imposing any restrictions on how the inputs and outputs can be weighted together. Unfortunately, this flexibility also has drawbacks. The underlying best practice production structure is typically very complex, which can make it difficult to understand efficiency evaluations. This flexibility may also motivate DMUs to pick specialized input‒output combinations simply to appear more efficient, particularly in applications where they are rewarded based on their DEA performance. In this paper, we therefore propose an approach that retains the fundamental principles of DEA while reducing flexibility in the evaluations. Our approach entails performing ex post k-centroid clustering of DMUs according to their input‒output mix patterns. The resulting mixed-integer programming problem seeks to put the centroids (as prototypes of their generated clusters) in their best possible light. This clustering enables us to work with a less complex underlying technology, which simplifies the evaluations and enhances their interpretability. Furthermore, it limits the possibility of DMUs inflating their performance by selecting extreme input‒output combinations. We demonstrate our approach with a simple numerical example and a complex data set involving Brazilian electricity distribution companies, providing clear and realistic illustrations of its application.An attractive feature of standard data envelopment analysis (DEA) is that decision-making units (DMUs) are put in their best possible light. This is accomplished by not imposing any restrictions on how the inputs and outputs can be weighted together. Unfortunately, this flexibility also has drawbacks. The underlying best practice production structure is typically very complex, which can make it difficult to understand efficiency evaluations. This flexibility may also motivate DMUs to pick specialized input‒output combinations simply to appear more efficient, particularly in applications where they are rewarded based on their DEA performance. In this paper, we therefore propose an approach that retains the fundamental principles of DEA while reducing flexibility in the evaluations. Our approach entails performing ex post k-centroid clustering of DMUs according to their input‒output mix patterns. The resulting mixed-integer programming problem seeks to put the centroids (as prototypes of their generated clusters) in their best possible light. This clustering enables us to work with a less complex underlying technology, which simplifies the evaluations and enhances their interpretability. Furthermore, it limits the possibility of DMUs inflating their performance by selecting extreme input‒output combinations. We demonstrate our approach with a simple numerical example and a complex data set involving Brazilian electricity distribution companies, providing clear and realistic illustrations of its application.

This paper considers optimal design of queueing networks in which each node consists of a single-server FIFO queue and an infinite-server queue, which is referred to as incubation queue. Upon service completion at a FIFO queue, a job splits (forks) into two parts: the first part is routed to the next node on its route, and the second part is placed in the incubation queue. Routing of the jobs of multiple types is governed by a central decision maker that decides on the routes for each job type and aims to minimize the mean turnaround time of the jobs, i.e., the time spent in the system until service completion at the FIFO queue in the last node, and at all incubation queues on the job's route, which may be viewed as a join operation. We provide explicit results for the turnaround time when all service and inter-arrival time distributions are exponential and invoke the Queueing Network Analyzer when these distributions are general. We then develop a Simulated Annealing approach to find the optimal routing configuration. We apply our approach to determine the optimal routing configuration in a chemistry analyzer line.

Given access to the hypergraph through a subset query oracle in the query model, we give sublinear time algorithms for Hitting-Set with almost tight parameterized query complexity. In parameterized query complexity, we estimate the number of queries to the oracle based on the parameter $k$, the size of the Hitting-Set. The subset query oracle we use in this paper is called Generalized $d$-partite Independent Set query oracle (GPIS) and it was introduced by Bishnu et al. (ISAAC'18). GPIS is a generalization to hypergraphs of the Bipartite Independent Set query oracle (BIS) introduced by Beame et al. (ITCS'18 and TALG'20) for estimating the number of edges in graphs. Formally, GPIS is defined as follows: GPIS oracle for a $d$-uniform hypergraph $\mathcal{H}$ takes as input $d$ pairwise disjoint non-empty subsets $A_1, \ldots, A_d$ of vertices in $\cal H$ and answers whether there is a hyperedge in $\mathcal{H}$ that intersects each set $A_i$, where $i \in \{1, \, 2, \, \ldots, d\}$. } For $d=2$, the GPIS oracle is nothing but BIS oracle. We show that $d$-Hitting-Set, the hitting set problem for $d$-uniform hypergraphs, can be solved using $\widetilde{\mathcal{O}}_d(k^{d} \log n)$ GPIS queries. Additionally, we also showed that $d$-Decesion-Hitting-Set, the decision version of $d$-Hitting-Set can be solved with $\widetilde{\mathcal{O}}_d\left( \min \left\{ k^d\log n, k^{2d^2} \right\} \right)$ {\sc GPIS} queries. We complement these parameterized upper bounds with an almost matching parameterized lower bound that states that any algorithm that solves $d$-Decesion-Hitting-Set requires $\Omega \left( \binom{k+d}{d} \right)$ GPIS queries., Comment: 22 pages. A preliminary version has appeared in ISAAC'19 and the full version has been accepted in JCSS

Survival models with time-varying covariates (TVCs) are widely used in the literature on credit risk prediction. However, when these covariates are endogenous, the inclusion procedure has been limited to practices such as lagging these variables or treating them as exogenous. That leads to possible biased estimators (depending on the strength of the exogeneity assumption) and a lack of prediction framework that consolidates the joint evolution of the survival process and the endogenous TVCs. The use of joint models is a suitable approach for handling endogeneity, however, it comes at a high computational cost. We propose a joint model for bivariate endogenous TVCs and discrete survival data using integrated nested Laplace approximation (INLA). We illustrate the implementation via simulations and build a model for full-prepayment consumer loans. We also propose a methodology for individual survival prediction using the Laplace method that leads to more accurate approximations than comparable approaches. We evidence the superiority of joint models over the traditional survival approach for an out-of-sample and out-of-time analysis.

Round robin tournaments are omnipresent in sport competitions and beyond. We propose two new integer programming formulations for scheduling a round robin tournament, one of which we call the matching formulation. We analytically compare their linear relaxations with the linear relaxation of a well-known traditional formulation. We find that the matching formulation is stronger than the other formulations, while its LP relaxation is still being solvable in polynomial time. In addition, we provide an exponentially sized class of valid inequalities for the matching formulation. Complementing our theoretical assessment of the strength of the different formulations, we also experimentally show that the matching formulation is superior on a broad set of instances. Finally, we describe a branch-and-price algorithm for finding round robin tournaments that is based on the matching formulation.

We propose a new test to detect change points in financial risk measures, based on the cumulative sum (CUSUM) procedure applied to the Wilcoxon statistic within a popular class of loss functions for risk measures. The proposed test efficiently captures change points jointly in two risk measure series: Value-at-Risk (VaR) and Expected Shortfall (ES), estimated by (semi)parametric models. We derive the asymptotic distribution of the proposed statistic and adopt a stationary bootstrapping technique to obtain the p-values of the test statistic. Monte Carlo simulation results show that our proposed test has better size control and higher power than the alternative tests under various change point scenarios. An empirical study of risk measures based on the S&P 500 index illustrates that our proposed test is able to detect change points that are consistent with well-known market events.

We study a typical daily drayage problem concerning the last-mile logistics at seaports for inland container supply chains. A set of trucks available at an inland container terminal must fulfil shippers’ requests of transporting containers within time windows and, to do so, can perform multiple daily trips. A request may entail picking up or delivering containers either at the shippers’ premises, the inland terminal or the seaport. Demand for empty containers can be satisfied by either using the available limited stock at the inland terminal, by street-turning or, ultimately, by retrieving them at a local depot for empties resulting in extra mileage. Hence, the minimization of routing costs also entails synchronizing trucks’ trips that retrieve and add empty containers to the inland terminal stock to avoid unnecessary visits to the empty depot. After modelling the problem mathematically, we develop an exact column-and-row generation approach embedded in a branch-and-price framework. To accelerate the solving process of the pricing problem, we propose effective strategies by combining a set of tailored pricing algorithms. These strategies perform well on a set of adapted Solomon's instances up to 100 nodes and against a standard branch-and-cut solver. Finally, experiments on real-world instances, inspired by a case study of an inland terminal at the Port of Rotterdam region, provide insights into current planning practices.

This paper considers the problem of finding near-optimal Markovian randomized (MR) policies for finite-state-action, infinite-horizon, constrained risk-sensitive Markov decision processes (CRSMDPs). Constraints are in the form of standard expected discounted cost functions as well as expected risk-sensitive discounted cost functions over finite and infinite horizons. The main contribution is to show that the problem possesses a solution if it is feasible, and to provide two methods for finding an approximate solution in the form of an ultimately stationary (US) MR policy. The latter is achieved through two approximating finite-horizon CRSMDPs which are constructed from the original CRSMDP by time-truncating the original objective and constraint cost functions, and suitably perturbing the constraint upper bounds. The first approximation gives a US policy which is $\epsilon$-optimal and feasible for the original problem, while the second approximation gives a near-optimal US policy whose violation of the original constraints is bounded above by a specified $\epsilon$. A key step in the proofs is an appropriate choice of a metric that makes the set of infinite-horizon MR policies and the feasible regions of the three CRSMDPs compact, and the objective and constraint functions continuous. A linear-programming-based formulation for solving the approximating finite-horizon CRSMDPs is also given., Comment: 38 pages