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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.

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

In dial-a-ride systems involving autonomous vehicles circulating along a circuit, a fleet of vehicles must serve clients who request rides between stations of the circuit such that the total number of pickup and drop-off operations is minimized. In this paper, we focus on a unitary variant where each client requests a single place in the vehicles and all the clients must be served within a single tour of the circuit. Such unitary variant induces a combinatorial optimization problem for which we introduce a nontrivial special case that is polynomially solvable when the capacity of each vehicle is at most 2 but it is NP-Hard otherwise. We also study the polytope associated with the solutions to this problem. We introduce new families of valid inequalities and give necessary and sufficient conditions under which they are facet-defining. Based on these inequalities, we devise an efficient branch-and-cut algorithm that outperforms the state-of-the-art commercial solvers.

International audience; Emergency department overcrowding is a global issue that poses a great threat to patient health and safety. The timeliness of medical services provided to patients is crucial to emergency departments as it directly impacts the mortality and morbidity of urgent patients. However, critical resources (e.g., doctors and nurses) are typically constrained due to the limited financial budget. Thus, hospital administrators may need to investigate solutions to improve the efficiency of the emergency department. In this work, we study the dynamic problem of scheduling patients to doctors, aiming at minimizing the total weighted tardiness. We propose a simple reoptimization heuristic based on multiple queues of patients in accordance with their urgency levels, and then combine it with an effective variable neighborhood search. We also propose a scenario-based planning approach that uses sampled scenarios to anticipate future events and the variable neighborhood search to schedule patients. The methods are adapted to handle a problem variant where information on arrival time and urgency level of some patients can be received in advance by the emergency department. With a comprehensive computational study on two sets of realistic instances from Hong Kong SAR of China and Italy, we validate the performance of the proposed methods, evaluating the benefits of having more doctors and receiving early information.

In this paper, we consider the contextual variant of the MNL-Bandit problem. More specifically, we consider a dynamic set optimization problem, where a decision-maker offers a subset (assortment) of products to a consumer and observes the response in every round. Consumers purchase products to maximize their utility. We assume that a set of attributes describe the products, and the mean utility of a product is linear in the values of these attributes. We model consumer choice behavior using the widely used Multinomial Logit (MNL) model and consider the decision maker problem of dynamically learning the model parameters while optimizing cumulative revenue over the selling horizon $T$. Though this problem has attracted considerable attention in recent times, many existing methods often involve solving an intractable non-convex optimization problem. Their theoretical performance guarantees depend on a problem-dependent parameter which could be prohibitively large. In particular, existing algorithms for this problem have regret bounded by $O(\sqrt{\kappa d T})$, where $\kappa$ is a problem-dependent constant that can have an exponential dependency on the number of attributes. In this paper, we propose an optimistic algorithm and show that the regret is bounded by $O(\sqrt{dT} + \kappa)$, significantly improving the performance over existing methods. Further, we propose a convex relaxation of the optimization step, which allows for tractable decision-making while retaining the favourable regret guarantee., Comment: Accepted to be published at Elsevier European Journal of Operational Research (EJOR)