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As one of the most popular techniques for performance evaluation, Data Envelopment Analysis (DEA) has been widely applied in many areas. However, the self-evaluation used in DEA leaves it open to much criticism. Moreover, most researchers have ignored the fact that reality abounds with uncertainty and have assumed that the data used for evaluation is deterministic and accurate. Both assumptions make it difficult to evaluate the efficiency of real-world production processes correctly and reasonably. In this paper, we propose a series of robust cross-efficiency (RCE) models based on robust optimization theory and cross-efficiency to deal with these problems. First of all, the proposed RCE models allow the conservatism level to be adjusted easily to suit the attitude of the decision-maker towards uncertainty. In addition, the RCE models have better discrimination power than the existing robust CCR models. We present two applications to demonstrate the effectiveness and stability of our models. [ABSTRACT FROM AUTHOR]

The pharmaceutical supply chain (PSC) is a highly important strategic issue in the healthcare domain because of its significant effect on human wellbeing and healthcare costs. This paper provides a mathematical optimization model to design a PSC by considering the drug's corruption. Given the importance of the sustainable development goals, three objectives are considered: economic, social, and environmental. The cost of fixed installation, transportation, holding, collection, distribution, recycling and disposal is reduced by the economic objective. A reduction in greenhouse gas emissions, water use, and nonrenewable energy consumption is achieved by the environmental objective. Based on the social objective, the number of employment opportunities, economic growth, job satisfaction, and national self-sufficiency are all increased, while the number of days lost due to work-related accidents decreases. To achieve the weight of elements in environmental and social objectives, the fuzzy best–worst method is used. Due to the inherent uncertainty in the PSC, its main parameters are referred to as unpredictable, which calls for a robust optimization approach to eliminate the model parameters' uncertainty. A fuzzy programming approach is used to solve the developed model. Numerical evidence drawn from a practical case shows that the suggested model is efficacious and valid. We suggest that the priorities and challenges of sustainable growth contribute to the determination of the PSC's managerial and operational characteristics. [ABSTRACT FROM AUTHOR]

The magnitude of the recent forest fires, the time required to extinguish them, and the damage they caused have attracted the attention of all humanity. If the current trend continues, it will cause great irreversible losses. There is a great need for scientific studies to prevent or reduce the damages of these fires. In this context, this paper proposes algorithms and mathematical models for generating the routes of unmanned aerial vehicles to detect forest fires that may occur especially in regions far from residential areas. A novel heuristic dispatching rule and a simulation-based optimization algorithm are proposed. The striking features of the proposed algorithms are that the routes are created with a focus on minimizing the fire probabilities. The uncertainties and dynamics of real-life are also considered. Various scenarios have experimented on a realistic case. Experimental results and findings are promising. [ABSTRACT FROM AUTHOR]

While theoretical studies on parametric multiobjective programs (mpMOPs) have been steadily progressing, the algorithmic development has been comparatively limited despite the fact that parametric optimization can provide a complete parametric description of the efficient set. This paper puts forward the premise that parametrization of the efficient set of nonparametric MOPs can be combined with solving parametric MOPs because the algorithms performing the former can also be used to achieve the latter.This strategy is realized through (i) development of a generalized scalarization, (ii) a computational study of selected parametric optimization algorithms, and (iii) applications in a real-life context. Several variants of a generalized weighted-sum scalarization allow one to scalarize mpMOPs to match the capabilities of algorithms. Parametric multiobjective quadratic programs are scalarized into parametric quadratic programs (mpQPs) with linear and/or quadratic constraints. In the computational study, three algorithms capable of solving mpQPs are examined on synthetic instances and two of the algorithms are applied to decision-making problems in statistics and portfolio optimization. The real-life context reveals the interplay between the scalarizations and provides additional insight into the obtained parametric solution sets. [ABSTRACT FROM AUTHOR]

Supply contracts are designed to minimize inventory costs or to hedge against undesirable events (e.g., shortages) in the face of demand or supply uncertainty. In particular, replenishment terms stipulated by supply contracts need to be optimized with respect to overall costs, profits, service levels, etc. In this paper, we shall be primarily interested in minimizing an inventory cost function with respect to a constant replenishment rate. Consider a single-product inventory system under continuous review with constant replenishment and compound Poisson demands subject to lost-sales. The system incurs inventory carrying costs and lost-sales penalties, where the carrying cost is a linear function of on-hand inventory and a lost-sales penalty is incurred per lost sale occurrence as a function of lost-sale size. We first derive an integro-differential equation for the expected cumulative cost until and including the first lost-sale occurrence. From this equation, we obtain a closed form expression for the time-average inventory cost, and provide an algorithm for a numerical computation of the optimal replenishment rate that minimizes the aforementioned time-average cost function. In particular, we consider two special cases of lost-sales penalty functions: constant penalty and loss-proportional penalty. We further consider special demand size distributions, such as constant, uniform and Gamma, and take advantage of their functional form to further simplify the optimization algorithm. In particular, for the special case of exponential demand sizes, we exhibit a closed form expression for the optimal replenishment rate and its corresponding cost. Finally, a numerical study is carried out to illustrate the results. [ABSTRACT FROM AUTHOR]

In many service systems, the service rates of the servers or the machines degrade over time due to a variety of reasons like fatigue, deficiency (due to manufacturing defect or energy loss, deformation, or excessive heat), and lack of proper maintenance. To make a service system beneficial for both customers and management points of view, it is imperative that models are developed to understand the impact of degradation. In this paper, we study M A P / P H / 1 - type queueing models incorporating degradation, failures/breakdowns and repairs. The degradation and to restore to normalcy in the service rate we look at two scenarios. In the first one, the service is restored to normalcy immediately after the server becomes idle or a fixed number of services is offered. In the second one, the restoration takes a random time that is modeled using a phase type distribution. Also, there are a variety of reasons that lead to failures/breakdowns of the server. We model these using (possibly) different phase type distributions. Both the models are studied analytically using matrix-analytic methods and illustrative numerical examples bringing out the qualitative behavior of the impact of degrading services are discussed. Two cost optimization problems whose solutions are obtained using particle swarm optimization technique along with a few illustrative examples are presented. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a duality theory for nonsmooth optimization problems with vanishing constraints (MPVC) defined by locally Lipschitz functions. In order to do this, we first formulate a new mixed-type dual problem for the considered MPVC, which is a generalization of Wolfe and Mond–Weir dual problems. Since this dual problem depends on the feasible points of the primal problem, we introduce another mixed-type dual problem that does not have this dependence. Then, we present the weak, strong, converse, restricted converse, and the strict converse duality results for these parametric dual problems. Finally, we compae the results of the article written by Mishra et al. (Ann Oper Res 243(1):249–272, 2016) with our results and state the correct version of some of its incorrect theorems. [ABSTRACT FROM AUTHOR]

The training phase is the most crucial stage during the machine learning process. In the case of labeled data and supervised learning, machine learning entails minimizing the loss function under various constraints. We provide an innovative model for learning with numerous data sets, resulting from the application of multicriteria optimization techniques to existing deep learning algorithms. Data fitting is formulated as a multicriteria model in which each criterion measures the data fitting error on a specific data set. This is an optimization model involving a vector-valued function, and it has to be analyzed using the notion of Pareto efficiency. We present stability results for efficient solutions in the presence of input and output data perturbations. The multiple data set environment comes into play to eliminate the bias caused by the selection of a specific training set. To apply this concept, we present a scalarization strategy as well as numerical experiments in digit classification using MNIST data. [ABSTRACT FROM AUTHOR]

We revisit in this article the Two-Fund Separation Theorem as a simple technique for the Mean–Variance optimization of large portfolios. The proposed approach is fast and scalable and provides equivalent results of commonly used ML techniques but, with computing time differences counted in hours (1 min vs. several hours). In the empirical application, we consider three geographic areas (China, US, and French stock markets) and show that the Two-Fund Separation Theorem holds exactly when no constraints are imposed and is approximately true with (realistic) positive constraints on weights. This technique is shown to be of interest to both scholars and practitioners involved in portfolio optimization tasks. [ABSTRACT FROM AUTHOR]

Efficiency plays a crucial role in portfolio optimization. This notion is formulated by means of stochastic optimization techniques. Very often this problem is subject to partial uncertainty or incomplete information on the probability distribution and on the preferences expressed by means of the utility function. In this case both the objective function and the underlying probability measure are not known with precision. To address this kind of issues, we propose to model the notion of incomplete information by means of set-valued analysis and, therefore, we propose two different extensions of the classical model. In the first one we rely on the notion of set-valued function while the second one utilizes the notion of set-valued probability. For both of them we investigate stability properties. These results are also linked to the notion of robustness of the aforementioned problem. Finally we apply the obtained results to portfolio theory and stochastic dominance. [ABSTRACT FROM AUTHOR]

The efficiency evaluation of the healthcare chain network becomes crucial as healthcare systems seek to enhance patient satisfaction and reduce costs during the health check. This study proposes a mixed-integer linear programming model that resolves the patient selection problem for influential diagnosis-related groups treatments by considering the approximate solution approach. This research's objective is to apply the minimum response time for the arrival time of two types of patients (regular and urgent) by presenting the Poisson distributed and queuing theory. Second, a process for resolving the optimal solutions for waiting time and the total number of patient arrival times to the hospital to achieve the target at a minimum supply chain cost. Furthermore, based on the obtained results applied for the patients with a first-come-first-serve policy and to meet overall arrival time on time, the percentage of patients waiting time at the healthcare center is reduced to under 30% for the emergency patient. At the same time, the percentage of regular patients who do not receive the treatment service time earlier and do not refer to the hospital punctuality is increased to more than 70%. Those theories determined that more healthcare costs and dissatisfaction for regular patients, while in contrast, for emergency patients, are decreased waiting time and healthcare cost services. [ABSTRACT FROM AUTHOR]

Organ transplantation is a crucial task in the healthcare supply chain, which organizes the supply and demand for various vital organs. In this regard, dealing with uncertainty is one of the main challengings in designing an organ transplant supply chain. To address this gap, in the present research, a mathematical formulation and solution method is proposed to optimize the organ transplants supply chain under shipment time uncertainty. A possibilistic programming model and simulation-based solution method are developed for organ transplant center location, allocation, and distribution. The proposed mathematical model optimizes the overall cost by considering the fuzzy uncertainty of organ demands and transportation time. Moreover, a novel simulation-based optimization is applied using the credibility theory to deal with the uncertainty in the optimization of this mathematical model. In addition, the proposed model and solution method are evaluated by implementing different test problems. The numerical results demonstrate that the optimal credibility level is between 0.2 and 0.6 in all tested cases. Moreover, the patient's satisfaction rate is higher than the viability rate in the designed organ supply chain. [ABSTRACT FROM AUTHOR]

Currently, the presence of data uncertainty and noise raises critical issues to be handled on both theoretical and computational grounds. Therefore, robustification and robust optimization have gained attention from theoretical and practical points of view for the establishment of a modeling framework in mathematical optimization to immunize solutions against diverse uncertainties. Data of both the input and output variables, underlying the problems to be addressed, are affected by the noise of different kinds, such that standard statistical models alone may not be sufficient to ensure trustworthy results due to the complexity of the model. Consequently, we propose including parametric uncertainties reflecting future scenarios in multivariate adaptive regression splines (MARS), which, in turn, show great promise for fitting nonlinear multivariate functions, where additive and interactive effects of the predictors are employed to assess the response variable. We robustify MARS through the usage of robust optimization techniques. Due to the large complexity of the underlying model in prior studies, we applied a so-called weak robustification. Now, we exploit a geometrical and combinatorial approach to allow for a more complete robustification, by formulating Robust MARS (RMARS) under Cross-Polytope Uncertainty. In this study, we use RMARS for energy data and demonstrate its superior performance through a simulation study. [ABSTRACT FROM AUTHOR]

We consider a system that generates a reward at some predefined decreasing rate as its virtual age increases. Periodic maintenance (PM) is performed to restore the system to as-good-as new condition, i.e., its virtual age is decreased to zero after each maintenance action. However, the system has a given deterministic initial lifetime and each maintenance action also results in a depletion of the remaining system's lifetime. Whenever the lifetime expires, the system is replaced by a new identical one at some predefined cost. From the application perspective the considered setting is primarily motivated by the practice of battery-powered systems, e.g., sensors, that need to be remotely monitored. We formulate a general repair-replacement problem with an infinite time horizon, where we seek an optimal number of PM actions and an optimal PM interval. We describe global optimization techniques for solving a general case of the problem under some reasonably mild assumptions on the reward and lifetime depletion rates. For the special case of a constant lifetime depletion per each maintenance action, some analytic observations are provided. Finally, we also demonstrate that for sufficiently large replacement costs the infinite-horizon problem can be solved by leveraging the results for the related finite-horizon problem previously considered in the literature. [ABSTRACT FROM AUTHOR]

In order for a system to stay operational, its components need maintenance. We consider two stakeholders—a system operator and a maintenance workshop—and a contract governing their joint activities. Components in the operating systems that are to be maintained are sent to the maintenance workshop, which should perform all maintenance activities on time in order to satisfy the contract. The maintained components are then sent back to be used in the operating systems. Our modeling of this system-of-systems includes stocks of damaged and repaired components, the workshop scheduling, and the planning of preventive maintenance for the operating systems. Our modeling is based on a mixed-binary linear optimization (MBLP) model of a preventive maintenance scheduling problem with so-called interval costs over a finite and discretized time horizon. We generalize and extend this model with the flow of components through the workshop, including the stocks of spare components. The resulting scheduling model—a mixed-integer optimization (MILP) model—is then utilized to optimize the main contract in a bi-objective setting: maximizing the availability of repaired (or new) components and minimizing the costs of maintaining the operating systems over the time horizon. We analyze the main contract and briefly discuss a turn-around time contract. Our results concern the effect of our modeling on the levels of the stocks of components over time, in particular minimizing the risk for lack of spare components. [ABSTRACT FROM AUTHOR]

The Unsplittable Flow on a Path (UFP) problem has garnered considerable attention as a challenging combinatorial optimization problem with notable practical implications. Steered by its pivotal applications in power engineering, the present work formulates a novel generalization of UFP, wherein demands and capacities in the input instance are monotone step functions over the set of edges. As an initial step towards tackling this generalization, we draw on and extend ideas from prior research to devise a quasi-polynomial time approximation scheme under the premise that the demands and capacities lie in a quasi-polynomial range. Second, retaining the same assumption, an efficient logarithmic approximation is introduced for the single-source variant of the problem. Finally, we round up the contributions by designing a (kind of) black-box reduction that, under some mild conditions, allows to translate LP-based approximation algorithms for the studied problem into their counterparts for the Alternating Current Optimal Power Flow problem—a fundamental workflow in operation and control of power systems. [ABSTRACT FROM AUTHOR]

The variation of and the interrelation between different energy markets significantly affect the competitiveness of various energy technologies, therefore complicate the decision-making problem for a complex energy system consisting of multiple competing technologies, especially in a long-term time frame. The interrelations between these markets have not been accounted for in the existing energy system modelling efforts, leading to a distortion of understanding of the market impact on the technological choices and operations in the real world. This study investigates the strategic and operational decision-making problem for such an energy system characterized by three competing technologies from crude oil, natural gas, and coal. A stochastic programming model is constructed by incorporating multiple volatile energy prices interrelated with each other. Oil price is modelled by the mean-reverting Ornstein–Uhlenbeck process and serves as the exogenous variable in the ARIMAX models for natural gas and downstream plastic prices. The K-means clustering method is employed to extract a handful of distinctive patterns from a large number of simulated price projections to enhance the computing efficiency without losing retaining critical information and insights from the price co-movement. The model results suggest that the high volatility of the energy market weakens the possibility of selecting the corresponding technology. The oil-based route, for example, gradually loses its market share to the coal approach, attributed to a higher volatile oil market. The proposed method is applicable to other problems of the same kind with high-dimensional stochastic variables. [ABSTRACT FROM AUTHOR]

Multiobjective optimization problems have a significant role in modeling and optimizing the framework of different real-life issues. It may not always be possible to obtain a single solution that satisfies each objective efficiently; however, there is ample opportunity to get a compromise solution to multiobjective programming problems (MOPPs). Neutrosophic set (NS) is the extension of fuzzy and intuitionistic fuzzy sets. Thus, based on NS, this study presents neutrosophic optimization models for MOPP under the neutrosophic fuzzy environment. We have developed three models while keeping in mind the maximal satisfactory degree of decision-maker(s). The proposed models are then applied to various discussed numerical examples, and solution results are compared with other approaches. Also, the propounded models are implemented in the pharmaceutical supply chain planning problem. The sensitivity analysis of the obtained outcomes at different criteria has been performed. At last, the conclusion and future research scope have been depicted effectively. [ABSTRACT FROM AUTHOR]