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The low-carbon supply chain is one of the predominant topics towards a green economy and it establishes the opportunity to reduce carbon emissions across the product value chain. This paper focuses on recycling and optimized sourcing in the paper industry as a case company. The main objective is to engage the case company with their supplier networks to diminish the greenhouse gases (GHG) emissions and cost in their production process. It proposes a model to support the selection of the best green supplier and an allocation of order among the potential suppliers. The proposed model contains a two-phase hybrid approach. The first phase presents the rating and selection of potential suppliers by considering economics (cost), operational factors (quality and delivery), and environmental criteria (recycle capability and GHG emission control) using Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (Fuzzy TOPSIS) methodology. The second phase presents the order allocation process using multi-objective linear programming in order to minimize cost, material rejection, late delivery, recycle waste and $$\mathrm{CO}_{2}$$ emissions in the production process. A case study from a paper manufacturing industry is presented to elucidate the effectiveness of the proposed model. The results demonstrate a 26.2 % reduction of carbon emission by using recycle products in the production process. The firm benefits by forming a systematic methodology for green supplier evaluation and order allocation. Finally, a conclusion and a suggested direction of future research are introduced. [ABSTRACT FROM AUTHOR]

The impacts of increased paper recycling on the U.S. pulp and paper sector are investigated, using the North American Pulp And Paper (NAPAP) model. This dynamic spatial equilibrium model forecasts the amount of pulp, paper and paperboard exchanged in a multi-region market, and the corresponding prices. The core of the model is a recursive price-endogenous linear programming system that simulates the behavior of a competitive industry. The model has been used to make forecasts of key variables describing the sector from 1986 to 2012, based on three recycling policy scenarios. Waste reduction policies that succeed in reducing demand for paper would have the greatest impact on the amount of wood used. But the minimum recycled content policies envisaged currently would have no more effect than what will come about due to unregulated market forces. [ABSTRACT FROM AUTHOR]

Development and application of the data envelopment analysis (DEA) method, have been the subject of numerous reviews. In this paper, we consider the papers that apply DEA methods specifically to financial services, or which use financial services data to experiment with a newly introduced DEA model. We examine 620 papers published in journals indexed in the Web of Science database, from 1985 to April 2016. We analyse the sample applying citations network analysis. This paper investigates the DEA method and its applications in financial services. We analyse the diffusion of DEA in three sub-samples: (1) banking groups, (2) money market funds, and (3) insurance groups by identifying the main paths, that is, the main flows of the ideas underlying each area of research. This allows us to highlight the main approaches, models and efficiency types used in each research areas. No unique methodological preference emerges within these areas. Innovations in the DEA methodologies (network models, slacks based models, directional distance models and Nash bargaining game) clearly dominate recent research. For each subsample, we describe the geographical distribution of these studies, and provide some basic statistics related to the most active journals and scholars. [ABSTRACT FROM AUTHOR]

Operations in areas of importance to society are frequently modeled as mixed-integer linear programming (MILP) problems. While MILP problems suffer from combinatorial complexity, Lagrangian Relaxation has been a beacon of hope to resolve the associated difficulties through decomposition. Due to the non-smooth nature of Lagrangian dual functions, the coordination aspect of the method has posed serious challenges. This paper presents several significant historical milestones (beginning with Polyak's pioneering work in 1967) toward improving Lagrangian Relaxation coordination through improved optimization of non-smooth functionals. Finally, this paper presents the most recent developments in Lagrangian Relaxation for fast resolution of MILP problems. The paper also briefly discusses the opportunities that Lagrangian Relaxation can provide at this point in time. [ABSTRACT FROM AUTHOR]

The multi-objective integer programming problem often occurs in multi-criteria decision-making situations, where the decision variables are integers. In the present paper, we have discussed an algorithm for finding all efficient solutions of a multi-objective integer quadratic programming problem. The proposed algorithm is based on the aspect that efficient solutions of a multi-objective integer quadratic programming problem can be obtained by enumerating ranked solutions of an integer quadratic programming problem. For determining ranked solutions of an integer quadratic programming problem, we have constructed a related integer linear programming problem and from ranked solutions of this integer linear programming problem, ranked solutions of the original integer quadratic programming problem are generated. Theoretically, we have shown that the developed method generates the set of all efficient solutions in a finite number of steps, and numerically we have elaborated the working of our algorithm and compared our results with existing algorithms. Further, we have analyzed that the developed method is efficient for solving a multi-objective integer quadratic programming problem with a large number of constraints, variables and objectives. [ABSTRACT FROM AUTHOR]

The paper examines the sensitivity for the solution of linear programming problems using Bayesian techniques, when samples for the coefficients of the objective function are uncertain. When data is available, we estimate the solution of the linear program and provide statistical measures of uncertainty through the posterior distributions of the solution in the light of the data. When data is not available, these techniques examine the sensitivity of the solution to random variation in the coefficients of the linear problem. The new techniques are based on two posteriors emerging from the inequalities of Karush–Kuhn–Tucker conditions. The first posterior is asymptotic and does not require data. The second posterior is finite-sample-based and is used whenever data is available or if random samples can be drawn from the joint distribution of coefficients. A by-product of our framework is a robust solution. We illustrate the new techniques in two empirical applications to the case of uncertain Data Envelopment Analysis efficiency, involving two large samples, of US commercial banks and a sample of European commercial banks regulated by the Single Supervisory Mechanism. We analyse whether some pre-determined criteria, associated with size and new supervisory framework, can adequately affect the solution of linear program. The results provide evidence of substantial improvements in statistical structure with respect to sensitivities and robustification. Our methodology can serve as a consistency check of the statistical inference for the solution of linear programming problems in efficiency under uncertainty in data. [ABSTRACT FROM AUTHOR]

Outsourcing project activities to contractors has become more and more popular in recent years, and activity contractors can increase the revenue of a project through cooperation. In this paper we consider cooperation between activity contractors through resource reallocation, and address two main issues. First, we seek to find the optimal scheme for resource reallocation among contractors. To this end, a linear programming model is established, and some properties of the optimal resource reallocation scheme are discussed. Second, we propose several revenue sharing schemes for contractors based on a cooperative game theory framework. Three schemes are introduced and compared: a scheme in the core, the Shapley value, and a proportional revenue sharing scheme. We show that the cooperative game of activity contractors in a general project network does not necessarily have a nonempty core. However, we identify a special class of project network for which the core of the cooperative game of activity contractors always exists and an allocation in the core is proposed based on shadow prices. The managerial insights we obtain in this paper are as follows. (i) Contractors should cooperate. (ii) Resources should not be transferred between contractors with high transferring costs. (iii) Resources are always transferred from contractors on non-critical paths to contractors on critical paths, and on critical paths, resources are always transferred from low efficiency contractors to high efficiency contractors. [ABSTRACT FROM AUTHOR]

This paper seeks to solve the long-term transmission expansion planning problem in power systems more effectively by reducing the solution search space and the computational effort. The proposed methodology finds and adds cutting planes based on structural insights about bus angle differences along paths. Two lemmas and a theorem are proposed which formally establish the validity of these cutting planes onto the underlying mathematical formulations. These path-based bus angle difference constraints, which tighten the relaxed feasible region, are used in combination with branch-and-bound to find lower bounds on the optimal investment of the transmission expansion planning problem. This work also creates an algorithm that automates the process of finding and applying the most effective valid inequalities, resulting in significantly reduced testing and computational time. The algorithm is implemented in Python, using Gurobi to add constraints and solve the exact DCOPF-based transmission expansion problem. This paper uses two different-sized systems to illustrate the effectiveness of the proposed framework: the GOC 500-bus system and a modified Polish 2383-bus system. [ABSTRACT FROM AUTHOR]

In this paper, a new production, allocation, location, inventory holding, distribution, and flow problems for a new sustainable-resilient health care network related to the COVID-19 pandemic under uncertainty is developed that also integrated sustainability aspects and resiliency concepts. Then, a multi-period, multi-product, multi-objective, and multi-echelon mixed-integer linear programming model for the current network is formulated and designed. Formulating a new MILP model to design a sustainable-resilience healthcare network during the COVID-19 pandemic and developing three hybrid meta-heuristic algorithms are among the most important contributions of this research. In order to estimate the values of the required demand for medicines, the simulation approach is employed. To cope with uncertain parameters, stochastic chance-constraint programming is proposed. This paper also proposed three meta-heuristic methods including Multi-Objective Teaching–learning-based optimization (TLBO), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA) to find Pareto solutions. Since heuristic approaches are sensitive to input parameters, the Taguchi approach is suggested to control and tune the parameters. A comparison is performed by using eight assessment metrics to validate the quality of the obtained Pareto frontier by the heuristic methods on the experiment problems. To validate the current model, a set of sensitivity analysis on important parameters and a real case study in the United States are provided. Based on the empirical experimental results, computational time and eight assessment metrics proposed methodology seems to work well for the considered problems. The results show that by raising the transportation costs, the total cost and the environmental impacts of sustainability increased steadily and the trend of the social responsibility of staff rose gradually between − 20 and 0%, but, dropped suddenly from 0 to + 20%. Also in terms of the on-resiliency of the proposed network, the trends climbed slightly and steadily. Applications of this paper can be useful for hospitals, pharmacies, distributors, medicine manufacturers and the Ministry of Health. [ABSTRACT FROM AUTHOR]

Organization's sustainability performance is influenced by its suppliers' sustainability performance. This relationship makes sustainable supplier development a strategic competitive option for a buyer or focal organization. When considering sustainable supplier development practices (SSDPs) adoption, organizations have to balance and consider their limited financial resources and operational constraints. It becomes necessary to both select the best SSDPs set and investment allocation among the selected SSDP set such that the organization can maximize overall sustainability performance level. In this paper, an integrated formal modeling methodology using DEMATEL, the NK model, and multi-objective linear programming model is used support this objective. The proposed methodology is evaluated in a practical sustainable supply chain field study of an equipment manufacturing company in China. Through case study, we found that the interdependency among SSDPs must be considered in SSDPs selection and investment allocation problem. Theoretical, managerial and methodology implications, conclusions, and directions for future research are also presented. [ABSTRACT FROM AUTHOR]

Global supply chains engage in economic exchanges and flows of capital across borders. The free flow of economic goods opens opportunities for organizations to optimize supply chains across global networks and develop socially embedded interdependent relationships. This study explores issues related to multi-echelon supply chains and the effect of economic integration on a major beverage company's distribution in the emerging Association of Southeast Asian Nations (ASEAN) Economic Community (AEC). Case-based modeling is conducted to resolve discrepancies in perceptions of supply chain network formation between academic research and industry. This paper determines the network configuration involving minimum gross cost while considering the impacts of barriers to resource accessibility and external economic decisions on infrastructure in a real-world supply chain network where end products of in-house manufacturing are acquired from external sources and incorporated in warehouses. A mixed-integer linear programming model was developed to design a multi-stage supply chain network using ILOG LOGIC NET. The model explores location and capacity selection for plants and warehouses in parallel with capacity selection for suppliers and transportation in the AEC, and we determine the optimal flow of products and product families through the network medium. Three different scenarios were evaluated to obtain differing resolutions that can empower decision-makers to understand influences on overall supply chain networks based on futuristic development preferences and regional economic integration. [ABSTRACT FROM AUTHOR]

In this study, we consider the robust knapsack problem defined by the model of Bertsimas and Sim (Operations Research 52(1):35–53, 2004) where each item weight is uncertain and is defined with an interval. The problem is to choose a subset of items that is feasible for all of the cases in which up to a pre-specified number of items are allowed to take maximum weights simultaneously while maximizing the sum of profits of chosen items. Several integer optimization formulations for the problem have been proposed, however the strength of the upper bounds obtained from their LP-relaxations have not been theoretically analyzed and compared. In this paper, we establish a theoretical relationship among those formulations in terms of their LP-relaxations. Especially, we theoretically prove that previously proposed strong formulations (two extended formulations and a formulation using submodularity) yield the same LP-relaxation bound. In addition, through computational tests with benchmark instances, we analyze the trade-off between the strength of the lower bounds and the required computation time to solve the LP-relaxations. The results show that the formulation using submodularity shows competitive theoretical and computational performance. [ABSTRACT FROM AUTHOR]

The aim of this paper is to compare the performance of a local solution technique—namely Sequential Linear Programming (SLP) employing random starting points—with state-of-the-art global solvers such as Baron and more sophisticated local solvers such as Sequential Quadratic Programming and Interior Point for the pooling problem. These problems can have many local optima, and we present a small example that illustrates how this can occur. We demonstrate that SLP—usually deemed obsolete since the arrival of fast reliable SQP solvers, Interior Point Methods and sophisticated global solvers—is still the method of choice for an important class of pooling problems when the criterion is the quality of the solution found within a given acceptable time budget. On this measure SLP significantly ourperforms all other tested algorithms. In addition we introduce a new formulation, the qq-formulation, for the case of fixed demands, that exclusively uses proportional variables. We compare the performance of SLP and the global solver Baron on the qq-formulation and other common formulations. While Baron with the qq-formulation generates weaker bounds than with the other formulations tested, for both SLP and Baron the qq-formulation finds the best solutions within a given time budget. The qq-formulation can be strengthened by pq-like cuts in which case the same bounds as for the pq-formulation are obtained. However the associated time penalty due to the additional constraints results in poorer solution quality within the time budget. [ABSTRACT FROM AUTHOR]

Every year, natural disasters such as earthquakes, floods, volcanos, etc. cause millions of victims. So a quick response to these disasters is vital to reduce their negative consequences. Vehicle routing models can make important contributions to faster response, and thus, save lives. This paper proposes a vehicle routing problem to deliver relief resources from origins to destinations in response to disasters. For this purpose, a multi-period, multi-depot, multi-trip mixed-integer linear programming model is developed. Minimizing the sum of arrival times is considered as a service-based objective function for the increase of the survival rate. For the first time, the problem is solved using a grouping metaheuristic algorithm. Then its performance is compared with two other grouping algorithms. To evaluate the solution method, the algorithms are implemented on various test problems and compared statistically. Additionally, to show the validity of the model, sensitivity analyses are performed and managerial insights are given. [ABSTRACT FROM AUTHOR]

Allocating the fixed cost among a set of users in a fair way is an important issue both in management and economic research. Recently, Du et al. (Eur J Oper Res 235(1): 206-214, 2014) proposed a novel approach for allocating the fixed cost based on the game cross-efficiency method by taking the game relations among users in efficiency evaluation. This paper proves that the novel approach of Du et al. (Eur J Oper Res 235(1): 206-214, 2014) is equivalent to the efficiency maximization approach of Li et al. (Omega 41(1): 55-60, 2013), and may exist multiple optimal cost allocation plans. Taking into account the game relations in the allocation process, this paper proposes a cooperative game approach, and uses the nucleolus as a solution to the proposed cooperative game. The proposed approach in this paper is illustrated with a dataset from the prior literature and a real dataset of a steel and iron enterprise in China. [ABSTRACT FROM AUTHOR]

This paper develops an algorithm for solving quadratic fractional integer programming problems with bounded variables (QFIPBV). The method provides complete ranking and scanning of the integer feasible solutions of QFIPBV by establishing the existence of a linear or a linear fractional function, which acts as a lower bound on the values of the objective function of QFIPBV over the entire feasible set. The method involves ranking and scanning of the set of optimal integer feasible solutions of the linear or linear fractional program so constructed which requires introduction of various cuts at intermediate steps, for which, a new technique has been developed in the current paper. Numerical examples are included in support of the theory. [ABSTRACT FROM AUTHOR]

The bounded degree sum-of-squares (BSOS) hierarchy of Lasserre et al. (EURO J Comput Optim 1-31, 2015) constructs lower bounds for a general polynomial optimization problem with compact feasible set, by solving a sequence of semi-definite programming (SDP) problems. Lasserre, Toh, and Yang prove that these lower bounds converge to the optimal value of the original problem, under some assumptions. In this paper, we analyze the BSOS hierarchy and study its numerical performance on a specific class of bilinear programming problems, called pooling problems, that arise in the refinery and chemical process industries. [ABSTRACT FROM AUTHOR]

This paper is concerned with the convergence property of Dikin's algorithm applied to linearly constrained smooth convex programs. We study a version of Dikin's algorithm in which a second-order approximation of the objective function is minimized at each iteration together with an affine transformation of the variables. We prove that the sequence generated by the algorithm globally converges to a limit point at a local linear rate if the objective function satisfies a Hessian similarity condition. The result is of a theoretical nature in the sense that in order to ensure that the limit point is an ε-optimal solution, one may have to restrict the steplength to the order of O(ε). The analysis does not depend on non-degeneracy assumptions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel model of multi-issue bankruptcy problem inspired from a real problem of abatement of emissions of different pollutants in which pollutants can have more than one effect on atmosphere. In our model, therefore, several perfectly divisible goods (estates) have to be allocated among certain set of agents (claimants) that have exactly one claim which is used in all estates simultaneously. In other words, unlike of the multi-issue bankruptcy problems already existent in the literature, this model study situations with multi-dimensional states, one for each issue and where each agent claims the same to the different issues in which participates. In this context, we present an allocation rule that generalizes the well-known constrained equal awards rule from a procedure derived from analyzing this rule for classical bankruptcy problems as the solution to a sucession of linear programming problems. Next, we carry out an study of its main properties, and we characterize it using the well-known property of consistency. [ABSTRACT FROM AUTHOR]

The geometric–arithmetic index GA of a graph is defined as sum of weights of all edges of graph. The weight of one edge is quotient of the geometric and arithmetic mean of degrees of its end vertices. The predictive power of GA for physico-chemical properties is somewhat better than the predictive power of other connectivity indices. Let G(k, n) be the set of connected simple n-vertex graphs with minimum vertex degree k. In this paper we characterized graphs on which GA index attains minimum value, when the number of vertices of minimum degree k is n - 1 and n - 2 . We also gave a conjecture about the structure of the extremal graphs on which this index attains its minimum value and lower bound for this index where k is less or equal to q 0 , and q 0 is approximately 0.0874. For k greater or equal to q 0 and k or n are even, extremal graphs in this set for which GA index attains its minimum value, are regular graphs of degree k. [ABSTRACT FROM AUTHOR]

Meeting the customer's power demands is crucial for energy companies, even when unexpected and consecutive failures are present. This task has considerably increased its complexity due to the high integration of renewable energies and their intermittent behaviors. Therefore, it is important to achieve reliable power supply based on a criterion closer to real-life system operations and capable of addressing consecutive failures. The N-1-1 contingency involves the loss of a single transmission line or generation unit, followed by systems adjustments. Afterward, the power system experiences a subsequent loss of an additional generation unit or transmission line. This paper presents a power system unit commitment problem considering the N-1-1 reliability criterion with operations compliance check on economic dispatch and power flows under contingency states and renewable energy integration. Corrective actions are also included to determine the time that the failed components are restored. To address the complexity caused by renewable energy integration, the reliable unit commitment is achieved under the worst-case renewable output. The formulation results in an extremely large-scale adaptive robust mixed-integer linear programming model. For an efficient solution, a variation of the nested column-and-constraint generation algorithm is designed. Besides using the susceptance and phase angles to model the power flow, the linear sensitivity factors are also applied for improving the computational performance. The proposed models and algorithms are evaluated on modified IEEE 6-bus, 14-bus, and 118-bus test systems to confirm their effectiveness. [ABSTRACT FROM AUTHOR]

The paper aims to present a multi-product, multi-stage, multi-period, and multi-objective, probabilistic mixed-integer linear programming model for a sustainable forward and reverse logistics network problem. It looks at original and return products to determine both flows in the supply chain—forward and reverse—simultaneously. Besides, to establish centres of forward and reverse logistics activities and make a decision for transportation strategy in a more close-to-real manner, the demand is considered uncertain. We attempt to represent all major dimensions in the objective functions: First objective function is minimizing the processing, transportation, fixed establishing cost and costs of CO2 emission as environmental impacts. Furthermore, the processing time of reverse logistics activities is developed as the second objective function. Finally, in the third objective function, it is tried to maximize social responsibility. Indeed, a complete sustainable approach is developed in this paper. In addition, this model provides novel environmental constraint and social matters in the objective functions as its innovation and contribution. Another contribution of this paper is using probabilistic programming to manage uncertain parameters. Moreover, a non-dominated sorting genetic algorithm (NSGA-II) is configured to achieve Pareto front solutions. The performance of the NSGA-II is compared with a multi-objective particle swarm optimization (MOPSO) by proposing 10 appropriate test problems according to five comparison metrics using analysis of variance (ANOVA) to validate the modeling approach. Overall, according to the results of ANOVA and the comparison metrics, the performance of NSGA-II algorithm is more satisfying compared with that of MOPSO algorithm. [ABSTRACT FROM AUTHOR]

For daily airport operations, the insufficient number and the improper scheduling of ground support vehicles are the main causes of flight delays. In this paper, a novel network model is proposed to complement the optimal scheduling of ferry vehicles for the flight ground support service. In the process of model construction, we first innovatively construct a ferry vehicle capacity network by having the introduced virtual flights and the ferry vehicle depot as nodes, in which the directed edges indicate that the two nodes associated may be consecutively served by the same ferry vehicle. Based on the capacity network, a mixed integer programming model is constructed to minimize the number of ferry vehicles needed. In addition, this paper shows that the mixed integer programming is equivalent to a linear programming when the service start time of each flight is fixed, which makes the solving process more efficient, and the linear programming model can be applied to solve the minimum node-disjoint path cover of directed acyclic graphs. The efficiency and accuracy of the method are validated by the actual flight data obtained from Beijing Capital International Airport. This study will provide a methodological reference for the optimal scheduling of airport ferry vehicles. [ABSTRACT FROM AUTHOR]

In this research, an agro-supply chain in the context of both economic and environmental issues has been investigated. To this end, a bi-objective model is formulated as a mixed-integer linear programming that aims to minimize the total costs and CO2 emissions. It generates the integration between purchasing, transporting, and storing decisions, considering specific characteristics of agro-products such as seasonality, perishability, and uncertainty. This study provides a different set of temperature conditions for preserving products from spoilage. In addition, a robust optimization approach is used to tackle the uncertainty in this paper. Then, ε -constraint method is used to convert the bi-objective model to a single one. To solve the problem, Lagrangian relaxation algorithm is applied as an efficient approach giving lower bounds for the original problem and used for estimating upper bounds. At the end, a real case study is presented to give valuable insight via assessing the impacts of uncertainty in system costs. [ABSTRACT FROM AUTHOR]

This paper proposes a two-step approach to build portfolio models. The first step employs the Data Envelopment Analysis (DEA) to select assets attaining efficient financial performance according to a set of indicators used as inputs and outputs. The second step builds interval multiobjective portfolio models to obtain the optimal composition of efficient portfolios previously identified with respect to investor preferences. The usefulness of this proposed methodology is illustrated through a selected sample of diversified Exchange Traded Funds (ETFs) operating in the US energy sector. Our results with respect to all models and time horizons mainly show that: (i) ETFs related to nuclear energy are more often viewed as efficient according to all DEA models considered; (ii) the efficient portfolios do not contain any ETFs related to the renewable energy sector; and (iii) natural gas and oil are the sectors that have the most ETFs represented in efficient portfolios. [ABSTRACT FROM AUTHOR]

The paper defines new distances between univariate probability distributions, based on the concept of the CVaR norm. We consider the problem of approximation of a discrete distribution by some other discrete distribution. The approximating distribution has a smaller number of atoms than the original one. Such problems, for instance, must be solved for generation of scenarios in stochastic programming. The quality of the approximation is evaluated with new distances suggested in this paper. We use CVaR constraints to assure that the approximating distribution has tail characteristics similar to the target distribution. The numerical algorithm is based on two main steps: (i) optimal placement of positions of atoms of the approximating distribution with fixed probabilities; (ii) optimization of probabilities with fixed positions of atoms. These two steps are iterated to find both optimal atom positions and probabilities. Numerical experiments show high efficiency of the proposed algorithms, solved with convex and linear programming. [ABSTRACT FROM AUTHOR]

Nowadays, data envelopment analysis (DEA) is a well-established non-parametric methodology for performance evaluation and benchmarking. DEA has witnessed a widespread use in many application areas since the publication of the seminal paper by Charnes, Cooper and Rhodes in 1978. However, to the best of our knowledge, no published work formally addressed out-of-sample evaluation in DEA. In this paper, we fill this gap by proposing a framework for the out-of-sample evaluation of decision making units. We tested the performance of the proposed framework in risk assessment and bankruptcy prediction of companies listed on the London Stock Exchange. Numerical results demonstrate that the proposed out-of-sample evaluation framework for DEA is capable of delivering an outstanding performance and thus opens a new avenue for research and applications in risk modelling and analysis using DEA as a non-parametric frontier-based classifier and makes DEA a real contender in industry applications in banking and investment. [ABSTRACT FROM AUTHOR]

This paper explores the study of multi-choice multi-objective transportation problem (MCMTP) under the light of conic scalarizing function. MCMTP is a multi-objective transportation problem (MOTP) where the parameters such as cost, demand and supply are treated as multi-choice parameters. A general transformation procedure using binary variables is illustrated to reduce MCMTP into MOTP. Most of the MOTPs are solved by goal programming (GP) approach, but the solution of MOTP may not be satisfied all times by the decision maker when the objective functions of the proposed problem contains interval-valued aspiration levels. To overcome this difficulty, here we propose the approaches of revised multi-choice goal programming (RMCGP) and conic scalarizing function into the MOTP, and then we compare among the solutions. Two numerical examples are presented to show the feasibility and usefulness of our paper. The paper ends with a conclusion and an outlook on future studies. [ABSTRACT FROM AUTHOR]

The Weapon-Target Assignment (WTA) problem aims to assign a set of weapons to a number of assets (targets), such that the expected value of survived targets is minimized. The WTA problem is a nonlinear combinatorial optimization problem known to be NP-hard. This paper applies several existing techniques to linearize the WTA problem. One linearization technique (Camm et al. in Oper Res 50(6):946–955, 2002) approximates the nonlinear terms of the WTA problem via convex piecewise linear functions and provides heuristic solutions to the WTA problem. Such approximation problems are, though, relatively easy to solve from the computational point of view even for large-scale problem instances. Another approach proposed by O'Hanley et al. (Eur J Oper Res 230(1):63–75, 2013) linearizes the WTA problem exactly at the expense of incorporating a significant number of additional variables and constraints, which makes many large-scale problem instances intractable. Motivated by the results of computational experiments with these existing solution approaches, a specialized new exact solution approach is developed, which is called branch-and-adjust. The proposed solution approach involves the compact piecewise linear convex under-approximation of the WTA objective function and solves the WTA problem exactly. The algorithm builds on top of any existing branch-and-cut or branch-and-bound algorithm and can be implemented using the tools provided by state-of-the-art mixed integer linear programming solvers. Numerical experiments demonstrate that the proposed specialized algorithm is capable of handling very large scale problem instances with up to 1500 weapons and 1000 targets, obtaining solutions with optimality gaps of up to 2.0 % within 2 h of computational runtime. [ABSTRACT FROM AUTHOR]

This paper deals with a multiobjective portfolio selection problem involving expected wealth (or return), coherent risk measures, deviation measures, and "level II order book data", i.e., natural restrictions provoked by the existence of several levels of both bid and ask quotes with the corresponding depth. Obviously, the incorporation of the order book information makes our study much more realistic, since it is more closely related to the real behavior of many financial markets. Besides, ambiguity may be incorporated, which allows us to overcome the model-risk, since a potential discrepancy between the real (and maybe unknown) probabilities and the estimated ones is taken into account. Though the portfolio choice problem is not at all linear, its dual problem becomes a linear goal programming problem, and, consequently, the absence of duality gap allows us to solve the portfolio choice problem in an easy way. Furthermore, the double dual problem is linear too, and its solution also leads to the Pareto-efficient frontier. Lastly, we explore the influence on the Pareto-efficient frontier of the existence of "golden strategies", i.e., investment strategies whose tail (or downside) risk is strictly lower than their price. Numerical experiments involving all the findings are implemented in a derivative market where both future contracts and call/put options may be traded. [ABSTRACT FROM AUTHOR]

The linear production game is concerned with allocating the total payoff of an enterprise among the owners of the resources in a fair way. With cooperative game theory providing a mathematical framework for sharing the benefit of the cooperation, the Shapley value is one of the widely used solution concepts as a fair measurement in this area. Finding the exact Shapley value for linear production games is, however, challenging when the number of players exceeds 30. This paper describes the use of linear programming sensitivity analysis for a more efficient computation of the Shapley value. The paper also proposes a stratified sampling technique to estimate the Shapley value for large-scale linear production games. Computational results show the effectiveness of the proposed methods compared to others. [ABSTRACT FROM AUTHOR]

The story of linear programming is one with all the elements of a grand historical drama. The original idea of testing if a polyhedron is non-empty by using a variable elimination to project down one dimension at a time until a tautology emerges dates back to a paper by Fourier in 1823. This gets re-invented in the 1930s by Motzkin. The real interest in linear programming happens during World War II when mathematicians ponder best ways of utilising resources at a time when they are constrained. The problem of optimising a linear function over a set of linear inequalities becomes the focus of the effort. Dantzig's Simplex Method is announced and the Rand Corporation becomes a hot bed of computational mathematics. The range of applications of this modelling approach grows and the powerful machinery of numerical analysis and numerical linear algebra becomes a major driver for the advancement of computing machines. In the 1970s, constructs of theoretical computer science indicate that linear programming may in fact define the frontier of tractable problems that can be solved effectively on large instances. This raised a series of questions and answers: Is the Simplex Method a polynomial-time method and if not can we construct novel polynomial time methods, etc. And that is how the Ellipsoid Method from the Soviet Union and the Interior Point Method from Bell Labs make their way into this story as the heroics of Khachiyan and Karmarkar. We have called this paper a primer on linear programming since it only gives the reader a quick narrative of the grand historical drama. Hopefully it motivates a young reader to delve deeper and add another chapter. [ABSTRACT FROM AUTHOR]

In this paper a new scheduling problem is presented, which originates from the steel processing industry. The optimal scheduling of a steel forge is investigated with the goal of minimizing setup and storage costs under strict deadlines and special resource constraints. The main distinctive feature of the problem is the deterioration of some equipment, in this case, the so-called forging dies. While the aging effect has been widely investigated in scheduling approaches, where production speed decreases through time, durability deterioration caused by equipment setup has not been addressed yet. In this paper a mixed-integer linear programming model is proposed for solving the problem. The model uses a uniform discrete time representation and resource-balance constraints based on the resource–task network model formulation method. The proposed method was tested on 3-week long schedules based on real industrial scenarios. Computational results show that the approach is able to provide optimal short-term schedules in reasonable time. [ABSTRACT FROM AUTHOR]

The human societies are threatened by natural disasters. Thus, preparedness and response planning is necessary to eliminate or mitigate their negative effects. Relief network design plays an important role in the efficient response to the affected people. This paper addresses the problem of relief logistics network design under interval uncertainty and the risk of facility disruption. A mixed-integer linear programming model is proposed (1) to consider distribution center (DC) disruption (2) to support the disrupted DC by backup plan (3) to take in to the account both supply and evacuation issues (4) and finally, to mitigate disruption impact by investment. Moreover, robust optimization methodology is applied to hedge against uncertain environments. We conduct computational experiments by using generated instances and a real-world case to perform sensitivity analysis and provide managerial insights. The results show that the total cost of relief network increases by increasing the conservatism level. Moreover, the result show that the total cost of the network can be decrease by reducing the interval of uncertain parameters. As a result, providing more information and better estimation about uncertain parameters can reduce network costs. Disruption probability effect is also investigated and the result indicates that the network tries to establish more reliable facilities as the disruption probability increases. To demonstrate superiority of reliable network described in this paper over the classic network, a Monte Carlo procedure is used to compare two networks and results confirmed superiority of reliable network. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability of multistage stochastic programming with recourse in a way that is different from that used in studying stability of two-stage stochastic programs. Here, we transform the multistage programs into mathematical programs in the space Rn x Lp with a simple objective function and multistage stochastic constraints. By investigating the continuity of the multistage multifunction defined by the multistage stochastic constraints and applying epi-convergence theory we obtain stability results for linear and linear-quadratic multistage stochastic programs. [ABSTRACT FROM AUTHOR]

This paper presents a simplified and self-contained global convergence proof for the affine scaling algorithm applied to degenerate linear programming problems. Convergence of the sequence of dual estimates to the center of the optimal dual face is also proven. In addition, we give a sharp rate of convergence result for the sequence of objective function values. All these results are proved with respect to the long step version of the affine scaling algorithm in which we move a fraction λ, where λ ϵ (0,2/3], of the step to the boundary of the feasible region. [ABSTRACT FROM AUTHOR]

In contrast to methods of parametric linear programming which were developed soon after the invention of the simplex algorithm and are easily included as an extension of that method, techniques for parametric analysis on integer programs are not well known and require considerable effort to append them to an integer programming solution algorithm. The paper reviews some of the theory employed in parametric integer programming, then discusses algorithmic work in this area over the last 15 years when integer programs are solved by different methods. A summary of applications is included and the article concludes that parametric integer programming is a valuable tool of analysis awaiting further popularization. [ABSTRACT FROM AUTHOR]

This paper serves as an introduction to a series of three papers which are directed to different aspects of DEA (Data Envelopment Analysis) as follows: (1) uses and extensions of 'window analyses' to study DEA efficiency measures with an illustrative applications to maintenance activities for U.S. Air Force fighter wings, (2) a comparison of DEA and regression approaches to identifying and estimating sources of inefficiency by means of artificially generated data, and (3) an extension of ordinary (linear programming) sensitivity analyses to deal with special features that require attention in DEA. Background is supplied in this introductory paper with accompanying proofs and explanations to facilitate understanding of what DEA provides in the way of underpinning for the papers that follow. An attempt is made to bring readers abreast of recent progress in DEA research and uses. A synoptic history is presented along with brief references to related work, and problems requiring attention are also indicated and possible research approaches also suggested. [ABSTRACT FROM AUTHOR]

Inevitable simplifications of models of real world activities lead to some inadequacies. In the DEA literature several methods were proposed to overcome such difficulties. Some authors proposed to use specific production units in the primal space of inputs and outputs as a starting point in order to improve the frontier of the DEA models. In our previous papers, we introduced the notion of terminal units. It was proved that only terminal units form necessary and sufficient set of units for improving the frontier. In this paper, the relationship between all sets of units proposed for improving the frontier is established. Our theoretical results are confirmed by extensive and instructive graphical examples and also verified by computational experiments using real-life data sets. [ABSTRACT FROM AUTHOR]

The leader–follower facility location problem consists of a leader and a follower who are competitors that locate new facilities sequentially. Traditional studies have generally assumed that the leader has partial or full advance information of the follower's response when making a decision. However, this assumption might be invalid or impracticable in practice. In this paper, we consider that the leader needs to locate a predetermined number of new facilities without knowing anything about the follower's response. By separating the scenarios in which the follower responds with different numbers of new facilities, a minimax regret model is proposed for the leader to minimise its maximum possible loss. Based on the structural characteristics of the proposed model, a set of solving procedures is provided that transforms the follower's nonlinear (fraction) programming model into a linear model. In the numerical experiments, the proposed model is compared with two other location models, a deterministic model and a risk model, and the efficiency of the linearisation in decreasing the computation time is verified. The results show that the proposed model is more applicable to the leader when there is no information about the number or probability distribution of the follower's new facilities. [ABSTRACT FROM AUTHOR]

This paper proposes that data envelopment analysis (DEA) should be viewed as a method (or tool) for data-oriented analytics in performance evaluation and benchmarking. While computational algorithms have been developed to deal with large volumes of data (decision making units, inputs, and outputs) under the conventional DEA, valuable information hidden in big data that are represented by network structures should be extracted by DEA. These network structures, e.g., transportation and logistics systems, encompass a broader range of inter-linked metrics that cannot be modelled by conventional DEA. It is proposed that network DEA is related to the value dimension of big data. It is shown that network DEA is different from standard DEA, although it bears the name of DEA and some similarity with conventional DEA. Network DEA is big data enabled analytics (big DEA) when multiple (performance) metrics or attributes are linked through network structures. These network structures are too large or complex to be dealt with by conventional DEA. Unlike conventional DEA that are solved via linear programming, general network DEA corresponds to nonconvex optimization problems. This represents opportunities for developing techniques for solving non-linear network DEA models. Areas such as transportation and logistics system as well as supply chains have a great potential to use network DEA in big data modeling. [ABSTRACT FROM AUTHOR]

Data envelopment analysis (DEA) strives to evaluate the production units under their best conditions. DEA flexibility in selecting the appropriate input/output weights always results in unreal and zero weights. Treating decision-making units (DMUs) as black-box regardless of their internal structures misleads the DEA performance evaluation. While considering units as a network process, it is more likely to identify more inefficiency sources. This paper suggests using a new common set of weights (CSWs) approach to evaluate the units in both black-box and two-stage structures based on a unified criterion. Indeed, our contribution to this line of research is as follows: Firstly, we improve the model proposed by Kao and Hung (J Oper res Soc 56(10): 1196–1203, 2005) to calculate the CSWs in a linear-based optimization model. Secondly, a new CSWs method is suggested in the two-stage network DEA (NDEA) as multiple objectives fractional programming (MOFP) problem. Thirdly, the MOFP problem is converted into a single objective linear programming problem in the two-stage network case. Finally, an enlightening application is presented. [ABSTRACT FROM AUTHOR]

This paper proposes mathematical programming models with probabilistic constraints in order to address incident response and resource allocation problems for the planning of traffic incident management operations. For the incident response planning, we use the concept of quality of service during a potential incident to give the decision-maker the flexibility to determine the optimal policy in response to various possible situations. An integer programming model with probabilistic constraints is also proposed to address the incident response problem with stochastic resource requirements at the sites of incidents. For the resource allocation planning, we introduce a mathematical model to determine the number of service vehicles allocated to each depot to meet the resource requirements of the incidents by taking into account the stochastic nature of the resource requirement and incident occurrence probabilities. A detailed case study for the incident resource allocation problem is included to demonstrate the use of proposed model in a real-world context. The paper concludes with a summary of results and recommendations for future research. [ABSTRACT FROM AUTHOR]

An appropriate and sustainable waste management plan is required in different scenarios for global development. The main goal of this paper is to evaluate a waste management problem by investigating an integrated multi-objective environment through solid transportation problem. To develop sustainability, three objective functions are optimized by choosing as cost for economical opportunity, time for social satisfaction and carbon emission for environmental view. Cap and trade policy is regarded here to minimize carbon emission and to provide some economical opportunities to the system. To control hesitancy of this scenario, twofold uncertainty (type-2 intuitionistic fuzzy) is incorporated here, and this uncertainty is defuzzified by a ranking operator. A strategy is proposed here to optimize three factors of sustainability by an intellectual model formulation of solid waste management. To check the appropriateness of the proposed model, two numerical problems are evaluated using two advanced methods, namely, neutrosophic linear programming and ϵ -constraint method. The Pareto-optimal solutions are derived by the variation of cap value and fulfilling the criteria of sustainability. The obtained results indicate that cap and trade policy or waste management, or both are highly sophisticated for applying in real-world application. The overall conclusions recommend that a government or NGO should encourage transportation system, or the industry to minimize carbon emission by utilizing several carbon policies. It can assist to establish different new project of waste management in a discrete environment, based on sustainability. [ABSTRACT FROM AUTHOR]

An introduction to reports discussed within the issue is presented, which include the theory and application of data envelopment analysis (DEA).

The aim of this paper is to propose a regression-based approach for obtaining a set of weights for multi-criteria ABC inventory analysis, which differ across classification criteria but are common across inventory items and follow a predetermined descending ordering scheme regarding the relative importance of classification criteria. The proposed alternative is based on the Inequality Constrained Least Squared model and is to be compared with the existing linear and non-linear programming models available in the literature. [ABSTRACT FROM AUTHOR]

One of the shortcomings in the standard data envelopment analysis (DEA) self-evaluation models is the flexibility of choosing favorable DEA weights on inputs and outputs. This study uses the potential of DEA cross-efficiency evaluation and proposes a new mean-variance goal programming model for minimizing the risk of changing DEA weights for identification of high performed decision making units. The applicability of the proposed method in this paper is demonstrated through an application in Oman fishery, to address peer-judgment risk in fisheries. The suggested model also provides a list of fishers with maximum cross-efficiency scores. [ABSTRACT FROM AUTHOR]

Efficient budget allocation between different communication channels is one of the fundamental activities of any media planner. In this paper, we attempt to develop a multi-objective integer linear programming model to determine the optimal schedule of advertisements for a set of multiple products of a firm in a segmented market (influenced by both mass and segment-specific media) over a planning horizon. The objectives are to maximize the gross impressions of advertisements and simultaneously minimize the advertising expenditure. To incorporate continuous changes that occur in the market, the total planning horizon is divided into shorter time periods and decisions for each of the subsequent time periods are taken, bearing in mind the changes that have occurred in the preceding time periods. Based on the gap that exists in the extant literature, we also jointly consider, in our model, the notions of (a) carry-over effect of gross impressions, (b) spectrum effect of mass media on segments, and (c) cross-product effect. The model is solved through a goal programming approach to achieve the best trade-off between the conflicting objectives. Further, the model could be adapted to provide solutions in a wide variety of real-life situations. This is substantiated via a numerical analysis for a firm that advertises products in the Indian market through mass and segment-specific media. [ABSTRACT FROM AUTHOR]

The authors in a previous paper devised certain subcones of the semidefinite plus nonnegative cone and showed that satisfaction of the requirements for membership of those subcones can be detected by solving linear optimization problems (LPs) with O(n) variables and O(n2) constraints. They also devised LP-based algorithms for testing copositivity using the subcones. In this paper, they investigate the properties of the subcones in more detail and explore larger subcones of the positive semidefinite plus nonnegative cone whose satisfaction of the requirements for membership can be detected by solving LPs. They introduce a semidefinite basis (SD basis) that is a basis of the space of n×n symmetric matrices consisting of n(n+1)/2 symmetric semidefinite matrices. Using the SD basis, they devise two new subcones for which detection can be done by solving LPs with O(n2) variables and O(n2) constraints. The new subcones are larger than the ones in the previous paper and inherit their nice properties. The authors also examine the efficiency of those subcones in numerical experiments. The results show that the subcones are promising for testing copositivity as a useful application. [ABSTRACT FROM AUTHOR]

In this paper we propose a two-phase approach to solve the shift and break design problem using integer linear programming. In the first phase we create the shifts, while heuristically taking the breaks into account. In the second phase we assign breaks to each occurrence of any shift, one by one, repeating this until no improvement is found. On a set of benchmark instances, composed by both randomly-generated and real-life ones, this approach obtains better results than the current best known method for shift and break design problem. [ABSTRACT FROM AUTHOR]