Authors:Marcin Anholcer; János Fülöp Pages: 57 - 74 Abstract: In several multiobjective decision problems Pairwise Comparison Matrices (PCM) are applied to evaluate the decision variants. The problem that arises very often is the inconsistency of a given PCM. In such a situation it is important to approximate the PCM with a consistent one. One of the approaches is to minimize the distance between the matrices, most often the Euclidean distance. In the paper we consider the problem of minimizing the maximum distance. After applying the logarithmic transformation we are able to formulate the obtained subproblem as a Shortest Path Problem and solve it more efficiently. We analyze the structure of the set of optimal solutions and prove some of its properties. This allows us to provide an iterative algorithm that results in a unique, Pareto-efficient solution. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2888-x Issue No:Vol. 274, No. 1-2 (2019)

Authors:Mor Armony; Efrat Perel; Nir Perel; Uri Yechiali Pages: 75 - 100 Abstract: Exact analysis of a multi-server Markovian queueing system with cross selling in steady-state is presented. Cross selling attempt is initiated at the end of a customer’s service every time the number of customers in the system is below a threshold. Both probability generating functions (PGFs) and matrix geometric methods are employed. The relation between the methods is revealed by explicitly calculating the entries of the matrix geometric rate-matrix R. Those entries are expressed in terms of the roots of a determinant of a matrix related to the set of linear equations involving the PGFs. This is a further step towards understanding of the analytical relationship between the two methods. Numerical results are presented, showing the effect of the cross selling intensity and of the threshold level on the systems performance measures. Finally, for a given set of parameters, the optimal threshold level is determined. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2924-x Issue No:Vol. 274, No. 1-2 (2019)

Authors:Frédéric Babonneau; Alain Haurie Pages: 101 - 117 Abstract: This paper deals with the modeling of power flow in a transmission grid within the multi-sectoral multi-energy long-term regional energy model ETEM-SG. This extension of the model allows a better representation of demand response for flexible loads triggered by nodal marginal cost pricing. To keep the global model in the realm of linear programming one uses a linearized DC power flow model that represents the transmission grid with the main constraints on the power flowing through the different arcs of the electricity transmission network. Robust optimization is used to take into account the uncertainty on the capacity limits resulting from inter-regional transit. A numerical illustration is carried out for a data set corresponding roughly to the Leman Arc region. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2920-1 Issue No:Vol. 274, No. 1-2 (2019)

Authors:Pascale Bendotti; Pierre Fouilhoux; Cécile Rottner Pages: 119 - 130 Abstract: This article analyzes how the Unit Commitment Problem (UCP) complexity evolves with respect to the number n of units and T of time periods. A classical reduction from the knapsack problem shows that the UCP is NP-hard in the ordinary sense even for \(T=1\) . The main result of this article is that the UCP is strongly NP-hard. When the constraints are restricted to minimum up and down times, the UCP is shown to be polynomial for a fixed n. When either a unitary cost or amount of power is considered, the UCP is polynomial for \(T=1\) and strongly NP-hard for arbitrary T. The pricing subproblem commonly used in a UCP decomposition scheme is also shown to be strongly NP-hard for a subset of units. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2827-x Issue No:Vol. 274, No. 1-2 (2019)

Authors:Gerardo Berbeglia; Gautam Rayaprolu; Adrian Vetta Pages: 131 - 154 Abstract: We study the dynamic pricing problem faced by a monopolistic retailer who sells a storable product to forward-looking consumers. In this framework, the two major pricing policies (or mechanisms) studied in the literature are the preannounced (commitment) pricing policy and the contingent (threat or history dependent) pricing policy. We analyse and compare these pricing policies in the setting where the good can be purchased along a finite time horizon in indivisible atomic quantities. First, we show that, given linear storage costs, the retailer can compute an optimal preannounced pricing policy in polynomial time by solving a dynamic program. Moreover, under such a policy, we show that consumers do not need to store units in order to anticipate price rises. Second, under the contingent pricing policy rather than the preannounced pricing mechanism, (i) prices could be lower, (ii) retailer revenues could be higher, and (iii) consumer surplus could be higher. This result is surprising, in that these three facts are in complete contrast to the case of a retailer selling divisible storable goods (Dudine et al. in Am Econ Rev 96(5):1706–1719, 2006). Third, we quantify exactly how much more profitable a contingent policy could be with respect to a preannounced policy. Specifically, for a market with N consumers, a contingent policy can produce a multiplicative factor of \(\Omega (\log N)\) more revenues than a preannounced policy, and this bound is tight. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2916-x Issue No:Vol. 274, No. 1-2 (2019)

Authors:Matteo Brunelli; Michele Fedrizzi Pages: 155 - 169 Abstract: We propose a unifying approach to the problem of measuring the inconsistency of judgments. More precisely, we define a general framework to allow several well-known inconsistency indices to be expressed as special cases of this new formulation. We consider inconsistency indices as aggregations of ‘local’, i.e. triple-based, inconsistencies. We show that few reasonable assumptions guarantee a set of good properties for the obtained general inconsistency index. Under this representation, we prove a property of Pareto efficiency and show that OWA functions and t-conorms are suitable aggregation functions of local inconsistencies. We argue that the flexibility of this proposal allows tuning of the index. For example, by using different types of OWA functions, the analyst can obtain the desired balance between an averaging behavior and a ‘largest inconsistency-focused’ behavior. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2936-6 Issue No:Vol. 274, No. 1-2 (2019)

Authors:Sara Ceschia; Nguyen Dang; Patrick De Causmaecker; Stefaan Haspeslagh; Andrea Schaerf Pages: 171 - 186 Abstract: This paper reports on the Second International Nurse Rostering Competition (INRC-II). Its contributions are (1) a new problem formulation which, differently from INRC-I, is a multi-stage procedure, (2) a competition environment that, as in INRC-I, will continue to serve as a growing testbed for search approaches to the INRC-II problem, and (3) final results of the competition. We discuss also the competition environment, which is an infrastructure including problem and instance definitions, testbeds, validation/simulation tools and rules. The hardness of the competition instances has been evaluated through the behaviour of our own solvers, and confirmed by the solvers of the participants. Finally, we discuss general issues about both nurse rostering problems and optimisation competitions in general. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2816-0 Issue No:Vol. 274, No. 1-2 (2019)

Authors:Morteza Davari; Erik Demeulemeester Pages: 187 - 210 Abstract: The proactive and reactive resource-constrained project scheduling problem (PR-RCPSP), that has been introduced recently (Davari and Demeulemeester, 2017), deals with activity duration uncertainty in a very unique way. The optimal solution to an instance of the PR-RCPSP is a proactive and reactive policy (PR-policy) that is a combination of a baseline schedule and a set of required transitions (reactions). In this research, we introduce two interesting classes of reactions, namely the class of selection-based reactions and the class of buffer-based reactions, the latter in fact being a subset of the class of selection-based reactions. We also discuss the theoretical relevance of these two classes of reactions. We run some computational results and report the contributions of the selection-based reactions and the buffer-based reactions in the optimal solution. The results suggest that although both selection-based reactions and buffer-based reactions contribute largely in the construction of the optimal PR-policy, the contribution of the buffer-based reactions is of much greater importance. These results also indicate that the contributions of non-selection-based reactions (reactions that are not selection-based) and selection-but-not-buffer-based reactions (selection-based reactions that are not buffer-based) are very limited. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2899-7 Issue No:Vol. 274, No. 1-2 (2019)

Authors:A. A. Elsadany; A. M. Awad Pages: 211 - 240 Abstract: This paper investigates the difference between price and quantity competition in a mixed duopoly game. We describe the behavior of a duopolistic Bertrand competition market with environmental taxes. There are two cases. In the first, the public firm is privatized and in the second, it is not privatized. In case I, private duopoly (postprivatization) where players use different production methods and choose their prices with (bounded rationality and naive). In case II, mixed duopoly (preprivatization) in this case there are two levels for the market including standard objective of the private firm is to maximize profits and including another objective function of the public firm namely “private welfare maximization”. We study numerically the dynamical behaviors of the models. The Nash equilibrium loses stability through a period-doubling bifurcation and the market in the end gets to be disordered. The disordered behavior of the market has been controlled by using feedback control method. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2837-8 Issue No:Vol. 274, No. 1-2 (2019)

Authors:Alexander Franz; Julia Rieck; Jürgen Zimmermann Pages: 241 - 265 Abstract: In this paper, we consider a long-term unit commitment problem with thermal and renewable energy sources, where system operating costs have to be minimized. The problem is enhanced by adding pumped storages, where water is stored in reservoirs, being turbinated or pumped up if it is beneficial in terms of reducing the operating costs. We present a tight mixed-integer linear programming model with a redefinition of decision variables and a reformulation of constraints, e.g., for the spinning reserve. The model serves as a basis for a new decomposition method, where fix-and-optimize schemes are used. In particular, a time-oriented, a unit-oriented, and a generic fix-and-optimize procedure are presented. A computational performance analysis shows that the mixed-integer linear model is efficient in supporting the solution process for small- and medium-scale instances. Furthermore, the fix-and-optimize procedures are able to tackle even large-scale instances. Particularly, problem instances with real-world energy demands, power plant-specific characteristics, and a one-year planning horizon with hourly time steps are solved to near-optimality in reasonable time. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2900-5 Issue No:Vol. 274, No. 1-2 (2019)

Authors:Kevin Granville; Steve Drekic Pages: 267 - 290 Abstract: This paper analyzes a 2-class, single-server polling model operating under a \(k_i\) -limited service discipline with class-dependent switchover times. Arrivals to each class are assumed to follow a Poisson process with phase-type distributed service times. Within each queue, customers are impatient and renege (i.e., abandon the queue) if the time before entry into service exceeds an exponentially distributed patience time. We model the queueing system as a level-dependent quasi-birth-and-death process, and the steady-state joint queue length distribution as well as the per-class waiting time distributions are computed via the use of matrix analytic techniques. The impacts of reneging and choice of service time distribution are investigated through a series of numerical experiments, with a particular focus on the determination of \((k_1,k_2)\) which minimizes a cost function involving the expected time a customer spends waiting in the queue and an additional penalty cost should reneging take place. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2915-y Issue No:Vol. 274, No. 1-2 (2019)

Authors:A. Hernández-Bastida; M. P. Fernández-Sánchez Pages: 291 - 308 Abstract: This paper presents an alternative method to estimate the mean and the variance when using the program evaluation and review technique (PERT). Different levels of information, provided by an expert, are considered in the PERT scenario to obtain the values of the mean and the variance by means of a maximum entropy distribution approach. In our opinion, the information to be taken into account should be only that supplied by the expert. We also perform a numerical analysis to examine how the estimates vary if new information is added. From this, we conclude that the inclusion of new information (even for analytic purposes) produces significant changes in the estimates proposed. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2857-4 Issue No:Vol. 274, No. 1-2 (2019)

Authors:Chandra K. Jaggi; Mamta Gupta; Amrina Kausar; Sunil Tiwari Pages: 309 - 329 Abstract: With the prevalence of network technologies, the world is shrinking and it is observed that the decision policies of the players of the supply chain go hand in hand. Thus the optimal replenishment decisions of retailers cannot be taken in isolation and need to be integrated with that of the supplier. This research work establishes a supplier-retailer supply chain in which demand for the products is displayed stock dependent. Nowadays, trade credit is also seen as prime source of short term financing, thus the retailer takes the benefit of permissible delay in payments from the supplier. The objective of the proposed model is to obtain the optimal decisions of the supply chain under three different policies- centralized, Supplier-led Stackelberg policy and Nash equilibrium solution. In this study, the influence of trade credit offered by the supplier, replenishment decisions and integration among the players of supply chain through different centralized and decentralized policies is analyzed for deteriorating items where retailer faces displayed stock dependent demand with two storage facilities. The model is best suitable for the emerging retail markets or supermarkets with limited shelf space displaying consumable items such as grocery, consumer goods, etc. The results have been validated with the help of a numerical example. Sensitivity analysis has also been performed to study the effect of various parameters on the optimal solution. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2925-9 Issue No:Vol. 274, No. 1-2 (2019)

Authors:Feng Li; Qingyuan Zhu; Liang Liang Pages: 347 - 372 Abstract: In many real applications, there exist situations where some independent and decentralized entities will construct a common platform for production processes. A natural and essential problem for the common platform is to allocate the fixed cost or common revenue across these entities in an equitable way. Since there is no powerful central decision maker, each decision-making unit (DMU) might propose an allocation scheme that will favor itself, giving itself a minimal cost and/or a maximal revenue. It is clear that such allocations are egoistic and unacceptable to all DMUs except for the distributing DMU. In this paper, we will address the fixed cost allocation problem in this decentralized environment. For this purpose, we suggest a non-egoistic principle which states that each DMU should propose its allocation proposal in such a way that the maximal cost would be allocated to itself. Further, a preferred allocation scheme should assign each DMU at most its non-egoistic allocation and lead to efficiency scores at least as high as the efficiency scores based on non-egoistic allocations. To this end, we integrate a goal programming method with data envelopment analysis methodology to propose a new model under a set of common weights. The final allocation scheme is determined in such a way that the efficiency scores are maximized for all DMUs through minimizing the total deviation to goal efficiencies. Finally, both a numerical example from prior literature and an empirical study of nine truck fleets are provided to demonstrate the proposed approach. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2819-x Issue No:Vol. 274, No. 1-2 (2019)

Authors:Yongjun Li; Feng Li; Ali Emrouznejad; Liang Liang; Qiwei Xie Pages: 373 - 394 Abstract: 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. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2860-9 Issue No:Vol. 274, No. 1-2 (2019)

Authors:Ambrose Lo; Zhaofeng Tang Pages: 395 - 423 Abstract: The notion of Pareto optimality is commonly employed to formulate decisions that reconcile the conflicting interests of multiple agents with possibly different risk preferences. In the context of a one-period reinsurance market comprising an insurer and a reinsurer, both of which perceive risk via distortion risk measures, also known as dual utilities, this article characterizes the set of Pareto-optimal reinsurance policies analytically and visualizes the insurer–reinsurer trade-off structure geometrically. The search of these policies is tackled by translating it mathematically into a functional minimization problem involving a weighted average of the insurer’s risk and the reinsurer’s risk. The resulting solutions not only cast light on the structure of the Pareto-optimal contracts, but also allow us to portray the resulting insurer–reinsurer Pareto frontier graphically. In addition to providing a pictorial manifestation of the compromise reached between the insurer and reinsurer, an enormous merit of developing the Pareto frontier is the considerable ease with which Pareto-optimal reinsurance policies can be constructed even in the presence of the insurer’s and reinsurer’s individual risk constraints. A strikingly simple graphical search of these constrained policies is performed in the special cases of Value-at-Risk and Tail Value-at-Risk. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2820-4 Issue No:Vol. 274, No. 1-2 (2019)

Authors:Frédéric Meunier; Thomas Pradeau Pages: 447 - 469 Abstract: We consider a non-atomic congestion game on a graph, with several classes of players. Each player wants to go from his origin vertex to his destination vertex at the minimum cost and all players of a given class share the same characteristics: cost functions on each arc, and origin–destination pair. Under some mild conditions, it is known that a Nash equilibrium exists, but the computation of such an equilibrium in the multiclass case is an open problem for general functions. We consider the specific case where the cost functions are affine. We show that this problem is polynomially solvable when the number of vertices and the number of classes are fixed. In particular, it shows that the parallel two-terminal case with a fixed number of classes is polynomially solvable. On a more practical side, we propose an extension of Lemke’s algorithm able to solve this problem. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2817-z Issue No:Vol. 274, No. 1-2 (2019)

Authors:Hashem Omrani; Khatereh Shafaat; Arash Alizadeh Pages: 471 - 499 Abstract: Transportation sector with the consumption of 25% of energy play a major role in Iranian economy. This sector produces 27% of total undesirable greenhouse gases in Iran which has directly harmful effects on the environment. Hence, performance assessment of energy efficiency of transportation sector is one of the most important issues for policy makers. In this paper, energy efficiency of transportation sector of 20 provinces in Iran is evaluated based on data envelopment analysis (DEA)—cooperative game approach. First, selected inputs and outputs are categorized into energy and non-energy inputs and desirable and undesirable outputs. Then, classical DEA model is applied to evaluate and rank the provinces. Since, the classical DEA model can’t distinguish between efficient provinces, so, this paper ranks the provinces based on combination of cross-efficiency DEA and cooperative game approaches. In the cooperative game theory, each province is considered as a player and the suitable characteristic function is defined for players. Finally, by calculating the Shapley value for each player, the final ranks of transportation sectors in provinces are concluded. The results indicate that some smaller provinces have better energy efficiency in transportation sector in comparison with big provinces. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2803-5 Issue No:Vol. 274, No. 1-2 (2019)

Authors:Sergio Ortobelli; Noureddine Kouaissah; Tomáš Tichý Pages: 501 - 530 Abstract: In this paper, we examine the use of conditional expectation, either to reduce the dimensionality of large-scale portfolio problems or to propose alternative reward–risk performance measures. In particular, we focus on two financial problems. In the first part, we discuss and examine correlation measures (based on a conditional expectation) used to approximate the returns in large-scale portfolio problems. Then, we compare the impact of alternative return approximation methodologies on the ex-post wealth of a classic portfolio strategy. In this context, we show that correlation measures that use the conditional expectation perform better than the classic measures do. Moreover, the correlation measure typically used for returns in the domain of attraction of a stable law works better than the classic Pearson correlation does. In the second part, we propose new performance measures based on a conditional expectation that take into account the heavy tails of the return distributions. Then, we examine portfolio strategies based on optimizing the proposed performance measures. In particular, we compare the ex-post wealth obtained from applying the portfolio strategies, which use alternative performance measures based on a conditional expectation. In doing so, we propose an alternative use of conditional expectation in various portfolio problems. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-2890-3 Issue No:Vol. 274, No. 1-2 (2019)

Authors:Shahaboddin Shamshirband; Mohammad Shojafar; A. A. Rahmani Hosseinabadi; Maryam Kardgar; M. H. N. Md. Nasir; Rodina Ahmad Pages: 555 - 555 Abstract: The Editor-in-Chief has retracted this article because validity of the content of this article cannot be verified. PubDate: 2019-03-01 DOI: 10.1007/s10479-018-3103-9 Issue No:Vol. 274, No. 1-2 (2019)