Authors:John Martinovic; Markus Hähnel; Guntram Scheithauer; Waltenegus Dargie; Andreas Fischer Abstract: Based on an application in the field of server consolidation, we consider the one-dimensional cutting stock problem with nondeterministic item lengths. After a short introduction to the general topic we investigate the case of normally distributed item lengths in more detail. Within this framework, we present two lower bounds as well as two heuristics to obtain upper bounds, where the latter are either based on a related (ordinary) cutting stock problem or an adaptation of the first fit decreasing heuristic to the given stochastical context. For these approximation techniques, dominance relations are discussed, and theoretical performance results are stated. As a main contribution, we develop a characterization of feasible patterns by means of one linear and one quadratic inequality. Based on this, we derive two exact modeling approaches for the nondeterministic cutting stock problem, and provide results of numerical simulations. PubDate: 2018-07-18 DOI: 10.1007/s10288-018-0384-4

Authors:Johnny C. Ho; Ivar Massabò; Giuseppe Paletta; Alex J. Ruiz-Torres Abstract: This note proposes and analyzes a posterior tight worst-case bound for the longest processing time (LPT) heuristic for scheduling independent jobs on identical parallel machines with the objective of minimizing the makespan. It makes natural remarks on the well-known posterior worst-case bounds, and shows that the proposed bound can complement the well-known posterior bounds to synergistically achieve a better posterior worst-case bound for the LPT heuristic. Moreover, it gives some insight on LPT asymptotical optimality. PubDate: 2018-06-16 DOI: 10.1007/s10288-018-0381-7

Authors:Ramón Flores; Elisenda Molina; Juan Tejada Abstract: Following the original interpretation of the Shapley value as a priori evaluation of the prospects of a player in a multi-person interaction situation, we intend to apply the Shapley generalized value (introduced formally in Marichal et al. in Discrete Appl Math 155:26–43, 2007) as a tool for the assessment of a group of players that act as a unit in a coalitional game. We propose an alternative axiomatic characterization which does not use a direct formulation of the classical efficiency property. Relying on this valuation, we also analyze the profitability of a group. We motivate this use of the Shapley generalized value by means of two relevant applications in which it is used as an objective function by a decision maker who is trying to identify an optimal group of agents in a framework in which agents interact and the attained benefit can be modeled by means of a transferable utility game. PubDate: 2018-06-14 DOI: 10.1007/s10288-018-0380-8

Authors:Luciano Porretta; Daniele Catanzaro; Bjarni V. Halldórsson; Bernard Fortz Abstract: A point-interval \((I_v, p_v)\) is a pair constituted by an interval \(I_v\) of \({\mathbb {R}}\) and a point \(p_v \in I_v\) . A graph \(G=(V,E)\) is a Max-Point-Tolerance (MPT) graph if each vertex \(v\in V\) can be mapped to a point-interval in such a way that (u, v) is an edge of G iff \(I_u \cap I_v \supseteq \{p_u, p_v\}\) . MPT graphs constitute a superclass of interval graphs and naturally arise in genetic analysis as a way to represent specific relationships among DNA fragments extracted from a population of individuals. One of the most important applications of MPT graphs concerns the search for an association between major human diseases and chromosome regions from patients that exhibit loss of heterozygosity events. This task can be formulated as a minimum cost clique cover problem in a MPT graph and gives rise to a \({{\mathcal {N}}}{{\mathcal {P}}}\) -hard combinatorial optimization problem known in the literature as the Parsimonious Loss of Heterozygosity Problem (PLOHP). In this article, we investigate ways to speed up the best known exact solution algorithm for the PLOHP as well as techniques to enlarge the size of the instances that can be optimally solved. In particular, we present a Branch&Price algorithm for the PLOHP and we develop a number of preprocessing techniques and decomposition strategies to dramatically reduce the size of its instances. Computational experiments show that the proposed approach is 10–30 \(\times \) faster than previous approaches described in the literature, and suggest new directions for the development of future exact solution approaches that may prove of fundamental assistance in practice. PubDate: 2018-06-07 DOI: 10.1007/s10288-018-0377-3

Abstract: Support Vector Machine (SVM) is one of the most important class of machine learning models and algorithms, and has been successfully applied in various fields. Nonlinear optimization plays a crucial role in SVM methodology, both in defining the machine learning models and in designing convergent and efficient algorithms for large-scale training problems. In this paper we present the convex programming problems underlying SVM focusing on supervised binary classification. We analyze the most important and used optimization methods for SVM training problems, and we discuss how the properties of these problems can be incorporated in designing useful algorithms. PubDate: 2018-06-01 DOI: 10.1007/s10288-018-0378-2

Authors:Fayez F. Boctor; Marie-Claude Bolduc Abstract: To the best of our knowledge, this paper is the first one to suggest formulating the inventory replenishment problem as a bi-objective decision problem where, in addition to minimizing the sum of order and inventory holding costs, we should minimize the required storage space. Also, it develops two solution methods, called the exploratory method (EM) and the two-population evolutionary algorithm (TPEA), to solve the problem. The proposed methods generate a near-Pareto front of solutions with respect to the considered objectives. As the inventory replenishment problem have never been formulated as a bi-objective problem and as the literature does not provide any method to solve the considered bi-objective problem, we compared the results of the EM to three versions of the TPEA. The results obtained suggest that although the TPEA produces good near-Pareto solutions, the decision maker can apply a combination of both methods and choose among all the obtained solutions. PubDate: 2018-06-01 DOI: 10.1007/s10288-017-0362-2

Authors:Tran Van Su Abstract: This article presents necessary and sufficient optimality conditions for weakly efficient solution, Henig efficient solution, globally efficient solution and superefficient solution of vector equilibrium problem without constraints in terms of contingent derivatives in Banach spaces with stable functions. Using the steadiness and stability on a neighborhood of optimal point, necessary optimality conditions for efficient solutions are derived. Under suitable assumptions on generalized convexity, sufficient optimality conditions are established. Without assumptions on generalized convexity, a necessary and sufficient optimality condition for efficient solutions of unconstrained vector equilibrium problem is also given. Many examples to illustrate for the obtained results in the paper are derived as well. PubDate: 2018-06-01 DOI: 10.1007/s10288-017-0360-4

Authors:Hadi Charkhgard; Martin Savelsbergh; Masoud Talebian Abstract: We study the connection between biobjective mixed integer linear programming and normal form games with two players. We first investigate computing Nash equilibria of normal form games with two players using single-objective mixed integer linear programming. Then, we define the concept of efficient (Pareto optimal) Nash equilibria. This concept is precisely equivalent to the concept of efficient solutions in multi-objective optimization, where the solutions are Nash equilibria. We prove that the set of all points in the payoff (or objective) space of a normal form game with two players corresponding to the utilities of players in an efficient Nash equilibrium, the so-called nondominated Nash points, is finite. We demonstrate that biobjective mixed integer linear programming, where the utility of each player is an objective function, can be used to compute the set of nondominated Nash points. Finally, we illustrate how the nondominated Nash points can be used to determine the disagreement point of a bargaining problem. PubDate: 2018-06-01 DOI: 10.1007/s10288-017-0354-2

Authors:Mehmet Güray Güler Abstract: We consider a newsvendor that can increase the mean demand with advertising and reduce the variability in the demand by forecasting or market research. We analyze the problem under uniform and normal demand distributions. We also study the distribution-free case by using a lower bound on the newsvendor profit function. We show that when the budget is unlimited, the forecasting expenditure increases with the production cost until the cost of holding an inventory is equal to the cost of a lost sales. Although both expenditures increase with the product price, it turns out that the advertising expenditure is more important for the newsvendor: it allocates more to the advertising for products with higher prices if the budget is limited. It turns out that a newsvendor can benefit more from advertising (forecasting) if the market size (variability) is larger. Moreover, it is more profitable to allocate the expenditures into a single large market rather than allocating it to small segmented markets. The numerical studies show that the ability of forecasting makes a newsvendor more robust to the variance, i.e., the variability level is reduced significantly with the forecasting expenditure. PubDate: 2018-03-21 DOI: 10.1007/s10288-018-0374-6

Authors:Yves Crama; Michel Grabisch; Silvano Martello Abstract: This is the traditional triennial note used by the editors to give the readers of 4OR information on the state of the journal and its future. In the 3 years that have passed since the last editorial note (Liberti et al. in Q J Oper 13:1–13, 2015), three volumes (each containing four issues) of the journal have been published: vol. 13 (2015), vol. 14 (2016), and vol. 15 (2017). PubDate: 2018-02-26 DOI: 10.1007/s10288-018-0373-7