Authors:Gaia Nicosia; Andrea Pacifici; Ulrich Pferschy Pages: 15 - 29 Abstract: In this work we address a class of deterministic scheduling problems in which k agents compete for the usage of a single machine. The agents have their own objective functions and submit their tasks in successive steps to an external coordination subject, who sequences them by selecting the shortest task in each step. We look at the problem in two different settings and consider different combinations of cost functions. In a centralized perspective, generalizing previous results for the case with \(k=2\) agents, we characterize the set of Pareto efficient solutions as for a classical multicriteria optimization problems. On one hand we determine the number of Pareto efficient solutions and on the other hand we study the computational complexity of the associated decision problem. Then, we consider the problem from a single agent perspective. In particular, we provide a worst-case analysis on the performance of two natural heuristic algorithms, SPT and WSPT, that suggest to an agent how to sequence its own tasks when its objective is makespan, sum of completion times, or sum of weighted completion times. PubDate: 2018-03-01 DOI: 10.1007/s10288-017-0341-7 Issue No:Vol. 16, No. 1 (2018)
Authors:Kris Boudt; Edgars Jakobsons; Steven Vanduffel Pages: 31 - 50 Abstract: Several problems in operations research, such as the assembly line crew scheduling problem and the k-partitioning problem can be cast as the problem of finding the intra-column rearrangement (permutation) of a matrix such that the row sums show minimum variability. A necessary condition for optimality of the rearranged matrix is that for every block containing one or more columns it must hold that its row sums are oppositely ordered to the row sums of the remaining columns. We propose the block rearrangement algorithm with variance equalization (BRAVE) as a suitable method to achieve this situation. It uses a carefully motivated heuristic—based on an idea of variance equalization—to find optimal blocks of columns and rearranges them. When applied to the number partitioning problem, we show that BRAVE outperforms the well-known greedy algorithm and the Karmarkar–Karp differencing algorithm. PubDate: 2018-03-01 DOI: 10.1007/s10288-017-0344-4 Issue No:Vol. 16, No. 1 (2018)
Authors:Anton Bondarev; Alfred Greiner Pages: 51 - 65 Abstract: In this paper we analyze an inter-temporal optimization problem of a representative firm that invests in horizontal and vertical innovations and that faces a constraint with respect to total R&D spending. We find that there can exist two different steady-states of the economy when the amount of research spending falls short of an endogenously determined threshold: one with higher productivities and less new technologies being developed, and the other with more technologies being created and lower productivities. But, for a higher amount of R&D spending the steady-state becomes unique and the firm produces the whole spectrum of available technologies. Thus, a lock-in effect may arise that, however, can be overcome by raising R&D spending sufficiently. PubDate: 2018-03-01 DOI: 10.1007/s10288-017-0348-0 Issue No:Vol. 16, No. 1 (2018)
Authors:Ching-Hui Tang Pages: 67 - 94 Abstract: In this study, we deal with the problem of short-term transportation outsourcing for transshipment centers. The carrier needs to determine the numbers of outsourced and self-run trips for the different types of transportation tasks. Stochastic demands which are likely to occur in actual operation are considered. Different trip numbers need to be determined in sequence, so a two-stage stochastic programming technique is applied to formulate the problem. Two models are developed based upon practical considerations to help determine the optimal transportation outsourcing plan. A case study regarding the operations of a logistics carrier in Taiwan is performed. Several tests are also performed considering the number of demand scenarios, optimality gaps, variations in demands, outsourcing cost variations, and problem dimensions in order to better understand the performance of the two models. PubDate: 2018-03-01 DOI: 10.1007/s10288-017-0355-1 Issue No:Vol. 16, No. 1 (2018)
Authors:Weidong Li; Qianna Cui Pages: 95 - 104 Abstract: In this paper, we study a vector scheduling problem with rejection on a single machine, in which each job is characterized by a d-dimension vector and a penalty, in the sense that, jobs can be either rejected by paying a certain penalty or assigned to the machine. The objective is to minimize the sum of the maximum load over all dimensions of the total vector of all accepted jobs, and the total penalty of rejected jobs. We prove that the problem is NP-hard and design two approximation algorithms running in polynomial time. When d is a fixed constant, we present a fully polynomial time approximation scheme. PubDate: 2018-03-01 DOI: 10.1007/s10288-017-0356-0 Issue No:Vol. 16, No. 1 (2018)
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
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