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Abstract: Abstract This paper outlines a mathematical model to solve a scheduling problem for a company engineering and producing propellers to order. Nonås and Olsen (Comput Oper Res 32(9):2351–2382, 2005) have previously introduced a Mixed Integer Programming model for this production setting with the objective of minimizing the total tardiness. The mathematical model could however not be used to solve realistic sized problem instances, because of the very large solution time. We propose a new time indexed formulation that can solve most industrial problem instances in less than 10 min. This work is further extended by taking into account limited storage capacity and by proposing different methods to balance between total tardiness and maximum tardiness. We illustrate how the solution time and the criteria change for different setups of the mathematical model and suggest which setup to use for different scenarios. The paper also discusses how the new model can be extended to include unexpected events such as emergency orders and unavailable production equipment. PubDate: 2022-05-21
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Abstract: Matheuristics are heuristic algorithms based on mathematical tools such as the ones provided by mathematical programming, that are structurally general enough to be applied to different problems with little adaptations to their abstract structure. The result can be metaheuristic hybrids having components derived from the mathematical model of the problems of interest, but the mathematical techniques themselves can define general heuristic solution frameworks. In this paper, we focus our attention on mathematical programming and its contributions to developing effective heuristics. We briefly describe the mathematical tools available and then some matheuristic approaches, reporting some representative examples from the literature. We also take the opportunity to provide some ideas for possible future development. PubDate: 2022-05-09
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Abstract: Abstract Max–max, max–min, min–max and min–min optimization problems with a knapsack-type constraint containing a single numerical parameter are studied. The goal is to present optimal solutions for all possible values of the parameter. Algorithms with \(O(n\log n)\) and \(O(n^2)\) running times are proposed for the problems with a fixed parameter and for the general problem, respectively, where n is the number of items to be packed into the knapsack. The latter algorithm determines optimal solution values for all values of the parameter in \(O(n\log ^2 n)\) time. The problem of deciding whether there exists a single optimal solution for all values of the numerical parameter is proved to be NP-complete. PubDate: 2022-04-27
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Abstract: Abstract In this paper, for a robust nonsmooth semi-infinite objective optimization problem associated with data uncertainty, some constraint qualifications (CQs): Abadie CQ, Mangasarian-Fromovitz CQ, and Pshenichnyi-Levin-Valadire CQ are proposed. Sufficient conditions for them are also derived. Under these CQs, we establish both necessary and sufficient conditions for robust weak Pareto, Pareto, and Benson proper solutions. These conditions are the forms of Karush-Kuhn-Tucker rule. Moreover, the Wolfe and Mond-Weir duality schemes are also addressed. Finally, we employ the obtained results to present some conditions for linear programming. Examples are provided for analyzing and illustrating our results. PubDate: 2022-04-20
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Abstract: Abstract This work focuses on connectivity in a dynamic graph. An undirected graph is defined on a finite and discrete time interval. Edges can appear and disappear over time. The first objective of this work is to extend the notion of connected component to dynamic graphs in a new way. Persistent connected components are defined by their size, corresponding to the number of vertices, and their length, corresponding to the number of consecutive time steps they are present on. The second objective of this work is to develop an algorithm computing the largest, in terms of size and length, persistent connected components in a dynamic graph. PICCNIC algorithm (PersIstent Connected CompoNent InCremental Algorithm) is a polynomial time algorithm of minimal complexity. Another advantage of this algorithm is that it works online: knowing the evolution of the dynamic graph is not necessary to execute it. PICCNIC algorithm is implemented using the GraphStream library and experimented in order to carefully study the outcome of the algorithm according to different input graph types, as well as real data networks, to verify the theoretical complexity, and to confirm its feasibility for graphs of large size. PubDate: 2022-04-19
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Abstract: Abstract Multiple criteria sorting problem aims to assign objects evaluated on multiple criteria to ordered classes. In inverse multiple criteria sorting problem, the class assignments of objects are known and the decision maker can manipulate the scores of objects on criteria by implementing actions. Selected actions enable the improvement of objects’ final classification. As the decision maker chooses to implement more actions, better classifications may be obtained. The contribution of this paper is under two-folds. First, we decompose inverse multiple criteria sorting problem into two phases, where phase one is a pre-process that computes the minimum cost required for each feasible object-class pair considering the underlying sorting model. Phase two interacts with the decision maker to analyze the classification and budget related trade-offs, through an assignment model generated with the outputs of phase one. The second contribution is using a modified version of a regret-based approach available in the literature. This modification includes a tighter formulation of the regret model, and an interactive solution approach using a mixed integer program for computing the minimax regret value rather than a branch-and-bound approach. We present an example instance to illustrate the developed ideas and conduct computational tests on randomly generated instances. The simultaneous use of the decomposition approach, tighter formulation and the interactive algorithm reduces the computation time significantly. PubDate: 2022-04-07
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Abstract: A Correction to this paper has beed published: 10.1007/s10288-020-00442-1 PubDate: 2022-03-01 DOI: 10.1007/s10288-021-00479-w
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Abstract: Abstract It is common to report optimality gap values in the computational results section of papers related to the solution of optimization problems. Several years of refereeing experience have taught us that these gaps are often improperly defined or incorrectly computed. In this note, we offer some comments on this topic. PubDate: 2022-03-01 DOI: 10.1007/s10288-021-00483-0
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Abstract: Abstract This paper discusses a two-level hierarchical time minimization transportation problem, which is an important class of transportation problems arising in industries. This problem has been studied by various researchers (Sharma et al. in Eur J Oper Res 246:700–707, 2015; Sonia and Puri in TOP 12(2):301–330, 2004; Xie et al. in Comput Oper Res 86:124–139, 2017) and therefore, a number of polynomial time iterative algorithms are available to find its solution. All the existing algorithms, though efficient, have some shortcomings. The current study proposes an alternate solution algorithm for the problem that is more efficient in terms of computational time than the existing algorithms. The results justifying the underlying theory of the proposed algorithm are given. Further, a detailed comparison of the computational behaviour of all the algorithms for randomly generated instances of this problem, of different sizes validates the efficiency of the proposed algorithm. PubDate: 2022-03-01 DOI: 10.1007/s10288-020-00467-6
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Abstract: Abstract Multiple criteria decision aid methodologies support decision makers (DM) facing decisions involving conflicting objectives. DM’s preferences should be captured to provide meaningful recommendations. Preference elicitation aims at incorporating DM’s preferences in decision models. We propose a new preference elicitation tool for a ranking model based on reference points (RMP—Ranking with Multiple Profiles). Our methodology infers an RMP model from a list of pairwise comparisons provided by the DM. The inference algorithm makes use of a Mixed Integer mathematical programming formulation. We prove the applicability by performing extensive numerical experiments on datasets whose size corresponds to real-world problem. PubDate: 2022-03-01 DOI: 10.1007/s10288-020-00468-5
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Abstract: Abstract In this paper, we establish some quotient calculus rules in terms of contingent derivatives for the two extended-real-valued functions defined on a Banach space and study a nonsmooth multiobjective fractional programming problem with set, generalized inequality and equality constraints. We define a new parametric problem associated with these problem and introduce some concepts for the (local) weak minimizers to such problems. Some primal and dual necessary optimality conditions in terms of contingent derivatives for the local weak minimizers are provided. Under suitable assumptions, sufficient optimality conditions for the local weak minimizers which are very close to necessary optimality conditions are obtained. An application of the result for establishing three parametric, Mond–Weir and Wolfe dual problems and several various duality theorems for the same is presented. Some examples are also given for our findings. PubDate: 2022-03-01 DOI: 10.1007/s10288-020-00470-x
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Abstract: Abstract In this paper, we consider the (additive integrality) gap of the cutting stock problem (CSP) and the skiving stock problem (SSP). Formally, the gap is defined as the difference between the optimal values of the ILP and its LP relaxation. For both, the CSP and the SSP, this gap is known to be bounded by 2 if, for a given instance, the bin size is an integer multiple of any item size, hereinafter referred to as the divisible case. In recent years, some improvements of this upper bound have been proposed. More precisely, the constants 3/2 and 7/5 have been obtained for the SSP and the CSP, respectively, the latter of which has never been published in English language. In this article, we introduce two reduction strategies to significantly restrict the number of representative instances which have to be dealt with. Based on these observations, we derive the new and improved upper bound 4/3 for both problems under consideration. PubDate: 2022-03-01 DOI: 10.1007/s10288-020-00469-4
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Abstract: Abstract Even though sovereign bonds represent low-risk alternatives that give investors a healthy income, the risk assessment process for these bonds is still considered subjective because of the lack of criteria-related information and transparency of the methodologies used by international credit rating agencies. The 2007 economic crisis reflected the lack of clarity in procedures adopted by these agencies, although the financial sector was rigorously regulated. Intending to bring more transparency to the classification process, this paper presents the use of a methodology grounded in Rough Set Theory based on dominance, the Dominance-Based Rough Sets Approach (DRSA). This study takes related studies in the literature into consideration and seeks to show how the World Bank and credit rating agencies such as Standard & Poor's and Moody's can improve on how they tackle certain issues. Using the perspective obtained with DRSA, it was possible to verify the consistency of agencies' ratings and to induce rules for pattern recognition that can explain, using a set of non-redundant attributes, how the credit risk of sovereign bonds is classified. A significant rate of accuracy was obtained in the extrapolation using real data and the number of sovereign bonds analyzed was increased. Since this analysis only uses objective attributes, it was inferred that the absence of subjective attributes, i.e. political stability, provoke divergences in the results when compared to those provided by the credit rating agencies. PubDate: 2022-03-01 DOI: 10.1007/s10288-020-00471-w
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Abstract: Abstract Tower cranes are a key factor for both the operational and the economic success of large-scale construction projects. Cranes not only constitute a major position on the books, their role as the primary lifting equipment makes them a centerpiece of activities on the site as well. However, in contradiction to this and the considerable complexities of crane operations, decision support tools in the scientific literature are mostly limited to simulation-based sandbox tools or rather simplistic mathematical models. We address this issue by focusing on a crane selection and location planning problem which has been developed in a previous paper in cooperation with a partner from the construction industry. Loosely speaking, we consider a polygonal construction site with polygonal supply and demand areas located on it. Demand and supply areas have to be connected by selecting and locating cranes on-site. In doing so, both the areas’ specific lifting requirements and the cranes’ specifications such as lifting weight-dependent operating radius and operating height have to be respected. The goal is to minimize total crane-related costs while accounting for the cranes’ operating characteristics as well as interdependencies between cranes and on-site structures. In a previous paper, we have proven this problem to be NP-hard and have provided four mixed-integer programming formulations which have been computationally studied with standard solver CPLEX. In the current paper, we develop a simple, but competitive exact branch and bound approach that overcomes the limitations we encountered when employing CPLEX on our mixed-integer programs. PubDate: 2022-02-24 DOI: 10.1007/s10288-022-00503-7
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Abstract: Abstract Electre Tri is a set of methods designed to sort alternatives evaluated on several criteria into ordered categories. In these methods, alternatives are assigned to categories by comparing them with reference profiles that represent either the boundary or central elements of the category. The original Electre Tri-B method uses one limiting profile for separating a category from the category below. A more recent method, Electre Tri-nB, allows one to use several limiting profiles for the same purpose. We investigate the properties of Electre Tri-nB using a conjoint measurement framework. When the number of limiting profiles used to define each category is not restricted, Electre Tri-nB is easy to characterize axiomatically and is found to be equivalent to several other methods proposed in the literature. We extend this result in various directions. PubDate: 2022-02-21 DOI: 10.1007/s10288-022-00501-9
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Abstract: Abstract How to best deliver goods to consumers has been a logistics question since time immemorial. However, almost all traditional delivery models involved a form of company employees, whether employees of the company manufacturing the goods or whether employees of the company transporting the goods. With the growth of the gig economy, however, a new model not involving company employees has emerged: relying on crowdsourced delivery. Crowdsourced delivery involves enlisting individuals to deliver goods and interacting with these individuals using the internet. In crowdsourced delivery, the interaction with the individuals typically occurs through a platform. Importantly, the crowdsourced couriers are not employed by the platform and this has fundamentally changed the planning and execution of the delivery of goods: the delivery capacity is no longer under (full) control of the company managing the delivery. We present the challenges this introduces, review how the research community has proposed to handle some of these challenges, and elaborate on the challenges that have not yet been addressed. PubDate: 2022-01-21 DOI: 10.1007/s10288-021-00500-2
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