An integer-programming-based heuristic for the balanced loading problem

This paper presents an efficient heuristic algorithm for the one-dimensional loading problem in which the goal is to pack homogeneous blocks of given length and weight in a container in such a way that the center of gravity of the packed blocks is as close to a target point as possible. The proposed algorithm is based on the approximation of this problem as a knapsack problem. This algorithm has the same computational complexity but a better worst-case performance than the algorithm recently proposed by Amiouny et al. [Oper. Res. 40 (1992) 238]. Moreover, the computational results also show that, in general, it performs better on randomly generated problems.     

Computational experiments with a lazy version of a <Emphasis Type="Italic">K</Emphasis> quickest simple path ranking algorithm

The quickest path problem is related to the classical shortest path problem, but its objective function concerns the transmission time of a given amount of data throughout a path, which involves both cost and capacity. The K-quickest simple paths problem generalises the latter, by looking for a given number K of simple paths in non-decreasing order of transmission time. Two categories of algorithms are known for ranking simple paths according to the transmission time. One is the adaptation of deviation algorithms for ranking shortest simple paths (Pascoal et al. in Comput. Oper. Res. 32(3):509–520, 2005; Rosen et al. in Comput. Oper. Res. 18(6):571–584, 1991), and another is based on ranking shortest simple paths in a sequence of networks with fixed capacity lower bounds (Chen in Inf. Process. Lett. 50:89–92, 1994), and afterwards selecting the K quickest ones. After reviewing the quickest path and the K-quickest simple paths problems we describe a recent algorithm for ranking quickest simple paths (Pascoal et al. in Ann. Oper. Res. 147(1):5–21, 2006). This is a lazy version of Chen’s algorithm, able to interchange the calculation of new simple paths and the output of each k-quickest simple path. Finally, the described algorithm is computationally compared to its former version, as well as to deviation algorithms.      

New and efficient algorithms for transfer prices and inventory holding policies in two-enterprise supply chains

We consider a multi-period problem of fair transfer prices and inventory holding policies in two enterprise supply chains. This problem was formulated as a mixed integer non-linear program by Gjerdrum et al. (Eur J Oper Res 143:582–599, 2002). Existing global optimization methods to solve this problem are computationally expensive. We propose a continuous approach based on difference of convex functions (DC) programming and DC Algorithms (DCA) for solving this combinatorial optimization problem. The problem is first reformulated as a DC program via an exact penalty technique. Afterward, DCA, an efficient local approach in non-convex programming framework, is investigated to solve the resulting problem. For globally solving this problem, we investigate a combined DCA-Branch and Bound algorithm. DCA is applied to get lower bounds while upper bounds are computed from a relaxation problem. The numerical results on several test problems show that the proposed algorithms are efficient: DCA provides a good integer solution in a short CPU time although it works on a continuous domain, and the combined DCA-Branch and Bound finds an \(\epsilon \) -optimal solution for large-scale problems in a reasonable time.     

Metaheuristics with disposal facility positioning for the waste collection VRP with time windows

This paper improves heuristic algorithms presented in Benjamin and Beasley (Comput Oper Res 37(12):2270–2280, 2010) for solving the waste collection vehicle routing problem with time windows, particularly the real life waste collection benchmark problems from Kim et al. (Comput Oper Res 33(12):3624–3642, 2006). These consist of ten test problems, involving up to 2,092 customers and 19 waste disposal facilities. The main difference between this paper and Benjamin and Beasley (Comput Oper Res 37(12):2270–2280, 2010) is that here we use a disposal facility positioning (DFP) procedure to evaluate routes for our algorithms. Since the problem involves multiple disposal facilities, the objective of DFP is to choose the best disposal facilities to go on the vehicle route. Computational results indicate that our algorithms with DFP produce substantially better quality routes than previous approaches in the literature.     

A polynomial-time algorithm to find an equitable home-away assignment

We propose a polynomial-time algorithm to find an equitable home-away assignment for a given timetable of a round-robin tournament. Our results give an answer to a problem raised by Elf et al. (Oper. Res. Lett. 31 (2003) 343), which concerns the computational complexity of the break minimization problem in sports timetabling.     

Consistent extensions and subsolutions of the core for the multichoice transferable-utility games

Abstract

We extend the reduced games introduced by Davis and Maschler (Naval Res. Log. Q. 12:223–259, 1965) and Moulin (J. Econ. Theory. 36:120–148, 1985) to multichoice transferable-utility games. First, we provide an example to illustrate that the core proposed by van den Nouweland et al. (Math Methods Oper. Res. 41:289–311, 1995) violates related consistency properties. Further, we propose the minimal consistent extensions of the core and the maximal consistent subsolutions of the core. We also provide an axiomatization based on related consistency properties and its converse.     

Tower-of-sets analysis for the Kise–Ibaraki–Mine algorithm

Kise et al. (Oper. Res. 26:121–126, 1978) give an O(n ²) time algorithm to find an optimal schedule for the single-machine number of late jobs problem with agreeable job release dates and due dates. Li et al. (Oper. Res. 58:508–509, 2010a) point out that their proof of optimality for their algorithm is incorrect by giving a counter-example. In this paper, using the concept of “tower-of-sets” from Lawler (Math. Comput. Model. 20:91–106, 1994), we construct the tower-of-sets of the early job set generated by the algorithm. Then we give a correct proof of optimality for the algorithm and show a new result that the early job set by the algorithm obtains not only the maximum number of jobs but also the smallest total processing time among all optimal schedules. The result can be applied to study the problems of the hard real-time systems.     

The Shapley value for shortest path games: a non-graph-based approach

The shortest path games are considered in this paper. The transportation of a good in a network has costs and benefits. The problem is to divide the profit of the transportation among the players. Fragnelli et al. (Math Methods Oper Res 52: 251–264, 2000) introduce the class of shortest path games and show it coincides with the class of monotone games. They also give a characterization of the Shapley value on this class of games. In this paper we consider further five characterizations of the Shapley value (Hart and Mas-Colell’s in Econometrica 57:589–614, 1989; Shapley’s in Contributions to the theory of games II, annals of mathematics studies, vol 28. Princeton University Press, Princeton, pp 307–317, 1953; Young’s in Int J Game Theory 14:65–72, 1985, Chun’s in Games Econ Behav 45:119–130, 1989; van den Brink’s in Int J Game Theory 30:309–319, 2001 axiomatizations), and conclude that all the mentioned axiomatizations are valid for the shortest path games. Fragnelli et al. (Math Methods Oper Res 52:251–264, 2000)’s axioms are based on the graph behind the problem, in this paper we do not consider graph specific axioms, we take $TU$ axioms only, that is we consider all shortest path problems and we take the viewpoint of an abstract decision maker who focuses rather on the abstract problem than on the concrete situations.     

Several versions of the devour digest tidy-up heuristic for unconstrained binary quadratic problems

The unconstrained binary quadratic minimization problem is known to be NP-hard and due to its computational challenge and application capability, it becomes more and more considered and involved by the recent research studies, including both exact and heuristic solution approaches. Our work is in line with what was suggested by Glover et al. (in Eur. J. Oper. Res. 137, 272–287, 2002) who proposed one pass heuristics as alternatives to the well-known Devour Digest Tidy-up procedure (DDT) of Boros et al. (in RRR 39-89, 1989). The “devour” step sets a term of the current representation to 0 or 1, and the “tidy-up” step substitutes the logical consequences derived from the “digest” step into the current quadratic function. We propose several versions of the DDT constructive heuristic based on the alternative representation of the quadratic function. We also present an efficient implementation of local search using one-flip and two-flip moves that simultaneously change the values of one or two binary variables. Computational experiments performed on instances up to 7000 variables show the efficiency of our implementation in terms of quality improvement and CPU use enhancement.     

Numerical Evaluation of Dynamic Behavior of Ornstein–Uhlenbeck Processes Modified by Various Boundaries and its Application to Pricing Barrier Options

In financial engineering, one often encounters barrier options in which an action promised in the contract is taken if the underlying asset value becomes too high or too low. In order to compute the corresponding prices, it is necessary to capture the dynamic behavior of the associated stochastic process modified by boundaries. To the best knowledge of the authors, there is no algorithmic approach available to compute such prices repeatedly in a systematic manner. The purpose of this paper is to develop computational algorithms to capture the dynamic behavior of Ornstein-Uhlenbeck processes modified by various boundaries based on the Ehrenfest approximation approach established in Sumita et al. (J Oper Res Soc Jpn 49:256–278, 2006). As an application, we evaluate the prices of up-and-out call options maturing at time τ _M with strike price K _S written on a discount bond maturing at time T, demonstrating the usefulness, speed and accuracy of the proposed computational algorithms.     

Efficient model for interval goal programming with arbitrary penalty function

Penalty function is a key factor in interval goal programming (IGP), especially for decision makers weighing resources vis-à-vis goals. Many approaches (Chang et al. J Oper Res Soc 57:469–473, 2006; Chang and Lin Eur J Oper Res 199, 9–20, 2009; Jones et al. Omega 23, 41–48, 1995; Romero Eur J Oper Res 153, 675–686, 2004; Vitoriano and Romero J Oper Res Soc 50, 1280–1283, 1999)have been proposed for treating several types of penalty functions in the past several decades. The recent approach of Chang and Lin (Eur J Oper Res 199, 9–20, 2009) considers the S-shaped penalty function. Although there are many approaches cited in literature, all are complicated and inefficient. The current paper proposes a novel and concise uniform model to treat any arbitrary penalty function in IGP. The efficiency and usefulness of the proposed model are demonstrated in several numeric examples.     

A simple GAP-canceling algorithm for the generalized maximum flow problem

We give a simple primal algorithm for the generalized maximum flow problem that repeatedly finds and cancels generalized augmenting paths (GAPs). We use ideas of Wallacher (A generalization of the minimum-mean cycle selection rule in cycle canceling algorithms, 1991) to find GAPs that have a good trade-off between the gain of the GAP and the residual capacity of its arcs; our algorithm may be viewed as a special case of Wayne’s algorithm for the generalized minimum-cost circulation problem (Wayne in Math Oper Res 27:445–459, 2002). Most previous algorithms for the generalized maximum flow problem are dual-based; the few previous primal algorithms (including Wayne in Math Oper Res 27:445–459, 2002) require subroutines to test the feasibility of linear programs with two variables per inequality (TVPIs). We give an O(mn) time algorithm for finding negative-cost GAPs which can be used in place of the TVPI tester. This yields an algorithm with O(m log(mB/ε)) iterations of O(mn) time to compute an ε-optimal flow, or O(m ² log (mB)) iterations to compute an optimal flow, for an overall running time of O(m ³ nlog(mB)). The fastest known running time for this problem is , and is due to Radzik (Theor Comput Sci 312:75–97, 2004), building on earlier work of Goldfarb et al. (Math Oper Res 22:793–802, 1997). David P. Williamson is supported in part by an IBM Faculty Partnership Award and NSF grant CCF-0514628.     

Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs

The asymmetric travelling salesman problem with replenishment arcs (RATSP), arising from work related to aircraft routing, is a generalisation of the well-known ATSP. In this paper, we introduce a polynomial size mixed-integer linear programming (MILP) formulation for the RATSP, and improve an existing exponential size ILP formulation of Zhu [The aircraft rotation problem, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1994] by proposing two classes of stronger cuts. We present results that under certain conditions, these two classes of stronger cuts are facet-defining for the RATS polytope, and that ATSP facets can be lifted, to give RATSP facets. We implement our polyhedral findings and develop a Lagrangean relaxation (LR)-based branch-and-bound (BNB) algorithm for the RATSP, and compare this method with solving the polynomial size formulation using ILOG Cplex 9.0, using both randomly generated problems and aircraft routing problems. Finally we compare our methods with the existing method of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408-427]. It turns out that both of our methods are much faster than that of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408-427], and that the LR-based BNB method is more efficient for problems that resemble the aircraft rotation problems.     

A smoothing SAA method for a stochastic mathematical program with complementarity constraints

A smoothing sample average approximation (SAA) method based on the log-exponential function is proposed for solving a stochastic mathematical program with complementarity constraints (SMPCC) considered by Birbil et al. (S. I. Birbil, G. Gürkan, O. Listes: Solving stochastic mathematical programs with complementarity constraints using simulation, Math. Oper. Res. 31 (2006), 739–760). It is demonstrated that, under suitable conditions, the optimal solution of the smoothed SAA problem converges almost surely to that of the true problem as the sample size tends to infinity. Moreover, under a strong second-order sufficient condition for SMPCC, the almost sure convergence of Karash-Kuhn-Tucker points of the smoothed SAA problem is established by Robinson’s stability theory. Some preliminary numerical results are reported to show the efficiency of our method.     

On the convexity of step out–step in sequencing games

The main result of this paper is the convexity of step out–step in (SoSi) sequencing games, a class of relaxed sequencing games first analyzed by Musegaas et al. (Eur J Oper Res 246:894–906, 2015). The proof makes use of a polynomial time algorithm determining the value and an optimal processing order for an arbitrary coalition in a SoSi sequencing game. In particular, we use that in determining an optimal processing order of a coalition, the algorithm can start from the optimal processing order found for any subcoalition of smaller size and thus all information on such an optimal processing order can be used.     

A regularized point cloud registration approach for orthogonal transformations

An important part of the well-known iterative closest point algorithm (ICP) is the variational problem. Several variants of the variational problem are known, such as point-to-point, point-to-plane, generalized ICP, and normal ICP (NICP). This paper proposes a closed-form exact solution for orthogonal registration of point clouds based on the generalized point-to-point ICP algorithm. We use points and normal vectors to align 3D point clouds, while the common point-to-point approach uses only the coordinates of points. The paper also presents a closed-form approximate solution to the variational problem of the NICP. In addition, the paper introduces a regularization approach and proposes reliable algorithms for solving variational problems using closed-form solutions. The performance of the algorithms is compared with that of common algorithms for solving variational problems of the ICP algorithm. The proposed paper is significantly extended version of Makovetskii et al. (CCIS 1090, 217–231, 2019).

     

A linear-time algorithm for the bottleneck transportation problem with a fixed number of sources

We investigate a special case of the bottleneck transportation problem where the number s of sources is bounded by a constant and not part of the input. For the subcase s=2, a best-possible linear-time algorithm has been derived by Varadarajan [Oper. Res. Lett. 10 (1991) 525–529]. In this note we show that for any fixed number s⩾1, the bottleneck transportation problem with s sources can be solved in linear-time. The algorithm is conceptually simple, and easy to implement.     

Simulated annealing and genetic algorithms for minimizing mean flow time in an open shop

This paper considers the problem of scheduling n jobs on m machines in an open shop environment so that the sum of completion times or mean flow time becomes minimal. It continues recent work by Bräsel et al. [H. Bräsel, A. Herms, M. Mörig, T. Tautenhahn, T. Tusch, F. Werner, Heuristic constructive algorithms for open shop scheduling to minmize mean flow time, European J. Oper. Res., in press (doi.10.1016/j.ejor.2007.02.057)] on constructive algorithms. For this strongly NP-hard problem, we present two iterative algorithms, namely a simulated annealing and a genetic algorithm. For the simulated annealing algorithm, several neighborhoods are suggested and tested together with the control parameters of the algorithm. For the genetic algorithm, new genetic operators are suggested based on the representation of a solution by the rank matrix describing the job and machine orders. Extensive computational results are presented for problems with up to 50 jobs and 50 machines, respectively. The algorithms are compared relative to each other, and the quality of the results is also estimated partially by a lower bound for the corresponding preemptive open shop problem. For most of the problems, the genetic algorithm is superior when fixing the same number of 30 000 generated solutions for each algorithm. However, in contrast to makespan minimization problems, where the focus is on problems with an equal number of jobs and machines, it turns out that problems with a larger number of jobs than machines are the hardest problems.     

A type of efficient feasible SQP algorithms for inequality constrained optimization

In this paper, motivated by Zhu et al. methods [Z.B. Zhu, K.C. Zhang, J.B. Jian, An improved SQP algorithm for inequality constrained optimization, Math. Meth. Oper. Res. 58 (2003) 271-282; Zhibin Zhu, Jinbao Jian, An efficient feasible SQP algorithm for inequality constrained optimization, Nonlinear Anal. Real World Appl. 10(2) (2009) 1220-1228], we propose a type of efficient feasible SQP algorithms to solve nonlinear inequality constrained optimization problems. By solving only one QP subproblem with a subset of the constraints estimated as active, a class of revised feasible descent directions are generated per single iteration. These methods are implementable and globally convergent. We also prove that the algorithms have superlinear convergence rate under some mild conditions.     

Hybrid rounding techniques for knapsack problems

We address the classical knapsack problem and a variant in which an upper bound is imposed on the number of items that can be selected. We show that appropriate combinations of rounding techniques yield novel and more powerful ways of rounding. Moreover, we present a linear-storage polynomial time approximation scheme (PTAS) and a fully polynomial time approximation scheme (FPTAS) that compute an approximate solution, of any fixed accuracy, in linear time. These linear complexity bounds give a substantial improvement of the best previously known polynomial bounds [A. Caprara, et al., Approximation algorithms for knapsack problems with cardinality constraints, European J. Oper. Res. 123 (2000) 333-345].