Comput Oper Res Research Articles

Efficient branch-and-bound algorithms for finding triangle-constrained 2-clubs

In the Vertex Triangle 2-Club problem, we are given an undirected graph G and aim to find a maximum-vertex subgraph of G that has diameter at most 2 and in which every vertex is contained in at least ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell $$\\end{document} triangles in the subgraph. So far, the only algorithm for solving Vertex Triangle 2-Club relies on an ILP formulation (Almeida and Brás in Comput Oper Res 111:258–270, 2019). In this work, we develop a combinatorial branch-and-bound algorithm that, coupled with a set of data reduction rules, outperforms the existing implementation and is able to find optimal solutions on sparse real-world graphs with more than 100,000 vertices in a few minutes. We also extend our algorithm to the Edge Triangle 2-Club problem where the triangle constraint is imposed on all edges of the subgraph.

An alternate approach to solve two-level hierarchical time minimization transportation problem

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.

A polyhedral study of event-based models for the resource-constrained project scheduling problem

In this paper, we study event-based mixed-integer programming (MIP) formulations for the resource-constrained project scheduling problem (RCPSP) that represent an alternative to the more common time-indexed model (DDT) (Pritsker et al. in Manag Sci 16(1):93–108, 1969; Christofides et al. in Eur J Oper Res 29(3):262–273, 1987) for the case when the scheduling horizon is large. In contrast to time-indexed models, the size of event-based models does not depend on the time horizon. For two event-based models OOE and SEE introduced by Koné et al. (Comput Oper Res 38(1):3–13, 2011), we first present new valid inequalities that strengthen the original formulation. Furthermore, we state a new event-based model, the Interval Event-Based Model (IEE), and deduce natural linear transformations between all three models. Those transformations yield the strict domination order IEE succ SEE succ OOE for their respective linear programming relaxations, meaning that the new IEE model has the strongest linear relaxation among all known event-based models. In addition, we show that DDT can be retrieved from IEE by subsequent expansion and projection of the underlying solution space. This yields a unified polyhedral view on a complete branch of MIP models for the RCPSP. Finally, we also compare the computational performance between all models on common test instances of the PSPLIB (Kolisch and Sprecher in Eur J Oper Res 96(1):205–216, 1997).

Mathematical modelling of a tollbooth system with two parallel skill-based servers and two vehicle types

This paper considers a tollbooth system with two parallel heterogeneous servers and two vehicle types (say, cars and trucks), where one server collects tolls from vehicles of both types and the other only serves one type of them. With such characteristic, the system is referred to as “skill-based servers” for brevity in this paper. Meanwhile, vehicles are accommodated in a single common lane and get served on the “global First-Come-First-Served” basis. In fact, such a system and its variants are commonly encountered and their performance measures are of great significance to managers. We first develop a Quasi-Birth-Death process to explicitly model this tollbooth system. Then by applying spectral expansion technique, we derive the stationary probabilities for the computation of the system’s performance measures, such as mean queue size and the idle probability of each server. The Laplace–Stieltjes transforms of an arbitrary vehicle’s sojourn time is derived as well. Finally, numerical results are presented to show the impact of parameters’ selection upon performance measures, and they have intriguing managerial implications. The results also reveal that the tollbooth system with skill-based servers is much more efficient compared to the system with dedicated servers, which has been studied by Melange et al. (Comput Oper Res 71:23–33, 2016), especially in rush hours.

Optimization of wireless sensor networks deployment with coverage and connectivity constraints

Wireless sensor networks have been widely deployed in the last decades to provide various services, like environmental monitoring or object tracking. Such a network is composed of a set of sensor nodes which are used to sense and transmit collected information to a base station. To achieve this goal, two properties have to be guaranteed: (i) the sensor nodes must be placed such that the whole environment of interest (represented by a set of targets) is covered, and (ii) every sensor node can transmit its data to the base station (through other sensor nodes). In this paper, we consider the Minimum Connected k-Coverage (MCkC) problem, where a positive integer $$k \ge 1$$ defines the coverage multiplicity of the targets. We propose two mathematical programming formulations for the MCkC problem on square grid graphs and random graphs. We compare them to a recent model proposed by Rebai et al. (Comput Oper Res 59:11–21, 2015). We use a standard mixed integer linear programming solver to solve several instances with different formulations. In our results, we point out the quality of the LP-bound of each formulation as well as the total CPU time or the proportion of solved instances to optimality within a given CPU time.

Discrete particle swarm optimization algorithms for two variants of the static data segment location problem

We consider the static data segment location problem in information networks. This problem was introduced by Sen et al. (Comput Oper Res, 62:282–295 2015). We consider the problem of optimally locating large volumes of digital content that is accessed via a distributed network. A database is pre-partitioned into multiple segments and the problem is one of placing these segments at servers located in different regions. We need to jointly consider four specific subproblems: (1) the problem of locating servers in the network, (2) the problem of allocating specific data segments to each of the servers, (3) the problem of assigning users to the servers based on their query patterns, and, (4) routing queries through the network. We consider two variants of this problem depending on the topology of the network through which the servers are connected: a mesh topology and a tree topology. In this paper, we develop a solution approach based on a discrete particle swarm optimization approach. We demonstrate the superiority of our approach by comparing its performance against solutions to benchmark instances obtained previously using a simulated annealing approach (Networks, 68(1):4–22 2016b).

Lawler’s minmax cost problem under uncertainty

The well-known \(O(n^2)\) minmax cost algorithm of Lawler (Manag Sci 19(5):544–546, 1973) was developed to minimize the maximum cost of jobs processed by a single machine under precedence constraints. We first develop a fast updating algorithm to obtain optimal solutions for two neighboring instances. This method will be used throughout this article. Then we consider job cost functions that depend on the completion time and on one or more additional numerical parameters. The parameters are uncertain and take values from given intervals. Under the uncertainty, we apply the minmax regret criterion for choosing a solution. We generalize results by Brauner et al. (J Sched, 2015) for decomposable cost functions with deterministic processing times and a single uncertain parameter to general cost functions. We describe different conditions, under which minmax regret solutions can be obtained with the time complexity \(O(n^3)\) or \(O(n^2)\). Then the updating algorithm is applied to the lateness model by Kasperski (Oper Res Lett 33:431–436, 2005) where both the processing time and the due date of each job are uncertain. The original \(O(n^4)\) running time is improved to the time complexity \(O(n^3)\). Finally, we extend the cost functions with a single uncertain parameter to those with a vector of additional uncertain parameters, improve one of the complexity results by Volgenant and Duin (Comput Oper Res 37:909–915, 2010) and solve some new problems.

New results on two-machine flow-shop scheduling with rejection

In this paper, we consider the off-line and on-line two-machine flow-shop scheduling problems with rejection. The objective is to minimize the sum of the makespan of accepted jobs and the total rejection penalty of rejected jobs. For the off-line version, Shabtay and Gasper (Comput Oper Res 39:1087---1096, 2012) showed that this problem is NP-hard and then provided a pseudo-polynomial-time algorithm, two 2-approximation algorithms and a fully polynomial-time approximation scheme. We further study some special cases in this paper. We show that this problem is still NP-hard even when all jobs have the same processing time on one of the machines or all jobs have the same rejection penalty. Furthermore, we also showed that this problem can be solved in polynomialtime algorithm when all jobs satisfy the agreeable condition on their processing times and rejection penalties. For the on-line version without rejection, Chen and Woeginger [in: Du DZ, Pardalos PM (eds.) Minimax and Applications, 1995] showed that the competitive ratio of any determined on-line algorithm is at least 2. We further show that the competitive ratio of any determined on-line algorithm is at least 2 even when all jobs have the same processing time on the first machine. Finally, for the on-line version with rejection, we present a class of on-line algorithms with the best-possible competitive ratio 2.

Analysis of assembly/disassembly queueing networks with blocking after service and general service times

In this paper, multi-stage assembly/disassembly (A/D) queueing networks are analyzed. We consider finite buffer capacities between the stations, generally distributed service times, and synchronization constraints at assembly and disassembly stations. We then describe a decomposition approach for the performance evaluation of such an (A/D) system, especially for the throughput and the variance of the inter-departure times. The two-station subsystems are analyzed as G/G/1/N stopped-arrival queueing systems. The virtual arrival and service rates, and the coefficients of variation are determined using a heuristic approach. A system of decomposition equations which is solved iteratively is presented. Any solution to this system of equations indicates estimated values for the subsystems’ unknown parameters. The quality of the presented approximation procedure is tested against the results of various simulation experiments. We consider A/D queueing networks with blocking. Our paper extends the work of Manitz (Comput Oper Res 35:2520–2536, 2008) by considering disassembly operations. In addition to that, we give the variability measures of the output process at every station. By considering general service times, it generalizes the work of Gershwin and Burman (Ann Oper Res 93:91–115, 2000). Station failures can be incorporated with the completion-time concept proposed by Gaver (J R Stat Soc 24:73–90, 1962). A comparison to various simulation results shows that the queueing-model based approach presented in this paper yields very good approximations of performance measures.

Iterated Local Search for single-machine scheduling with sequence-dependent setup times to minimize total weighted tardiness

We present an Iterated Local Search (ILS) algorithm for solving the single-machine scheduling problem with sequence-dependent setup times to minimize the total weighted tardiness. The proposed ILS algorithm exhibits several distinguishing features, including a new neighborhood structure called Block Move and a fast incremental evaluation technique, for evaluating neighborhood solutions. Applying the proposed algorithm to solve 120 public benchmark instances widely used in the literature, we achieve highly competitive results compared with a recently proposed exact algorithm and five sets of best solutions of state-of-the-art metaheuristic algorithms in the literature. Specifically, ILS obtains the optimal solutions for 113 instances within a reasonable time, and it outperforms the previous best-known results obtained by metaheuristic algorithms for 34 instances and matches the best results for 82 instances. In addition, ILS is able to obtain the optimal solutions for the remaining seven instances under a relaxed time limit, and its computational efficiency is comparable with the state-of-the-art exact algorithm by Tanaka and Araki (Comput Oper Res 40:344---352, 2013). Finally, on analyzing some important features that affect the performance of ILS, we ascertain the significance of the proposed Block Move neighborhood and the fast incremental evaluation technique.

A hybrid simulated annealing-tabu search algorithm for the part selection and machine loading problems in flexible manufacturing systems

Part selection and machine loading are two major problems in the production planning phase of the flexible manufacturing systems. The problems have a combinatorial structure and usually, in practice, it is difficult to deal with this kind of problems using a mathematical programming model. In this paper, the above problems are formulated as a mixed-integer programming model which is handled sequentially and solved by a diversification-strategy-added version of the hybrid tabu search/simulated annealing algorithm of Zhang et al. (Comput Oper Res 35:282–294, 2008) presented in 2008. The performance of the algorithm is tested on eight random-generated problems with different sizes. The results are compared with those of the mathematical programming model, the original version of Zhang et al.’s (Comput Oper Res 35:282–294, 2008) algorithm and also a tabu search algorithm developed earlier by the authors.

A new heuristic for minimizing total completion time objective in permutation flow shop scheduling

A constructive heuristic for the permutation flow shop scheduling problem with the objective of minimizing total completion time is proposed in this paper. It is constructed using a population-based technique and also the insertion rule similar to that presented in the Nawaz–Enscore–Ham (Omega 11:91–95, 1983) heuristic for the makespan criterion. We show, through computational results, that the proposed heuristic performs better than the heuristic of Woo and Yim (Comput Oper Res 25:175–182, 1998) for small and large problem sizes and the heuristic of Framinan and Leisten (Omega 31:311–317, 2003) for small and medium problem sizes. However, the relative performance of the heuristic of Framinan and Leisten improves compared to the proposed method when the job size increases. The time complexity of the proposed method has been shown to be less than those required by the existing heuristics. The average CPU time of the proposed heuristic is significantly less than the heuristic of Framinan and Leisten for large jobs.

Max–min fair survivable networks

In this paper, we discuss applications of max–min fairness (MMF) in survivable networks. We focus on two specific applications intended to face failure situations and provide several computational results for each of them. The first application, called simple robust routing, generalizes the multipath routing in order to achieve acceptable levels of traffic demand satisfaction in case of single link failures while avoiding classical rerouting procedures. Such a method can be seen as a special case of dedicated resource recovery schemes. The second application is concerned with two shared resource restoration strategies and the corresponding problems of computing the MMF minimum traffic demand satisfaction ratio vectors associated with the set of single link failures. We consider the local rerouting and end-to-end rerouting without stub-release strategies. Computational results for realistic network instances provide a comparison of different routing and rerouting strategies in terms of traffic satisfaction rate. The question of estimating the bandwidth overhead, which can be required by the “simple robust routing scheme” in comparison with the classical restoration schemes, is also studied and answers based on computational results are provided. This work is in continuation of our earlier works on MMF (Nace et al., IEEE Trans Netw 14:1272–1281, 2006; Nace et al., Comput Oper Res 35:557–573, 2008).

A heuristic technique for inventory replenishment policy with increasing demand pattern and shortage allowance

In the growth stage of a product life cycle, the demand rate is usually unstable and follows an increasing pattern. The traditional inventory policies, which have been developed for stationary demand pattern, are not appropriate to this situation. Although there exist some researches in the past dealing with inventory policy for the case of increasing demand pattern, most of them focused on the inventory systems in which shortages are not allowed. In reality, the presence of shortages is sometimes economically preferable when holding cost is significant as compared with shortage cost. The aim of the research presented in this paper is, therefore, to develop a replenishment policy for inventory systems with nonlinear increasing demand pattern and shortage allowance in such a way that the total demand during a predefined planning horizon can be exactly met. A heuristic technique to help determine the operational parameters for the inventory policy is then developed. In the proposed heuristic technique, the consecutive improvement method developed by Wang (Comput Oper Res, 29:1819–1825, 2002) will first be used to help determine replenishment times. And then, a new concept of reduction cost, which is defined as the difference between the holding cost when shortage is allowed and the incurred shortage cost, is introduced and applied to help find the optimal shortage starting point in each replenishment cycle. Numerical experiments are also conducted to illustrate the applicability of the proposed technique.

Two heuristics for the one-dimensional bin-packing problem

In this paper we have proposed two heuristics for the one-dimensional bin-packing problem. One is a hybrid steady-state grouping genetic algorithm, whereas the other is an improved version of Perturbation MBS’ heuristic (Fleszar and Hindi in Comput Oper Res 29:821–839, 2002). A combined approach using these two heuristics gives results which are comparable with the best methods known so far.

A scatter search approach for general flowshop scheduling problem

This paper proposes a new evolutionary technique called scatter search for scheduling problems of a general flow-shop. Scatter search (SS) is applied to this problem as it is able to provide a wide exploration of the search space through intensification and diversification. In addition it has a unifying principle for joining solutions which exploit the adaptive memory principle to avoid generating or incorporating duplicate solutions at various stages of the problem. This methodology provides substantially better results than the Tabu search approach of Nowicki and Smutnicki (Manage Sci 42(6):797–813, 1996) and Jain and Meeran (Comput Oper Res 29:1873–1901, 2002). The proposed framework achieves an average deviation of 14.25% from the lower bound solution of benchmark problems of Demirkol et al. (Eur J Oper Res 109(1):137–141, 1998), while the scatter search technique gives the best solutions for 32 of 40 of their benchmark problems.