Showing papers in "Rairo-operations Research in 2012"

New algorithms for coupled tasks scheduling - a survey

Abstract: The coupled tasks scheduling problem is a class of scheduling problems introduced for beam steering software of sophisticated radar devices, called phased arrays. Due to increasing popularity of such radars, the importance of coupled tasks scheduling is constantly growing. Unfortunately, most of the coupled tasks problems are NP-hard, and only a few practically usable algorithms for such problems were found. This paper provides a survey of already known complexity results of various variants of coupled tasks problems. Then, it complements previous results by providing experimental results of two new polynomial algorithms for coupled tasks scheduling, which are: an exact algorithm for 1|(1,4,1),strictchains |C max problem, and a fast heuristic algorithm for more general 1|(1,2k, 1), strictchains |C max problem, where k ∈ ℕ.

A hybrid genetic algorithm for the vehicle routing problem with three-dimensional loading constraints

Abstract: This paper addresses a Three-Dimensional Loading Capacitated Vehicle Routing Problem (3L-CVRP) which combines a three-dimensional loading problem and vehicle routing problem in distribution logistics. The problem requires the combinatorial optimization of a feasible loading solution and a successive routing of vehicles to satisfy client demands, where all vehicles must start and terminate at a central depot. In spite of its clear practical significance in the real world of distribution management, 3L-CVRP in literature is very limited for its high combinatorial complexity. We solve this problem by a hybrid approach which combines Genetic Algorithm and Tabu Search (GATS). Genetic algorithm is developed for vehicle routing and tabu search for three-dimensional loading, while these two algorithms are integrated for the combinatorial problem. We computationally evaluate this hybrid genetic algorithm on all publicly available test instances, and obtain new best solutions for several instances.

M/M/1 retrial queue with collisions and working vacation interruption under N-policy

Abstract: Consider an M/M/1 retrial queue with collisions and working vacation interruption under N-policy. We use a quasi birth and death process to describe the considered system and derive a condition for the stability of the model. Using the matrix-analytic method, we obtain the stationary probability distribution and some performance measures. Furthermore, we prove the conditional stochastic decomposition for the queue length in the orbit. Finally, some numerical examples are presented.

Analysis of a MX/G(a,b)/1 queueing system with vacation interruption

Abstract: In this paper, a batch arrival general bulk service queueing system with interrupted vacation (secondary job) is considered. At a service completion epoch, if the server finds at least ‘a ’ customers waiting for service say ξ , he serves a batch of min (ξ , b) customers, where b ≥ a . On the other hand, if the queue length is at the most ‘a -1’, the server leaves for a secondary job (vacation) of random length. It is assumed that the secondary job is interrupted abruptly and the server resumes for primary service, if the queue size reaches ‘a ’, during the secondary job period. On completion of the secondary job, the server remains in the system (dormant period) until the queue length reaches ‘a ’. For the proposed model, the probability generating function of the steady state queue size distribution at an arbitrary time is obtained. Various performance measures are derived. A cost model for the queueing system is also developed. To optimize the cost, a numerical illustration is provided.

An analysis of supply chain decisions with asymmetrical retailers : effects of disruptions and static service cost on coordination mechanism

Abstract: The risk of demand or production cost disruption is one of the challenging problems in the supply chain management This paper explores a generalized supply chain game model incorporating the possible disruptions We find that a nonlinear Grove wholesale price scheme can fully coordinate such a supply chain even when both market demand and production cost are disrupted The nonlinear Grove wholesale price scheme has three sides to coordinate the decision behavior of the players One is that the mechanism can induce the retail pricing decided by the dominant retailer to be equal with that of the channel; the second is that the mechanism can induce fringe retailers to be not priced out of the market; the third is that the mechanism can ensure that the manufacturer uses minimum incentives to induce the dominant retailer to sell its product as well as providing the demand-stimulating service Disruptions from both demand side and production cost side may also affect the wholesale price, order quantity as well as retail price, and the share of the dominant retailer and the subsidy rate provided by the manufacturer are unity of opposites We also find that it is optimal for the manufacturer to keep the original production plan when the joint-disruption amount is sufficiently small

On a dual network exterior point simplex type algorithm and its computational behavior

Abstract: The minimum cost network flow problem, (MCNFP) con- stitutes a wide category of network flow problems. Recently a new dual network exterior point simplex algorithm (DNEPSA) for the MCNFP has been developed. This algorithm belongs to a special "exterior point simplex type" category. Similar to the classical dual network simplex al- gorithm (DNSA), this algorithm starts with a dual feasible tree-solution and after a number of iterations, it produces a solution that is both pri- mal and dual feasible, i.e. it is optimal. However, contrary to the DNSA, the new algorithm does not always maintain a dual feasible solution. Instead, it produces tree-solutions that can be infeasible for the dual problem and at the same time infeasible for the primal problem. In this paper, we present for the first time, the mathematical proof of cor- rectness of DNEPSA, a detailed comparative computational study of DNEPSA and DNSA on sparse and dense random problem instances, a statistical analysis of the experimental results, and finally some new results on the empirical complexity of DNEPSA. The analysis proves the superiority of DNEPSA compared to DNSA in terms of cpu time and iterations.

Metasearch information fusion using linear programming

Abstract: For a specific query merging the returned results from multiple search engines, in the form of a metasearch aggregation, can provide significant improvement in the quality of relevant documents. This paper suggests a minimax linear programming (LP) formulation for fusion of multiple search engines results. The paper proposes a weighting method to include the importance weights of the underlying search engines. This is a two-phase approach which in the first phase a new method for computing the importance weights of the search engines is introduced and in the second stage a minimax LP model for finding relevant search engines results is formulated. To evaluate the retrieval effectiveness of the suggested method, the 50 queries of the 2002 TREC Web track were utilized and submitted to three popular Web search engines called Ask, Bing and Google. The returned results were aggregated using two exiting approaches, three high-performance commercial Web metasearch engines and our proposed technique. The efficiency of the generated lists was measured using TREC-Style Average Precision (TSAP). The new findings demonstrate that the suggested model improved the quality of merging considerably

A polarized adaptive schedule generation scheme for the resource-constrained project scheduling problem

Abstract: This paper presents a hybrid schedule generation scheme for solving the resource-constrained project scheduling problem. The scheme, which is called the Polarized Adaptive Scheduling Scheme (PASS), can operate in a spectrum between two poles, namely the parallel and serial schedule generation schemes. A polarizer parameter in the range between zero and one indicates how similarly the PASS behaves like each of its two poles. The presented hybrid is incorporated into a novel genetic algorithm that never degenerates, resulting in an effective self-adaptive procedure. The key point of this genetic algorithm is the embedding of the polarizer parameter as a gene in the genomes used. Through this embedding, the procedure learns via monitoring its own performance and incorporates this knowledge in conducting the search process. The computational experiments indicate that the procedure can produce optimal solutions for a large percentage of benchmark instances. FullText for HTML: https://doi.org/10.1051/ro/2012006

Algorithms for the two dimensional bin packing problem with partial conflicts

Abstract: The two-dimensional bin packing problem is a well-known problem for which several exact and approximation methods were proposed. In real life applications, such as in Hazardous Material transportation, transported items may be partially incompatible, and have to be separated by a safety distance. This complication has not yet been considered in the literature. This paper introduces this extension called the two-dimensional bin packing problem with partial conflicts (2BPPC) which is a 2BP with distance constraints between given items to respect, if they are packed within a same bin. The problem is NP-hard since it generalizes the BP, already NP-hard. This study presents a mathematical model, two heuristics and a multi-start genetic algorithm for this new problem. FullText for HTML: https://doi.org/10.1051/ro/2012007

Aspects of Impatience in a Finite Buffer Queue

Abstract: In a multi server queuing system, buffer size is often larger than the number of servers. This necessitates queuing and waiting for some customers. Customers become impatient while waiting for service. Additionally, they may also become impatient if service is not offered at the desired rate. This paper analyses a finite buffer multi server queuing system with the additional restriction that customers may balk as well as renege. Closed form expressions of a number of performance measures are presented. A design problem is discussed to demonstrate the results derived.

Multiperiod supply chain network equilibrium model with electronic commerce and multicriteria decision-making

Abstract: In this paper, we develop a supply chain network equilibrium model in which electronic commerce in the presence of both B2B (business-to-business) and B2C (business-to-consumer) transactions, multiperiod decision-making and multicriteria decision-making are integrated. The model consists of three tiers of decision-makers (manufacturers, retailers and consumers at demand markets) who compete within a tier but may cooperate between tiers. Both manufacturers and retailers are concerned with maximization of profit as well as minimization of risk, whereas consumers take both the prices charged by manufacturers and retailers, along with the corresponding costs of transacting, in making their consumption decisions. Increasing relationship levels are assumed to decrease costs of transacting as well as risk costs. Establishing and maintaining these relationship levels incur some costs that have to be borne by the various decision-makers. We study the interaction among different tiers of decision-makers, describe their multicriteria decision-making behavior and derive the optimality conditions as well as the equilibrium conditions which are then shown to satisfy a finite-dimensional variational inequality problem. We then establish qualitative properties of the equilibrium model under some reasonable assumptions and illustrate the model with several numerical examples.

A study on the budget constrained facility location model considering inventory management cost

Abstract: One of the important issues on the distribution network design is to incorporate inventory management cost into the facility location model. This paper deals with a network model making the decisions on the facility location such as the number of DCs and their locations as well as the decisions on the inventory management such as the ordering quantity and the level of safety stock at each DC. The considered model differs from the previous works by classifying the related costs into the operating cost and the investment cost. For this model, a solution procedure based on the Lagrangian relaxation method was proposed and tested for its effectiveness with various numerical examples.

Flow Polyhedra and Resource Constrained Project Scheduling Problems

Abstract: This paper aims at describing the way Flow machinery may be used in order to deal with Resource Constrained Project Scheduling Problems (RCPSP). In order to do it, it first introduces the Timed Flow Polyhedron related to a RCPSP instance. Next it states several structural results related to connectivity and to cut management. It keeps on with a description of the way this framework gives rise to a generic Insertion operator, which enables programmers to design greedy and local search algorithms. It ends with numerical experiments.

A study of the dynamic of influence through differential equations

Abstract: The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative and important element of the model with respect to other studies of this influence framework is the introduction of weights reflecting the importance that one agent gives to the others. These importance weights can be positive, negative or equal to zero, which corresponds to the stimulation of the agent by the 'weighted' one, the inhibition, or the absence of relation between the two agents in question, respectively. The exhortation obtained by an agent is defined by the weighted sum of the opinions received by all agents, and the updating rule is based on the sign of the exhortation. The use of continuous variables permits the application of differential equations systems to the analysis of the convergence of agents' decisions in long-time. We study the dynamic of some influence functions introduced originally in the discrete model, e.g., the majority and guru influence functions, but the approach allows the study of new concepts, like e.g. the weighted majority function. In the dynamic framework, we describe necessary and sufficient conditions for an agent to be follower of a coalition, and for a set to be the boss set or the approval set of an agent. %

Tangency portfolios in the LP solvable portfolio selection models

Abstract: A risk measure in a portfolio selection problem is linear programming (LP) solvable, if it has a linear formulation when the asset returns are represented by discrete random variables, i.e. , they are defined by their realizations under specified scenarios. The efficient frontier corresponding to an LP solvable model is a piecewise linear curve. In this paper we describe a method which realizes and produces a tangency portfolio as a by-product during the procedure of tracing out of the efficient frontier of risky assets in an LP solvable model, when our portfolio contains some risky assets and a riskless asset, using nonsmooth optimization methods. We show that the test of finding the tangency portfolio can be limited only for two portfolios. Also, we describe that how this method can be employed to trace out the efficient frontier corresponding to a portfolio selection problem in the presence of a riskless asset.

Branch-and-bound algorithm for total weighted tardiness minimization on parallel machines under release dates assumptions

Abstract: This paper deals with the parallel-machine scheduling problem with the aim of minimizing the total (weighted) tardiness under the assumption of different release dates. This problem has been proven to be NP-hard. We introduce some new lower and upper bounds based on different approaches. We propose a branch-and-bound algorithm to solve the weighted and unweighted total tardiness. Computational experiments were performed on a large set of instances and the obtained results showed that our algorithms are efficient.

Interactive compromise hypersphere method and its applications

Abstract: The paper focuses on multi-criteria problems. It presents the interactive compromise hypersphere method with sensitivity analysis as a decision tool in multi-objective programming problems. The method is based on finding a hypersphere (in the criteria space) which is closest to the set of chosen nondominated solutions. The proposed modifications of the compromise hypersphere method are based on using various metrics and analyzing their influence on the original method. Applications of the proposed method are presented in four multi-criteria problems: the assignment problem, the knapsack problem, the project management problem and the manufacturing problem.

Scheduling in the presence of processor networks : complexity and approximation

Abstract: Dans cet article, nous etudions le probleme de la minimisation de la longueur de l'ordonnancement pour un systeme multi-processeur en presence de delais de communication. Le delai de communication entre deux tâches $i$ et $j$ depend de la distance entre les processeurs executant ces deux tâches. Un algorithme simple, de complexite polynomiale quand la longueur de l'ordonnancement est au plus deux (le probleme devient $\mathcal{NP}$-complet quand la longueur de l'ordonnancement est au plus trois) existe, voir \cite{lahlouthesis} pour ces deux resultats. Nous demontrons qu'il n'existe pas d'algorithme polynomial $\rho$-approche avec $\rho < 4/3$ sous l'hypothese que ${\cal{P}} eq {\cal{NP}}$ pour la minimisation de la longueur de l'ordonnancement dans le cas ou le reseau de processeurs admet pour topologie une chaine ou un anneau et le graphe de precedence est un graphe biparti de profondeur un. Nous avons egalement developpe deux algorithmes d'approximation avec des garanties de performance constantes pour les versions limitees et non limitees sur le nombre de processeurs.