Showing papers in "Rairo-operations Research in 2015"
TL;DR: An advertising model in which goodwill affected by advertising effort has a positive effect on reference price and market demand is developed, and the relationships between system parameters and optimal solutions are analyzed.
Abstract: This paper develops an advertising model in which goodwill affected by advertising effort has a positive effect on reference price and market demand. In a finite planning horizon, the optimal advertising strategy is provided by solving the optimization problem on the basis of Pontryagin’s maximum principle, then the optimal sales price is obtained through one time pricing strategy. Furthermore, we extend this problem to an infinite planning horizon and present the corresponding optimal strategies. In addition, the relationships between system parameters and optimal solutions are analyzed. Numerical examples are employed to illustrate the effectiveness of the theoretical results, and to assess the sensitivity analysis of system parameters on the optimal strategies.
25 citations
TL;DR: In this paper, a new formulation is proposed for the dynamic berth allocation problem (DBAP), which was formulated as a non-linear mixed integer program, followed by incorporating techniques to present an equivalent mixedinteger program (MIP).
Abstract: International shipping is a multi-billion dollar business which has undergone significant growth during the last decade. Considerable benefits could be gained by improving and optimizing container terminal operations. One specific challenge facing container terminals is the berth allocation problem, referred to as (BAP). In this paper, a new formulation is proposed for the dynamic berth allocation problem (DBAP). Initially the problem was formulated as a non-linear mixed integer program, followed by incorporating techniques to present an equivalent mixed integer program (MIP). A genetic algorithm (GA) heuristic was developed and applied to different instances of the problems, and through computational experiments the best, average, and worst case performances were analyzed to determine the efficiency of the algorithms.
23 citations
TL;DR: A model based on goal programming and network data envelopment analysis (NDEA) enables decision makers to compare supply chains with predetermined goals.
Abstract: Today, one of the most important problems of decision makers in most organizations is to choose the best supply chain. The main objective of this paper is to choose the best supply chain. To select the best supply chain this paper presents a model based on goal programming and network data envelopment analysis (NDEA). The proposed model enables decision makers to compare supply chains with predetermined goals. A case study is presented to validate the proposed model.
21 citations
TL;DR: In this paper, an extension of the reverse Wagner/Whitin dynamic production planning and inventory control model, a Memetic Algorithm and a Hybrid Algorithm (HA) were proposed to minimize the holding, the set up and preparation costs.
Abstract: This paper deals with the production planning and control problem of a single product involving combined manufacturing and remanufacturing operations. We investigate here a lot-sizing problem in which the demand for items can be satisfied by both the new and the remanufactured products. We assume that produced and recovered items are of the same quality. Two types of inventories are involved in this problem. The produced items are stored in the first inventory. The returned products are collected in the second inventory and then remanufactured. The objective of this study is to propose a manufacturing/remanufacturing policy that would minimize the holding, the set up and preparation costs. The decision variables are the manufacturing and the remanufacturing rates. The paper proposes an extension of the reverse Wagner/Whitin dynamic production planning and inventory control model, a Memetic Algorithm (MA) and a Hybrid Algorithm (HA). The HA was improved with a post-optimization procedure using Path Relinking. Numerical experiments were conducted on a set of 300 instances with up to 48 periods. The results show that both methods give high-quality solutions in moderate computational time.
17 citations
TL;DR: Results demonstrate that the proposed multi-criteria model is an effective tool for generating a set of more realistic and flexible optimal solution in solving facility location- allocation problems.
Abstract: Facility location-allocation (FLA) decisions play a significant role in the performance of supply network in many practical applications, such as emergency service system, supply chain system, public service system, etc . In this paper, a multi-criteria model (including multi-attribute and multi-objective) for optimal and efficient facility location-allocation patterns was proposed. We first utilize multi attribute decision making (MADM) method–DEA to evaluate the relative efficiency of each potential location, and then combine the efficiency identified from DEA as a goal in a multi objective decision making (MODM) framework by using goal programming. A hypothetical example is presented to illustrate the effectiveness and the efficiency of the proposed model. Results demonstrate that the proposed multi-criteria model is an effective tool for generating a set of more realistic and flexible optimal solution in solving facility location- allocation problems by adjusting the goal priorities with respect to the importance of each objective and the aspiration level with respect to desired target values. The proposed model is also flexible and general enough to consider other specific location decisions such as emergency facilities, undesirable facilities and supply chain design by combing specific location modeling goal with the DEA model.
16 citations
TL;DR: A generalized version of Consistent Neighborhood Search is proposed, its performance according to various criteria is discussed, and successful adaptations of CNS to three types of satellite range scheduling problems are presented.
Abstract: Many optimization problems require the use of a local search to find a satisfying solution in a reasonable amount of time, even if the optimality is not guaranteed. Usually, local search algorithms operate in a search space which contains complete solutions (feasible or not) to the problem. In contrast, in Consistent Neighborhood Search (CNS), after each variable assignment, the conflicting variables are deleted to keep the partial solution feasible, and the search can stop when all the variables have a value. In this paper, we propose a generalized version of CNS, discuss its performance according to various criteria, and present successful adaptations of CNS to three types of satellite range scheduling problems. Such problems are motivated by applications encountered by the French National Space and Aeronautic Agencies and the US Air Force Satellite Control Network. The described numerical experiments will demonstrate that CNS is a powerful and flexible method, which can be easily combined with efficient ingredients.
14 citations
TL;DR: A new classification scheme for integrated staff rostering and job scheduling problems is introduced, extending existing schemes for project and machine scheduling.
Abstract: In the last decades job scheduling, staff rostering and staff assignment have received considerable attention, as have combinations of these problems. However, given the wide range of variants of all three basic problems, the number of combinations is immense. In this paper we introduce a new classification scheme for integrated staff rostering and job scheduling problems, extending existing schemes for project and machine scheduling. We provide some elementary reductions and show how problems studied in the literature fit into this new classification scheme. Furthermore, some complexity results are presented.
13 citations
TL;DR: A new polynomial-time approximation algorithm with worst-case performance guarantee O (log m), where m is the number of machines is presented, to find a non-preemptive schedule with the minimum makespan.
Abstract: We consider the routing open shop problem which is a generalization of the open shop and the metric travelling salesman problems. The jobs are located in some transportation network, and the machines travel on the network to execute the jobs in the open shop environment. The machines are initially located at the same node (depot) and must return to the depot after completing all jobs. The goal is to find a non-preemptive schedule with the minimum makespan. We present a new polynomial-time approximation algorithm with worst-case performance guarantee O (log m ), where m is the number of machines.
12 citations
TL;DR: A mathematical model is developed to jointly optimize the order quantity, time interval for any two successive price changes, and the corresponding prices for deteriorating products with price and ramp-type time dependent demand.
Abstract: In this paper, we investigate the problem of simultaneously determining the order quantity and optimal prices for deteriorating products with price and ramp-type time dependent demand. We assume that a retailer has the opportunity to adjust prices before the end of the sales season to increase demand, decrease deterioration, and improve revenues. A mathematical model is developed to jointly optimize the order quantity, time interval for any two successive price changes, and the corresponding prices. An algorithm is provided to find the optimal solution to the proposed model. Finally, we use a numerical example to verify the availability of this model.
11 citations
TL;DR: Two lead time demand (LTD) distribution approach are proposed in this paper, one with normally distributed demand and another with distribution free demand, and it is shown that the respective budget and storage space constrained inventory models to be minimized are jointly convex in the decision variables.
Abstract: Regarding today’s business environment restrictions, one of significant concern of inventory manager is to determine optimal policies of inventory/production systems under some restrictions such as budget and storage space. Therefore here, a budget constraint on total inventory investment and a maximum permissible storage space constraint are added simultaneously to a stochastic continuous review mixed backorder and lost sales inventory system. This study also assumes that the received lot may contain some defective units with a beta-binomial random variable. Two lead time demand (LTD) distribution approach are proposed in this paper, one with normally distributed demand and another with distribution free demand. For each approach, a Lagrange multiplier method is applied in order to solve the discussed constrained inventory models and a solution procedure is developed to find optimal values. This study, also, shows that the respective budget and storage space constrained inventory models to be minimized are jointly convex in the decision variables. Numerical examples are also presented to illustrate the models.
11 citations
TL;DR: In this article, the first known inapproximability result for the Graphic TSP on cubic and subcubic graphs was given. But this result was based on the (1, 2)-TSP.
Abstract: We prove explicit approximation hardness results for the Graphic TSP on cubic and subcubic graphs as well as the new inapproximability bounds for the corresponding instances of the (1,2)-TSP. The result on the Graphic TSP for cubic graphs is the first known inapproximability result on that problem. The proof technique in this paper uses new modular constructions of simulating gadgets for the restricted cubic and subcubic instances. The modular constructions used in the paper could be also of independent interest.
TL;DR: In this paper, a batch arrival single server retrial queue with modified vacations under N -policy is considered, and the probability generating function of the steady state queue size distribution at an arbitrary time is obtained.
Abstract: In this paper, a batch arrival single server retrial queue with modified vacations under N -policy is considered. If an arriving batch of customers finds the server busy or on vacation, then the entire batch joins the orbit in order to seek the service again. Otherwise, one customer from the arriving batch receives the service, while the rest joins the orbit. The customers in the orbit will try for service one by one when the server is idle with a classical retrial policy with the retrial rate ‘jv ’, where ‘j ’ is the size of the orbit. At a service completion epoch, if the number of customers in the orbit is zero, then the server leaves for a secondary job (vacation) of random length. At a vacation completion epoch, if the orbit size is at least N , then the server remains in the system to render service for the primary customers or orbital customers. On the other hand, if the number of customers in the orbit is less than ‘N ’ at a vacation completion epoch, the server avails multiple vacations subject to maximum ‘M ’ repeated vacations. After availing ‘M ’ consecutive vacations, the server returns to the system to render service irrespective of the orbit size. The model is studied using supplementary variable technique. For the proposed queueing system, 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 developed. Numerical illustration is provided.
TL;DR: A new notation and a new formalism are proposed to identify and to classify instances of routing problems to allow everyone to position his work accurately in the literature, and to easily identify approaches and results comparable to his research.
Abstract: Vehicle Routing Problems have been some of the most studied problems in combinatorial optimisation because they have many applications in transportation and supply chain. They are usually known as Vehicle Routing Problems or VRPs. The related literature is quite large and diverse both in terms of variants of the problems and in terms of solving approaches. To identify the different variants of routing problems, authors generally use initialisms, in which various prefixes and suffixes indicate the presence of different assumptions or constraints. But this identification based on initialisms is inefficient. For example, two variants of a problem may be identified by the same abbreviation, whereas different abbreviations may be assigned to the same problem. This paper proposes a new notation and a new formalism to identify and to classify instances of routing problems. This contribution aims at filling in the gaps of the current identification system. The goal is to allow everyone to position his work accurately in the literature, and to easily identify approaches and results comparable to his research. The proposed notation is inspired by the scheduling formalism. It has four fields (π /α /β /γ ), respectively describing the type and horizon of the problem, the system structure, resources and demands, constraints and objectives to be optimized. 26 papers from the literature chosen for their disparity are classified using this notation to illustrate its usefulness and a software tool is proposed to make its use easier.
TL;DR: These algorithms can be used to decode an unobserved hidden semi-Markov process and it is the first time that the complexity is achieved to be the same as in the Viterbi for Hidden Markov models, i.e .
Abstract: In this paper we present a new Viterbi algorithm for Hidden semi-Markov models and also a second algorithm which is a generalization of the first. These algorithms can be used to decode an unobserved hidden semi-Markov process and it is the first time that the complexity is achieved to be the same as in the Viterbi for Hidden Markov models, i.e . a linear function of the number of observations and quadratic function of the number of hidden states. An example in DNA Analysis is also given.
TL;DR: The proposed exact procedure makes use of components from the multi-objective exact method Parallel Partitioning Method, and Pareto-optimal fronts have been computed for two benchmark instances from the literature.
Abstract: In this work, we propose a procedure to compute Pareto-optimal fronts for the bi-objective Minimum Diameter-Cost Spanning Tree problem (bi-MDCST). The bi-MDCST aims at finding spanning trees with minimum total cost and minimum diameter. Strategic decision problems for high-speed trains infrastructure, as well as tactical and operational optimization problems for network design and transportation can be modeled as bi-MDCST. The proposed exact procedure makes use of components from the multi-objective exact method Parallel Partitioning Method, and Pareto-optimal fronts have been computed for two benchmark instances from the literature. To the best of our knowledge, there are no works dedicated to providing Pareto-optimal fronts for the bi-MDCST.
TL;DR: A mathematical model is proposed which is tested with randomly generated instances and proposes exams planning taking into account the assignment of material and human resources in the community over a given horizon planning.
Abstract: In France, the Hospital Community of Territory has been defined since the settlement of the pricing by activity (T2A) in 2004, and the new hospital governance. This new community allows the pool- ing of the hospital's human and material resources of any place in the same territory. It aims at increasing the continuity of health care. A Hospital Community of Territory is made up of several distinct places, material and human resources. A medical exam needs one human re- source and one material resource, both of them compatible with the exam. The objective is to create a decision aid tool which will plan the exams with the assignment of the human resources and the material resources. In this paper, we propose a mathematical model which is tested with randomly generated instances. It proposes exams planning taking into account the assignment of material and human resources in the community over a given horizon planning.
TL;DR: A divisible load model is proposed and an algorithm for scheduling multilayer divisible computations is given that is tested in a series of computational experiments and draws conclusions on schedule patterns and determinants of the performance.
Abstract: We analyze scheduling multilayer divisible computations. Multilayer computations consist of a chain of parallel applications, such that one application produces input for the next one. A simple form of multilayer computations are MapReduce parallel applications. The operations of mapping and reducing are two divisible applications with precedence constraints. We propose a divisible load model and give an algorithm for scheduling multilayer divisible computations. The algorithm is tested in a series of computational experiments. We draw conclusions on schedule patterns and determinants of the performance.
TL;DR: An algorithm is suggested to solve a multi objective Set Covering problem with fuzzy linear fractional functionals as the objectives and obtains the complete set of efficient cover solutions for this problem.
Abstract: The Set Covering problem is one the of most important NP-complete 0-1 integer programming problems because it serves as a model for many real world problems like the crew scheduling problem, facility location problem, vehicle routing etc. In this paper, an algorithm is suggested to solve a multi objective Set Covering problem with fuzzy linear fractional functionals as the objectives. The algorithm obtains the complete set of efficient cover solutions for this problem. It is based on the cutting plane approach, but employs a more generalized and a much deeper form of the Dantzig cut. The fuzziness in the problem lies in the coefficients of the objective functions. In addition, the ordering between two fuzzy numbers is based on the possibility and necessity indices introduced by Dubois and Prade [Ranking fuzzy numbers in the setting of possibility theory. Inf. Sci. 30 (1983) 183–224.]. Our aim is to develop a method which provides the decision maker with a fuzzy solution. An illustrative numerical example is elaborated to clarify the theory and the solution algorithm.
TL;DR: The objective is to plan a route with an emphasis on the time and cost involved in refueling vehicles, tailored to find optimal routes with minimal halts at the refueling stations.
Abstract: Route planning and goods distribution are a major component of any logistics. Vehicle Routing Problem is a class of problems addressing the issues of logistics. Vehicle Routing Problem with Limited Refueling Halts is introduced in this paper. The objective is to plan a route with an emphasis on the time and cost involved in refueling vehicles. The method is tailored to find optimal routes with minimal halts at the refueling stations. The problem is modeled as a bi objective optimization problem and is solved using particle swarm optimization. A new mutation operator called greedy mutation operator is introduced. Experiments are conducted with available data sets and MATLABR2011a is used for implementation.
TL;DR: Under such assumptions, applying the quasi-birth-and-death process and the matrix-analytical approach, the system state probabilities are derived and various steady-state system performance measures such as the availability and the rate of occurrence of failure are reported.
Abstract: This paper considers a k -out-of-n :G system with N -policy and one repairman who takes multiple vacations, in which the operating times and repair times of components are governed by exponential distributions. Once an operating component breaks down, it is repaired by a repair facility. Moreover, the repair facility is subject to failure during the repair period which results in repair interruptions. Failed repair facility resumes repair after a random period of time. Under such assumptions, applying the quasi-birth-and-death process and the matrix-analytical approach, the system state probabilities are derived. In addition, various steady-state system performance measures such as the availability and the rate of occurrence of failure along with some numerical illustrations are reported. Finally, under a profit structure, we use the direct search method and the parabolic method to search for the optimal system parameters.
TL;DR: This work considers a Markovian clearing queueing system with setup times, and obtains the balking strategies of customers, the stationary distribution of system state, the expected queue length and the social optimal benefit.
Abstract: We consider a Markovian clearing queueing system with setup times. When the system is empty, the server gets into the state of vacation. Once a new customer arrives the system, an exponential setup time is required before the server renders the service again. The customers are accumulated according to Poisson arrival process and the service times are exponentially distributed. Upon their arrivals, customers decide whether to join or balk the queue based on a natural linear reward-cost structure which reflects their desire for service and their unwillingness to wait. According to the state of server under some condition, we obtain the balking strategies of customers, the stationary distribution of system state, the expected queue length and the social optimal benefit. Finally, some numerical experiments describe how the expected queue length and the social optimal benefit depend on the arrival rate, the service time and the setup time.
TL;DR: This paper describes a method for scheduling trains on the Hunter Valley Coal Chain rail network, demonstrates that the problem is very large making it difficult to solve with commercial MILP solvers, and shows that the Lagrangian heuristic is able to produce high quality solutions in a reasonable time.
Abstract: This paper describes a method for scheduling trains on the Hunter Valley Coal Chain rail network. Coal for a particular ship is railed from different mines to stockpiles at one of the Port’s terminals. The coal producers decide which mines will supply each order in what proportion, so there is no flexibility in the allocation of mines to cargoes. We are presented with a list of tonnes of coal which need to be transported from specified load points at mines to specified stockpiles at the port. The operators of the rail network provide a number of paths, with specified arrival and departure times, that can be used for coal movement. The requirement to assign coal trains to these existing paths makes this rail scheduling problem different to most of those discussed in the literature. In this paper we describe the problem in detail, demonstrate that it is very large making it difficult to solve with commercial MILP solvers, and show that our Lagrangian heuristic is able to produce high quality solutions in a reasonable amount of time.
TL;DR: An implicit enumeration algorithm is proposed which computes a minimum wcis in a graph with n vertices with a running time O ∗ (1.4655n ) and polynomial space and results are given that show that the enumeration program solves the mwcis problem for graphs whose number of vertices is less than 120.
Abstract: Modeling topologies in Wireless Sensor Networks principally uses domination theory in graphs. Indeed, many dominating structures have been proposed as virtual backbones for wireless networks. In this paper, we study a dominating set that we call Weakly Connected Independent Set (wcis ). Given an undirected connected graph G = (V,E ), we say that an independent set S in G is weakly connected if the spanning subgraph (V, [ S,V \ S ]) is connected, where [ S,V \ S ] is the set of edges having exactly one end in S . The minimum weakly independent connected set problem consists in determining a wcis of minimum size in G . First, we discuss some complexity and approximation results for that problem. Then we propose an implicit enumeration algorithm which computes a minimum wcis in a graph with n vertices with a running time O ∗ (1.4655n ) and polynomial space. Processing results are given that show that our enumeration program solves the mwcis problem for graphs whose number of vertices is less than 120.
TL;DR: Defining three heuristic methods based on column generation techniques, this paper proposes reasonable solutions for the industry.
Abstract: In this paper, we formulate and solve a real life coal blending problem using a Column Generation Approach. The objective of the model is to prescribe optimal mixes of coal to produce coke. The problem is formulated as a mixed integer program. It involves various types of constraints arising from technical considerations of the blending process. The model also incorporates nonlinear constraints. It results in a large-scale problem that cannot be solved by classical operations research methods. Defining three heuristic methods based on column generation techniques, this paper proposes reasonable solutions for the industry.
TL;DR: In this article, the authors investigate classes of threshold functions which arise as intersections of the class of all threshold functions with clones of Boolean functions, and provide a complete classification of such intersections in respect to whether they have finite characterizations.
Abstract: The class of threshold functions is known to be characterizable by functional equations or, equivalently, by pairs of relations, which are called relational constraints. It was shown by Hellerstein that this class cannot be characterized by a finite number of such objects. In this paper, we investigate classes of threshold functions which arise as intersections of the class of all threshold functions with clones of Boolean functions, and provide a complete classification of such intersections in respect to whether they have finite characterizations. Moreover, we provide a characterizing set of relational constraints for each class of threshold functions arising in this way.
TL;DR: A novel supply chain model that consists of three layers of non-cooperative manufacturers, distribution centers and retailers is proposed that determines the best manufacturing rates and identifies the logistic bottlenecks in dynamic supply chain networks.
Abstract: In this paper, we present a logistics service provider (LSP) constrained supply chain problem, particularly; we propose a novel supply chain model that consists of three layers of non-cooperative manufacturers, distribution centers and retailers. Products flow from the manufacturers across different warehouses to retailers via LSP. Inventories at warehouses follow smooth and continuous replenishment policy, i.e. , perpetual review. The supply chain is represented as an optimization model that maximizes the revenue of manufacturers meets the retailers’ demand and at the same time identifies the necessary warehouses, particularly for supply chains that are affected by leadtime (LT) variation such as fast response industry and short life products. The model solution is adaptive; it determines the best manufacturing rates and identifies the logistic bottlenecks in dynamic supply chain networks. Numerical solutions along with simulation experiments of different supply chain topologies are presented. The simulation results demonstrate the model capability to maximize the revenues by tuning the manufacturing rates and monitoring the workinprocess, products in transit as well as products in inventories
TL;DR: New elimination rules and several polynomially solvable cases for the two-stage hybrid flow shop problem with dedicated machines are developed and a worst case analysis for several heuristics is proposed.
Abstract: In this paper we develop new elimination rules and discuss several polynomially solvable cases for the two-stage hybrid flow shop problem with dedicated machines. We also propose a worst case analysis for several heuristics. Furthermore, we point out and correct several errors in the paper of Yang [J. Yang, A two-stage hybrid flow shop with dedicated machines at the first stage. Comput. Oper. Res. 40 (2013) 2836−2843].
TL;DR: This paper proposes an exact algorithm for optimizing a linear fractional function over the efficient set of a Multiple Objective Integer Linear Programming ( MOILP ) problem without having to enumerate all the efficient solutions.
Abstract: Mathematical optimization problems with a goal function, have many applications in various fields like financial sectors, management sciences and economic applications. Therefore, it is very important to have a powerful tool to solve such problems when the main criterion is not linear, particularly fractional, a ratio of two affine functions. In this paper, we propose an exact algorithm for optimizing a linear fractional function over the efficient set of a Multiple Objective Integer Linear Programming (MOILP ) problem without having to enumerate all the efficient solutions. We iteratively add some constraints, that eliminate the undesirable (not interested) points and reduce, progressively, the admissible region. At each iteration, the solution is being evaluated at the reduced gradient cost vector and a new direction that improves the objective function is then defined. The algorithm was coded in MATLAB environment and tested over different instances randomly generated.
TL;DR: An algorithm based on subgradient method and convex hull computation for solving the problem of determining the position of an unknown point in a given convex set such that its longest distance to a set of finite number of points is shortest is presented.
Abstract: An important problem in distance geometry is of determining the position of an unknown point in a given convex set such that its longest distance to a set of finite number of points is shortest. In this paper we present an algorithm based on subgradient method and convex hull computation for solving this problem. A recent improvement of Quickhull algorithm for computing the convex hull of a finite set of planar points is applied to fasten up the computations in our numerical experiments.
TL;DR: This paper examines an M/G/1 retrial queueing system with multiple vacations and different arrival rates, and the steady state queue size distribution of number of customers in the retrial group, expected number ofcustoms in theretrial group and expected number in the system is obtained.
Abstract: This paper examines an M/G/1 retrial queueing system with multiple vacations and different arrival rates. Whenever the system is empty, the server immediately takes a vacation. At a vacation completion epoch, if the number of customers in the orbit is at least one the server remains in the system to activate service, otherwise the server avails multiple vacations until at least one customer is recorded in the orbit. The primary arrival rate is λ 1 when the server in idle and the primary arrival rate is λ 2 when the server is busy or on vacation (λ 1 > λ 2 ). The steady state queue size distribution of number of customers in the retrial group, expected number of customers in the retrial group and expected number of customers in the system are obtained. Some special cases are also discussed. Numerical illustrations are also provided.