一种新的交通网络设计优化算法

交通网络设计问题是研究如何用定量的方法在已有交通网络上添加或扩容某些路段的问题.文章在回顾交通网络设计问题文献的基础上,提出了基于图论网络优化思想的解决该类问题的一种新思路,给出了启发式算法,并进行了算法复杂性分析,最后通过算例验证了其有效性.     

Jointly pricing and ordering for a multi-product multi-constraint newsvendor problem with supplier quantity discounts

We present an extension to the multi-product newsvendor problem by incorporating the retailer’s pricing decision as well as considering supplier quantity discount. The objective is to maximize the expected profit of the retailer through jointly determining the ordering quantities and selling prices for the products, subject to multiple capacity constraints. We formulate the problem as a Generalized Disjunctive Programming (GDP) model and develop a Lagrangian heuristic approach for its solution. Randomly produced instances involving up to 1000 products are used to test the proposed approach. Computational results show that the Lagrangian heuristic approach can present very good solutions to all instances in reasonable time.     

A Lagrangean heuristic for the maximal covering location problem

We develop a Lagrangean heuristic for the maximal covering location problem. Upper bounds are given by a vertex addition and substitution heuristic and lower bounds are produced through a subgradient optimization algorithm. The procedure was tested in networks of up to 150 vertices. A duality gap was generally present at the end of the heuristic for the larger problems. The test problems were run in an IBM 3090-600J ‘super-computer’; the maximum computing time was kept below three minutes of CPU.     

A bi-objective turning restriction design problem in urban road networks

This paper introduces a bi-objective turning restriction design problem (BOTRDP), which aims to simultaneously improve network traffic efficiency and reduce environmental pollution by implementing turning restrictions at selected intersections. A bi-level programming model is proposed to formulate the BOTRDP. The upper level problem aims to minimize both the total system travel time (TSTT) and the cost of total vehicle emissions (CTVE) from the viewpoint of traffic managers, and the lower level problem depicts travelers’ route choice behavior based on stochastic user equilibrium (SUE) theory. The modified artificial bee colony (ABC) heuristic is developed to find Pareto optimal turning restriction strategies. Different from the traditional ABC heuristic, crossover operators are captured to enhance the performance of the heuristic. The computational experiments show that incorporating crossover operators into the ABC heuristic can indeed improve its performance and that the proposed heuristic significantly outperforms the non-dominated sorting genetic algorithm (NSGA) even if different operators are randomly chosen and used in the NSGA as in our proposed heuristic. The results also illustrate that a Pareto optimal turning restriction strategy can obviously reduce the TSTT and the CTVE when compared with those without implementing the strategy, and that the number of Pareto optimal turning restriction designs is smaller when the network is more congested but greater network efficiency and air quality improvement can be achieved. The results also demonstrate that traffic information provision does have an impact on the number of Pareto optimal turning restriction designs. These results should have important implications on traffic management.     

A single machine scheduling problem with availability constraints and sequence-dependent setup costs

We study a single machine scheduling problem with availability constraints and sequence-dependent setup costs, with the aim of minimizing the makespan. To the authors’ knowledge, this problem has not been treated as such in the operations research literature. We derive in this paper a mixed integer programming model to deal with such scheduling problem. Computational tests showed that commercial solvers are capable of solving only small instances of the problem. Therefore, we propose two ways for reducing the execution time, namely a valid inequality that strengthen the linear relaxation and an efficient heuristic procedure that provides a starting feasible solution to the solver. A substantial gain is achieved both in terms of the linear programming relaxation bound and in terms of the time to obtain an integer optimum when we use the enhanced model in conjunction with providing to the solver the solution obtained by the proposed heuristic.     

Furniture supply chain tactical planning optimization using a time decomposition approach

We study the supply chain tactical planning problem of an integrated furniture company located in the Province of Québec, Canada. The paper presents a mathematical model for tactical planning of a subset of the supply chain. The decisions concern procurement, inventory, outsourcing and demand allocation policies. The goal is to define manufacturing and logistics policies that will allow the furniture company to have a competitive level of service at minimum cost. We consider planning horizon of 1 year and the time periods are based on weeks. We assume that customer’s demand is known and dynamic over the planning horizon. Supply chain planning is formulated as a large mixed integer programming model. We developed a heuristic using a time decomposition approach in order to obtain good solutions within reasonable time limit for large size problems. Computational results of the heuristic are reported. We also present the quantitative and qualitative results of the application of the mathematical model to a real industrial case.     

Production scheduling with supply and delivery considerations to minimize the makespan

In this paper we study a scheduling model that simultaneously considers production scheduling, material supply, and product delivery. One vehicle with limited loading capacity transports unprocessed jobs from the supplier’s warehouse to the factory in a fixed travelling time. Another capacitated vehicle travels between the factory and the customer to deliver finished jobs to the customer. The objective is to minimize the arrival time of the last delivered job to the customer. We show that the problem is NP-hard in the strong sense, and propose an O(n) time heuristic with a tight performance bound of 2. We identify some polynomially solvable cases of the problem, and develop heuristics with better performance bounds for some special cases of the problem. Computational results show that all the heuristics are effective in producing optimal or near-optimal solutions quickly.     

Finding a minimum cost path between a pair of nodes in a time-varying road network with a congestion charge

The minimum cost path problem in a time-varying road network is a complicated problem. The paper proposes two heuristic methods to solve the minimum cost path problem between a pair of nodes with a time-varying road network and a congestion charge. The heuristic methods are compared with an alternative exact method using real traffic information. Also, the heuristic methods are tested in a benchmark dataset and a London road network dataset. The heuristic methods can achieve good solutions in a reasonable running time.     

The Feeder-bus Network-design Problem

The potential for improving the cost-effectiveness of public transport operations by designing better integrated feeder-bus/rail rapid transit systems has been widely recognized. This paper defines the feeder-bus network-design problem (FBNDP) as that of designing a feeder-bus network to access an existing rail system. The FBNDP is considered under two different demand patterns, many-to-one (M-to-1) and many-to-many (M-to-M). We present a mathematical programming model for the M-to-1 FBNDP, and show that it can be generalized to the M-to-M FBNDP. The FBNDP is a large and difficult vehicle-routeing-type problem with an additional decision variable—operating frequency. A heuristic model is presented, which generalizes the ‘savings approach’ to incorporate operating frequency. The computational analysis shows that the proposed heuristic provides reasonable feeder-bus networks and consistent responses to ‘what if’ questions. A comparison indicates that the proposed heuristic provides solutions that are superior to manually designed networks. The advantages of this heuristic are particularly significant under variable demand.     

Wavelength assignment for reducing in-band crosstalk attack propagation in optical networks: ILP formulations and heuristic algorithms

Today’s Transparent Optical Networks (TONs) are highly vulnerable to various physical-layer attacks, such as high-power jamming, which can cause severe service disruption or even service denial. The transparency of TONs enables certain attacks to propagate through the network, not only increasing their damage proportions, but also making source identification and attack localization more difficult. High-power jamming attacks causing in-band crosstalk in switches are amongst the most malicious of such attacks. In this paper, we propose a wavelength assignment scheme to reduce their damage assuming limited attack propagation capabilities. This complements our previous work in Furdek et al. (M. Furdek, N. Skorin-Kapov, M. Grbac, Attack-aware wavelength assignment for localization of in-band crosstalk attack propagation, IEEE/OSA Journal of Optical Communications and Networking 2 (11) (2010) 1000–1009) where we investigated infinite jamming attack propagation to find an upper bound on the network vulnerability to such attacks. Here, we consider a more realistic scenario where crosstalk attacks can spread only via primary and/or secondary attackers and define new objective criteria for wavelength assignment, called the PAR (Primary Attack Radius) and SAR (Secondary Attack Radius), accordingly. We formulate the problem variants as integer linear programs (ILPs) with the objectives of minimizing the PAR and SAR values. Due to the intractability of the ILP formulations, for larger instances we propose GRASP (Greedy Randomized Adaptive Search Procedure) heuristic algorithms to find suboptimal solutions in reasonable time. Results show that these approaches can obtain solutions using the same number of wavelengths as classical wavelength assignment, while significantly reducing jamming attack damage proportions in optical networks.     

A bicriteria flowshop scheduling with a learning effect

In many situations, a worker’s ability improves as a result of repeating the same or similar tasks; this phenomenon is known as the learning effect. In this paper the learning effect is considered in a two-machine flowshop. The objective is to find a sequence that minimizes a weighted sum of total completion time and makespan. Total completion time and makespan are widely used performance measures in scheduling literature. To solve this scheduling problem, an integer programming model with n² + 6n variables and 7n constraints where n is the number of jobs is formulated. Because of the lengthy computing time and high computing complexity of the integer programming model, the problem with up to 30 jobs can be solved. A heuristic algorithm and a tabu search based heuristic algorithm are presented to solve large size problems. Experimental results show that the proposed heuristic methods can solve this problem with up to 300 jobs rapidly. According to the best of our knowledge, no work exists on the bicriteria flowshop with a learning effect.     

Design of a distributed fiber transport network with hubbing topology

This paper deals with the comprehensive design of a distributed network, whose structure includes a large-scale fiber transport network where switching centers are interconnected via optical fiber cable. For real-world applicability, this design study covers in an integrated framework all three major decision sets: locating hub facilities, placing conduits and installing cables therein. The complex problem is formulated as a simple variant of the classical network design model by judiciously redefining commodity-Rows. Exploiting the special structure of the problem, a dual-based heuristic is then developed which yields near-optimal design plans. Computational experiments show that the performance of the proposed heuristic is satisfactory in both speed and the quality of the design solutions generated.     

A ring-mesh topology design problem for optical transport networks

This paper deals with a ring-mesh network design problem arising from the deployment of an optical transport network. The problem seeks to find an optimal clustering of traffic demands in the network such that the total cost of optical add-drop multiplexer (OADM) and optical cross-connect (OXC) is minimized, while satisfying the OADM ring capacity constraint, the node cardinality constraint, and the OXC capacity constraint. We formulate the problem as an integer programming model and propose several alternative modeling techniques designed to improve the mathematical representation of the problem. We then develop various classes of valid inequalities to tighten the mathematical formulation of the problem and describe an algorithmic approach that coordinates tailored routines with a commercial solver CPLEX. We also propose an effective tabu search procedure for finding a good feasible solution as well as for providing a good incumbent solution for the column generation based heuristic procedure that enhances the solvability of the problem. Computational results exhibit the viability of the proposed method.     

Solving a capacitated hub location problem

In this paper we address a problem consisting of determining the routes and the hubs to be used in order to send, at minimum cost, a set of commodities from sources to destinations in a given capacitated network. The capacities and costs of the arcs and hubs are given, and the arcs connecting the hubs are not assumed to create a complete graph. We present a mixed integer linear programming formulation and describe two branch-and-cut algorithms based on decomposition techniques. We evaluate and compare these algorithms on instances with up to 25 commodities and 10 potential hubs. One of the contributions of this paper is to show that a Double Benders’ Decomposition approach outperforms the standard Benders’ Decomposition, which has been widely used in recent articles on similar problems. For larger instances we propose a heuristic approach based on a linear programming relaxation of the mixed integer model. The heuristic turns out to be very effective and the results of our computational experiments show that near-optimal solutions can be derived rapidly.     

Optimal location of public health centres which provide free and paid services

A model and a heuristic are presented for finding the most effective location of public health centres providing non-vital services in competition with existing private health centres. While private centres provide only services to customers who can pay for them, public centres provide both paid services to affluent customers, and subsidised services to customers belonging to low-income groups (a hierarchical structure). While low-income customers are assigned to fixed public centres, high-income customers can choose which centre to patronise. To find the solution of this problem, the equilibrium between maximum coverage of low-income population (within a pre-specified distance), and an adequate capture of high-income population must be found. Thus, in the public service, the revenues obtained from paid services are used to partly cover the costs of the subsidised services, and the number of centres that can be located depends on how many high-income clients can be captured. Capture of a high-income client happens when a public centre is located closer to the client than any of the existing private centres. Computational experience with optimal, as well as special heuristic, methods for solving this problem is described.     

Mathematical programming models for revenue management under customer choice

We study a network airline revenue management problem with discrete customer choice behavior. We discuss a choice model based on the concept of preference orders, in which customers can be grouped according to a list of options in decreasing order of preference. If a customer’s preferred option is not available, the customer moves to the next choice on the list with some probability. If that option is not available, the customer moves to the third choice on the list with some probability, and so forth until either the customer has no other choice but to leave or his/her request is accepted. Using this choice model as an input, we propose some mathematical programs to determine seat allocations. We also propose a post-optimization heuristic to refine the allocation suggested by the optimization model. Simulation results are presented to illustrate the effectiveness of our method, including comparisons with other models.     

Heuristics for Multi-Stage Interdiction of Stochastic Networks

We describe and compare heuristic solution methods for a multi-stage stochastic network interdiction problem. The problem is to maximize the probability of sufficient disruption of the flow of information or goods in a network whose characteristics are not certain. In this formulation, interdiction subject to a budget constraint is followed by operation of the network, which is then followed by a second interdiction subject to a second budget constraint. Computational results demonstrate and compare the effectiveness of heuristic algorithms. This problem is interesting in that computing an objective function value requires tremendous effort. We exhibit classes of instances in our computational experiments where local search based on a transformation neighborhood is dominated by a constructive neighborhood.     

Scheduling in network flow shops

We consider the general problem of static scheduling of a set of jobs in a network flow shop. In network flow shops, the scheduler not only has to sequence and schedule but also must concurrently determine the process routing of the jobs through the shop. In this paper, we establish the computational complexity of this new class of scheduling problem and propose a general purpose heuristic procedure. The performance of the heuristic is analyzed when makespan, cycle time and average flow time are the desired objectives.This research has been supported by the UCLA Academic Senate Grant #95.     

Exact and heuristic methods for placing ships in locks

The ship placement problem constitutes a daily challenge for planners in tide river harbours. In essence, it entails positioning a set of ships into as few lock chambers as possible while satisfying a number of general and specific placement constraints. These constraints make the ship placement problem different from traditional 2D bin packing. A mathematical formulation for the problem is presented. In addition, a decomposition model is developed which allows for computing optimal solutions in a reasonable time. A multi-order best fit heuristic for the ship placement problem is introduced, and its performance is compared with that of the left-right-left-back heuristic. Experiments on simulated and real-life instances show that the multi-order best fit heuristic beats the other heuristics by a landslide, while maintaining comparable calculation times. Finally, the new heuristic’s optimality gap is small, while it clearly outperforms the exact approach with respect to calculation time.     

A cross entropy approach to design of reliable networks

One of the most important parameters determining the performance of communication networks is network reliability. The network reliability strongly depends on not only topological layout of the communication networks but also reliability and availability of the communication facilities. The selection of optimal network topology is an NP-hard problem so that computation time of enumeration-based methods grows exponentially with network size. This paper presents a new solution approach based on cross-entropy method, called NCE, to design of communication networks. The design problem is to find a network topology with minimum cost such that all-terminal reliability is not less than a given level of reliability. To investigate the effectiveness of the proposed NCE, comparisons with other heuristic approaches given in the literature for the design problem are carried out in a three-stage experimental study. Computational results show that NCE is an effective heuristic approach to design of reliable networks.