Integrated service network design for a cross-docking supply chain network

This paper considers an integrated service network design problem for a given set of freight demands that is concerned with integration of locating cross-docking (CD) centers and allocating vehicles for the associated direct (transportation) services from origin node to a CD center or from a CD center to the destination node. For the vehicle allocation, direct services (sub-routes) should be determined for the given freight demands, and then the vehicle allocation has to be made in consideration of routing for the associated direct service fulfillment subject to vehicle capacity and service time restriction. The problem is modeled as a path-based formulation for which a tabu-search-based solution algorithm is proposed. To guarantee the performance of the proposed solution algorithm, strong valid inequalities are derived based on the polyhedral characteristics of the problem domain and an efficient separation heuristic is derived for identifying any violated valid inequalities. Computational experiments are performed to test the performance of the proposed solution algorithm and also that of a valid-inequality separation algorithm, which finds that the solution algorithm works quite well and the separation algorithm provides strengthened lower bounds. Its immediate application may be made to strategic (integrated) service network designs and to tactical service network planning for the CD network.     

A simultaneous bus route design and frequency setting problem for Tin Shui Wai,Hong Kong

A bus network design problem for Tin Shui Wai, a suburban residential area in Hong Kong, is investigated, which considers the bus services from the origins inside this suburban area to the destinations in the urban areas. The problem aims to improve the existing bus services by reducing the number of transfers and the total travel time of the users. This has been achieved by the proposed integrated solution method which can solve the route design and frequency setting problems simultaneously. In the proposed solution method, a genetic algorithm, which tackles the route design problem, is hybridized with a neighborhood search heuristic, which tackles the frequency setting problem. A new solution representation scheme and specific genetic operators are developed so that the genetic algorithm can search all possible route structures, rather than selecting routes from the predefined set. To avoid premature convergence, a diversity control mechanism is incorporated in the solution method based on a new definition of hamming distance. To illustrate the robustness and quality of solutions obtained, computational experiments are performed based on 1000 perturbed demand matrices. The t-test results show that the design obtained by the proposed solution method is robust under demand uncertainty, and the design is better than both the current design and the design obtained by solving the route design problem and the frequency setting problem sequentially. Compared with the current bus network design, the proposed method can generate a design which can simultaneously reduce the number of transfers and total travel time at least by 20.9% and 22.7% respectively. Numerical studies are also performed to illustrate the effectiveness of the diversity control mechanism introduced and the effects of weights on the two objective values.     

Solving nonlinear bilevel programming models of the equilibrium network design problem: A comparative review

Nonlinear bilevel programming problems, of which the equilibrium network design problem is one, are extremely difficult to solve. Even if an optimum solution is obtained, there is no sure way of knowing whether the solution is the global optimum or not, due to the nonconvexity of the bilevel programming problem. This paper reviews and discusses recent developments in solution methodologies for nonlinear programming models of the equilibrium network design problem. In particular, it provides a primer for descent-type algorithms reported in the technical literature and proposes certain enhancements thereof.     

Impact analysis of maritime cabotage legislations on liner hub-and-spoke shipping network design

Maritime cabotage is a legislation published by a particular coastal country, which is used to conduct the cargo transportation between its two domestic ports. This paper proposes a two-phase mathematical programming model to formulate the liner hub-and-spoke shipping network design problem subject to the maritime cabotage legislations, i.e., the hub location and feeder allocation problem for phase I and the ship route design with ship fleet deployment problem for phase II. The problem in phase I is formulated as a mixed-integer linear programming model. By developing a hub port expanding technique, the problem in phase II is formulated as a vehicle routing problem with pickup and delivery. A Lagrangian relaxation based solution method is proposed to solve it. Numerical implementations based on the Asia–Europe–Oceania shipping services are carried out to account for the impact analysis of the maritime cabotage legislations on liner hub-and-spoke shipping network design problem.     

A Polynomial Time Approximation Scheme for the Grade of Service Steiner Minimum Tree Problem

In this paper, we present the design of a Polynomial Time Approximation Scheme (PTAS) for the Grade of Service Steiner Minimum Tree (GOSST) problem, which is known to be NP-Complete. Previous research has focused on geometric analyses and different approximation algorithms have been designed. We propose a PTAS that provides a polynomial time, near-optimal solution with performance ratio 1+. The GOSST problem has some important applications. In network design, a fundamental issue for the physical construction of a network structure is the interconnection of many communication sites with the best choice of the connecting lines and the best allocation of the transmission capacities over these lines. Good solutions should provide paths with enough communication capacities between any two sites, with the least network construction costs. Also, the GOSST problem has applications in transportation, for road constructions and some potential uses in CAD in terms of interconnecting the elements on a plane to provide enough flux between any two elements.     

A general MPCC model and its solution algorithm for continuous network design problem

This paper formulates the continuous network design problem as a mathematical program with complementarity constraints (MPCC), with the upper level a nonlinear programming problem and the lower level a nonlinear complementarity problem. Unlike in most previous studies, the proposed framework is more general, in which both symmetric and asymmetric user equilibria can be captured. By applying the complementarity slackness condition of the lower-level problem, the original bilevel formulation can be converted into a single-level and smooth nonlinear programming problem. In order to solve the problem, a relaxation scheme is applied by progressively restricting the complementarity condition, which has been proven to be a rigorous approach under certain conditions. The model and solution algorithm are tested for well-known network design problems and promising results are shown.     

Logistics distribution network design with two commodity categories

In this paper, we study the design of a logistics distribution network consisting of a supplier, a set of potential warehouses, and a set of retailers. There are commodities from two product categories, that is, category A and category B, flowing across the network. The demand for commodities in product category A is stable. The demand for commodities in product category B is highly uncertain. We show that the network design problem to distribute the commodities in both product categories can be formulated as the uncapacitated facility location problem with monotone submodular costs and tackled using a cutting plane algorithm. We propose a strongly polynomial time algorithm for the nonlinear discrete optimization problem, which must be solved in each iteration of the cutting plane algorithm. We also provide the computational results, and summarize the insights based on the proposed model and the solution algorithm.     

Designing WDM Optical Networks Using Branch-and-Price

In this paper, we present an exact solution procedure for the design of two-layer wavelength division multiplexing (WDM) optical networks with wavelength changers and bifurcated flows. This design problem closely resembles the traditional multicommodity flow problem, except that in the case of WDM optical networks, we are concerned with the routing of multiple commodities in two network layers. Consequently, the corresponding optimization models have to deal with two types of multicommodity variables defined for each of the network layers. The proposed procedure represents one of the first branch-and-price algorithms for a general WDM optical network setting with no assumptions on the number of logical links that can be established between nodes in the network. We apply our procedure in a computational study with four different network configurations. Our results show that for the three tested network configurations our branch-and-price algorithm provides solutions that are on average less than 5 % from optimality. We also provide a comparison of our branch-and-price algorithm with two simple variants of the upper bounding heuristic procedure HLDA that is commonly used for WDM optical network design.     

Survivable capacitated network design problem: new formulation and Lagrangean relaxation

This work is focused on the analysis of the survivable capacitated network design problem. This problem can be stated as follows: Given a supply network with point-to-point traffic demands, specific survivability requirements, a set of available capacity ranges and their corresponding discrete costs for each arc, find minimum cost capacity expansions such that these demands can be met even if a network component fails. Solving this problem consists of selecting the links and their capacity, as well as the routings for each demand in every failure situation. This type of problem can be shown to be NP-hard. A new linear mixed-integer mathematical programming formulation is presented. An effective solution procedure based on Lagrangean relaxation is developed. Comparison heuristics and improvement heuristics are also described. Computational results using these procedures on different sizes of randomly generated networks are reported.     

Bandwidth allocation and access control in high-speed networks

The problem of bandwidth allocation and access regulation arises in the congestion control of Broadband ISDN networks. This paper assumes that a single user, described by an on-off fluid model, is connected to the network via a leaky bucket access control mechanism. The bandwidth allocated to this user and the leaky bucket parameters are to be selected so as to guarantee a negotiated level of delay probability at the access point and packet loss probability in the network which is modelled as an output buffer. The design problem is to minimize the allocated bandwidth subject to service guarantees and stability conditions for the input and output buffers. We provide a desirable feasible solution to the design problem. The paper studies the effect of non-conforming users on the network performance using the leaky bucket access control corresponding to this feasible solution. We provide expressions that quantify the impact of the leaky bucket parameters in access regulation and the worst-case queueing behavior at the output buffer. Finally, we discuss the extension of this methodology to the multiple leaky buckets case.This research was supported in part by IBM Research Contract No. 1374.     

A capacity scaling heuristic for the multicommodity capacitated network design problem

In this paper, we propose a capacity scaling heuristic using a column generation and row generation technique to address the multicommodity capacitated network design problem. The capacity scaling heuristic is an approximate iterative solution method for capacitated network problems based on changing arc capacities, which depend on flow volumes on the arcs. By combining a column and row generation technique and a strong formulation including forcing constraints, this heuristic derives high quality results, and computational effort can be reduced considerably. The capacity scaling heuristic offers one of the best current results among approximate solution algorithms designed to address the multicommodity capacitated network design problem.     

Fast, Efficient Equipment Placement Heuristics for Broadband Switched or Internet Router Networks

Planning and designing the next generation of IP router or switched broadband networks seems a daunting challenge considering the many complex, interacting factors affecting the performance and cost of such networks. Generally, this complexity implies that it may not even be clear what constitutes a “good” network design for a particular specification. Different network owners or operators may view the same solution differently, depending on their unique needs and perspectives. Nevertheless, we have observed a core common issue arising in the early stages of network design efforts involving leading-edge broadband switched technologies such as ATM, Frame Relay, and SMDS; or even Internet IP router networks. This core issue can be stated as follows: Given a set of service demands for the various network nodes, where should switching or routing equipment be placed to minimize the Installed First Cost of the network? Note that the specified service demands are usually projections for a future scenario and generally entail significant uncertainty. Despite this uncertainty, we have found that network owners and operators generally feel it is worthwhile to obtain high-level advice on equipment placement with a goal of minimizing Installed First Cost. This paper reports on a heuristic approach we have implemented for this problem that has evolved out of real network design projects. A tool with both a Solution Engine and an intuitive Graphical User Interface has been developed. The approach is highly efficient; for example, the tool can often handle LATA-sized networks in seconds or less on a workstation processor. By using only nodal demands rather than the more complex point-to-point demands usually required in tools of this sort, we have created an approach that is not only highly efficient, but is also a better match to real design projects in which demand data is generally scant and highly uncertain.     

An exact solution procedure for a cluster hub location problem

This paper proposes a new (MIP) model formulation and a new solution procedure for the hub network design problem under a non-restrictive policy introduced by Sung and Jin [Sung, C.S., Jin, H.W., 2001. Dual-based approach for a hub network design problem under non-restrictive policy. European Journal of Operational Research 132 (1), 88–105]. The model formulation contains significantly fewer variables so that optimal solutions for the LP-relaxation of the model can be determined for large instances using standard procedures for LP-models. Furthermore, the LP-relaxation provides very tight lower bounds. Computational results are given, which demonstrate that the new model formulation allows for solving much larger instances. It turned out that the new (exact) solution procedure, which utilises the new model formulation, is faster than the heuristic proposed by Sung and Jin (2001). It is also shown that the problem is np-hard.     

An MPEC formulation and its cutting constraint algorithm for continuous network design problem with multi-user classes

Continuous network design problem (CNDP) is to determine the set of link capacity expansions and the corresponding equilibrium flows for which the measures of performance index for the network is optimal. Conventionally, CNDP assumed users to be homogeneous, that is, all travelers on the same link of the network are identical insofar as congestion effect and they have the same value of time (VOT). In fact, it does not accord with the real situation that all have the same VOT. So, multiple user classes with different VOT should be considered. This paper examines the CNDP with different VOT for multiple user classes, which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). Then, the cut constraint algorithm (CCA) is presented to solve the problem. The numerical experiments on the examples from the literature are illustrated to demonstrate that our model and algorithm are feasible.     

Optimal use of hub facilities: A two-hub model with fixed arc costs

Summary We introduce a model of a communication network design problem involving the utilization of hub facilities. That is, for a problem with two sets of customers and no intraset demand we seek to determine how the hub node associated with each set should be utilized. We assume that the only costs are the fixed costs associated with creating each of the three types of connecting arcs. A key parameter is the “group” size which is the number of communication circuits which can be bundled together in an arc. The optimal design depends strongly on how closely the arcs can be filled to capacity. The general demand problem is shown to be NP-Hard. However, for unit demand, we derive an almost “all or nothing” result which specifies that all flow should be direct node-to-node or, on the other hand, all or almost all flow should go via the hubs. Research supported in part by Grant SAB-94-0115 from the Spanish Interministerial Commission of Science and Technology while this author was on sabbatical leave at the Polytechnic University of Catalonia in Barcelona.     

Hop Constrained Network Design Problem with Partial Survivability

This paper studies the hop constrained network design problem with partial survivability, namely, given an undirected network, a set of point-to-point demands (commodities), and transmission link costs, identify two node disjoint paths for each demand (commodity) to minimize the total costs subject to the constraints that each demand is routed and traverses at most a specified number of links (or hops) on both the paths.A mathematical programming formulation of the problem is presented and an efficient solution procedure based on the linear programming relaxation is developed. Extensive computational results across a number of networks are reported. These results indicate that the solution procedure is effective for a wide range of problem sizes.     

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.     

Locating Active Sensors on Traffic Networks

Sensors are used to monitor traffic in networks. For example, in transportation networks, they may be used to measure traffic volumes on given arcs and paths of the network. This paper refers to an active sensor when it reads identifications of vehicles, including their routes in the network, that the vehicles actively provide when they use the network. On the other hand, the conventional inductance loop detectors are passive sensors that mostly count vehicles at points in a network to obtain traffic volumes (e.g., vehicles per hour) on a lane or road of the network.This paper introduces a new set of network location problems that determine where to locate active sensors in order to monitor or manage particular classes of identified traffic streams. In particular, it focuses on the development of two generic locational decision models for active sensors, which seek to answer these questions: (1) “How many and where should such sensors be located to obtain sufficient information on flow volumes on specified paths?”, and (2) “Given that the traffic management planners have already located count detectors on some network arcs, how many and where should active sensors be located to get the maximum information on flow volumes on specified paths?”The problem is formulated and analyzed for three different scenarios depending on whether there are already count detectors on arcs and if so, whether all the arcs or a fraction of them have them. Location of an active sensor results in a set of linear equations in path flow variables, whose solution provide the path flows. The general problem, which is related to the set-covering problem, is shown to be NP-Hard, but special cases are devised, where an arc may carry only two routes, that are shown to be polynomially solvable. New graph theoretic models and theorems are obtained for the latter cases, including the introduction of the generalized edge-covering by nodes problem on the path intersection graph for these special cases. An exact algorithm for the special cases and an approximate one for the general case are presented.     

Designing a two-echelon distribution network under demand uncertainty

This paper proposes a comprehensive methodology for the stochastic multi-period two-echelon distribution network design problem (2E-DDP) where product flows to ship-to-points are directed from an upper layer of primary warehouses to distribution platforms (DPs) before being transported to the ship-to-points. A temporal hierarchy characterizes the design level dealing with DP location and capacity decisions, as well as the operational level involving transportation decisions as origin-destination flows. These design decisions must be calibrated to minimize the expected distribution cost associated with the two-echelon transportation schema on this network under stochastic demand. We consider a multi-period planning horizon where demand varies dynamically from one planning period to the next. Thus, the design of the two-echelon distribution network under uncertain customer demand gives rise to a complex multi-stage decisional problem. Given the strategic structure of the problem, we introduce alternative modeling approaches based on two-stage stochastic programming with recourse. We solve the resulting models using a Benders decomposition approach. The size of the scenario set is tuned using the sample average approximation (SAA) approach. Then, a scenario-based evaluation procedure is introduced to post-evaluate the design solutions obtained. We conduct extensive computational experiments based on several types of instances to validate the proposed models and assess the efficiency of the solution approaches. The evaluation of the quality of the stochastic solution underlines the impact of uncertainty in the two-echelon distribution network design problem (2E-DDP).