Exact approaches for the directed network design problem with relays

We study the directed network design problem with relays (DNDPR) whose aim is to construct a minimum cost network that enables the communication of a given set of origin-destination pairs. Thereby, expensive signal regeneration devices need to be placed to cover communication distances exceeding a predefined threshold. Applications of the DNDPR arise in telecommunications and transportation. We propose two new integer programming formulations for the DNDPR. The first one is a flow-based formulation with a pseudo-polynomial number of variables and constraints and the second is a cut-based formulation with an exponential number of constraints. Fractional distance values are handled efficiently by augmenting both models with an exponentially-sized set of infeasible path constraints. We develop branch-and-cut algorithms and also consider valid inequalities to strengthen the obtained dual bounds and to speed up convergence. The results of our extensive computational study on diverse sets of benchmark instances show that our algorithms outperform the previous state-of-the-art method based on column generation.     

Models and algorithms for the design of survivable multicommodity flow networks with general failure scenarios

We consider the design of a multicommodity flow network, in which point-to-point demands are routed across the network subject to link capacity restrictions. Such a design must build enough capacity and diverse routing paths through the network to ensure that feasible multicommodity flows continue to exist, even when components of the network fail. In this paper, we examine several methodologies to optimally design a minimum-cost survivable network that continues to support a multicommodity flow under any of a given set of failure scenarios, where each failure scenario consists of the simultaneous failure of multiple arcs. We begin by providing a single extensive form mixed-integer programming formulation for this problem, along with a Benders decomposition algorithm as an alternative to the extensive form approach. We next investigate strategies to improve the performance of the algorithm by augmenting the master problem with several valid inequalities such as cover constraints, connectivity constraints, and path constraints. For the smallest instances (eight nodes, 10 origin–destination pairs, and 10 failure scenarios), the Benders implementation consumes only 10% of the time required by the mixed-integer programming formulation, and our best augmentation strategy reduces the solution time by another 50%. For medium- and large-sized instances, the extensive form problem fails to terminate within 2 h on any instance, while our decomposition algorithms provide optimal solutions on all but two problem instances.     

A Simulated Annealing Approach to Communication Network Design

This paper explores the use of the meta-heuristic search algorithm Simulated Annealing for solving a minimum cost network synthesis problem. This problem is a common one in the design of telecommunication networks. The formulation we use models a number of practical problems with hop-limit, degree and capacity constraints. Emphasis is placed on a new approach that uses a knapsack polytope to select amongst a number of pre-computed traffic routes in order to synthesise the network. The advantage of this approach is that a subset of the best routes can be used instead of the whole set, thereby making the process of designing large networks practicable. Using simulated annealing, we solve moderately large networks (up to 30 nodes) efficiently.     

Exact approaches for the pickup and delivery problem with loading cost

In this paper, we propose a branch-and-cut algorithm and a branch-and-price algorithm to solve the pickup and delivery problem with loading cost (PDPLC), which is a new problem derived from the classic pickup and delivery problem (PDP) by considering the loading cost in the objective function. Applications of the PDPLC arise in healthcare transportation where the objective function is customer-centric or service-based. In the branch-and-price algorithm, we devise an ad hoc label-setting algorithm to solve the pricing problem and employ the bounded bidirectional search strategy to accelerate the label-setting algorithm. The proposed algorithms were tested on a set of instances generated by a common data generator in the literature. The computational results showed that the branch-and-price algorithm outperformed the branch-and-cut algorithm by a large margin, and can solve instances with 40 requests to optimality in a reasonable time frame.     

Multimodal hub location and hub network design

Through observations from real life hub networks, we introduce the multimodal hub location and hub network design problem. We approach the hub location problem from a network design perspective. In addition to the location and allocation decisions, we also study the decision on how the hub networks with different possible transportation modes must be designed. In this multimodal hub location and hub network design problem, we jointly consider transportation costs and travel times, which are studied separately in most hub location problems presented in the literature. We allow different transportation modes between hubs and different types of service time promises between origin–destination pairs while designing the hub network in the multimodal problem. We first propose a linear mixed integer programming model for this problem and then derive variants of the problem that might arise in certain applications. The models are enhanced via a set of effective valid inequalities and an efficient heuristic is developed. Computational analyses are presented on the various instances from the Turkish network and CAB data set.     

Vendor managed inventory in tramp shipping

This paper introduces a new problem to the OR community that combines traditional tramp shipping with a vendor managed inventory (VMI) service. Such a service may replace the more traditional contract of affreightment (COA) which for decades has been the standard agreement between a tramp shipping company and a charterer. We present a mathematical formulation describing the routing and scheduling problem faced by a tramp shipping company that offers a VMI service to its customers. The problem is formulated as an arc-flow model, and is then reformulated as a path-flow model which is solved using a hybrid approach that combines branch-and-price with a priori path-generation. To solve larger, and more realistic, instances we present a heuristic path-generation algorithm. Computational experiments show that the heuristic approach is much faster than the exact method, with insignificant reductions in solution quality. Further, we investigate the economic impact of introducing a VMI service, by comparing the results obtained with the new model with results obtained by solving the traditional routing and scheduling problem faced by tramp shipping companies using COA. The computational results show that it is possible to substantially increase supply chain profit and efficiency by replacing the traditional COAs with VMI services.     

Exact solution method to solve large scale integer quadratic multidimensional knapsack problems

In this paper we develop a branch-and-bound algorithm for solving a particular integer quadratic multi-knapsack problem. The problem we study is defined as the maximization of a concave separable quadratic objective function over a convex set of linear constraints and bounded integer variables. Our exact solution method is based on the computation of an upper bound and also includes pre-procedure techniques in order to reduce the problem size before starting the branch-and-bound process. We lead a numerical comparison between our method and three other existing algorithms. The approach we propose outperforms other procedures for large-scaled instances (up to 2000 variables and constraints). A extended abstract of this paper appeared in LNCS 4362, pp. 456–464, 2007.     

Two-level network design with intermediate facilities: An application to electrical distribution systems

We consider the two-level network design problem with intermediate facilities. This problem consists of designing a minimum cost network respecting some requirements, usually described in terms of the network topology or in terms of a desired flow of commodities between source and destination vertices. Each selected link must receive one of two types of edge facilities and the connection of different edge facilities requires a costly and capacitated vertex facility. We propose a hybrid decomposition approach which heuristically obtains tentative solutions for the vertex facilities number and location and use these solutions to limit the computational burden of a branch-and-cut algorithm. We test our method on instances of the power system secondary distribution network design problem. The results show that the method is efficient both in terms of solution quality and computational times.     

Exact and heuristic algorithms for solving the generalized minimum filter placement problem

We consider a problem of placing route-based filters in a communication network to limit the number of forged address attacks to a prescribed level. Nodes in the network communicate by exchanging packets along arcs, and the originating node embeds the origin and destination addresses within each packet that it sends. In the absence of a validation mechanism, one node can send packets to another node using a forged origin address to launch an attack against that node. Route-based filters can be established at various nodes on the communication network to protect against these attacks. A route-based filter examines each packet arriving at a node, and determines whether or not the origin address could be legitimate, based on the arc on which the packet arrives, the routing information, and possibly the destination. The problem we consider seeks to find a minimum cardinality subset of nodes to filter so that the prescribed level of security is achieved. We formulate a mixed-integer programming model for the problem and derive valid inequalities for this model by identifying polynomially-solvable subgraphs of the communication network. We also present three heuristics for solving the filter placement problem and evaluate their performance against the optimal solution provided by the mixed-integer programming model. The authors gratefully acknowledge the comments of two anonymous referees, whose input led to an improved version of this paper. Dr. Smith gratefully acknowledges the support of the Office of Naval Research under Grant #N00014-03-1-0510 and the Defense Advanced Research Projects Agency under Grant #N66001-01-1-8925.     

Design-balanced capacitated multicommodity network design with heterogeneous assets

Management of assets plays an essential role in determination of service plans operated by carriers in the transportation and logistics system. In this paper, we introduce certain issues related to management of heterogeneous assets in the well-known design-balanced capacitated multicommodity network design, where design-balanced requirements are explicitly defined based on heterogeneous assets.Taking vehicles as an example of heterogeneous assets, we first present an arc-based formulation for the proposed problem and discuss two associated subproblems. We then propose a tabu search based metaheuristic for this problem. Over a wide range of network design instances, we respectively compare our approach with CPLEX with one-hour and ten-hour time limits. Computational results demonstrate that the proposed approach performs very well in terms of solution quality and computing time, especially for large instances.     

Optimal design of supply chain networks under uncertain transient demand variations

We consider a detailed mathematical formulation for the problem of designing supply chain networks comprising multiproduct production facilities with shared production resources, warehouses, distribution centers and customer zones and operating under time varying demand uncertainty. Uncertainty is captured in terms of a number of likely scenarios possible to materialize during the lifetime of the network. The problem is formulated as a mixed-integer linear programming problem and solved to global optimality using standard branch-and-bound techniques. A case study concerned with the establishment of Europe-wide supply chain is used to illustrate the applicability and efficiency of the proposed approach. The results obtained provide a good indication of the value of having a model that takes into account the complex interactions that exist in such networks and the effect of inventory levels to the design and operation.     

A Dynamic Disaggregation Approach to Approximate Linear Programs for Network Revenue Management

The linear programming approach to approximate dynamic programming has received considerable attention in the recent network revenue management (RM) literature. A major challenge of the approach lies in solving the resulting approximate linear programs (ALPs), which often have a huge number of constraints and/or variables. Starting from a recently developed compact affine ALP for network RM, we develop a novel dynamic disaggregation algorithm to solve the problem, which combines column and constraint generation and exploits the structure of the underlying problem. We show that the formulation can be further tightened by considering structural properties satisfied by an optimal solution. We prove that the sum of dynamic bid‐prices across resources is concave over time. We also give a counterexample to demonstrate that the dynamic bid‐prices of individual resources are not concave in general. Numerical experiments demonstrate that dynamic disaggregation is often orders of magnitude faster than existing algorithms in the literature for problem instances with and without choice. In addition, adding the concavity constraints can further speed up the algorithm, often by an order of magnitude, for problem instances with choice.     

Joint Lot Sizing and Scheduling of Multiple Items with Sequence-Dependent Setup Costs

The objective of this research is to investigate the effects of setup-cost estimating methods on the lot sizing and scheduling of multiple products in multiple periods. These initial setup cost estimators (ISCEs) are used to estimate sequence-independent initial setup costs from sequence-dependent setup costs. A search of the literature reveals that, although sequence-dependent setup costs are frequently found in practice and ISCEs are frequently used, there is a dearth of research concerning the effect of using ISCEs. After a review of the literature, a mixed integer formulation of the joint problem of lot sizing and scheduling is presented, followed by a discussion of the difficulty in solving the formulation. Next, the six ISCEs evaluated are presented. These ISCEs range from simple (select the minimum setup cost) to complex (use the branch-and-bound solution to a traveling salesman-type problem). Each ISCE is evaluated using a full factorial design with five independent variables: demand distribution (three levels), demand trend (three levels), setup to inventory level (six levels), setup distribution (three levels), and setup variability (two levels). Two hypotheses are researched. Do the more computationally complex ISCEs produce lower overall costs than do the simpler ISCEs? Does the reduction in total cost justify the additional computation cost? The results of this study demonstrate that it may be incorrect to use “conventional wisdom'’when selecting an ISCE.     

一种求解时变网络下多式联运最短路的算法

在运输过程中,往往不止有一种运输方式,可能同时有多种运输方式交叉,即可能多式联运的方式存在,不同的运输方式之间需要通过转运才可实现.同时,在运输过程中,成本、运输时间、风险等因素会随着时间的不同而变化.首先,将运输网络进行变形,然后给出了在时变网络条件下多式联运的最短路模型,设计了求解时变条件下多式联运的最短路的算法,利用此算法可以获得从起点到终点之间的最短路,并对算法的计算复杂性进行了分析.最后给出一个应用算例.     

Strategic supply network planning with vendor selection under consideration of risk and demand uncertainty

We present a stochastic version of a three-layer supply network planning problem that includes the selection of vendors that must be equipped with company-specific tools. The configuration of a supply network must be determined by using demand forecasts for a long planning horizon to meet a given service level. The risk induced by the uncertain demand is explicitly considered by incorporating the conditional value at risk. The objective is to maximize the weighted sum of the expected net present value of discounted cash flows and the conditional value at risk. This would lead to a non-linear model formulation that is approximated by a mixed-integer linear model. This approximation is realized by a piecewise linearization of the expected backlogs and physical inventory as non-linear functions of cumulative production quantities. A two-stage stochastic programming approach is proposed. Our numerical analysis of generic test instances indicates that solving the linearized model formulation yields a robust and stable supply network configuration when demand is uncertain.     

Protein Threading by Linear Programming: Theoretical Analysis and Computational Results

In a previous paper (Xu, Li, Kim, and Xu, Journal of Bioinformatics and Computational Biology, vol. 1, no. 1, pp. 95–117, 2003), we have used an integer programming approach to implement a protein threading program RAPTOR for protein 3D structure prediction, based on the threading model treating pairwise contacts rigorously and allowing variable gaps. We have solved the integer program by the canonical branch-and-bound method. In this paper we present a branch-and-cut method, a careful theoretical analysis of our formulation and why our approach is so effective. The result of cutting plane analysis is that two types of well-known cuts for this problem are already implied in the constraint set, which provides us some intuition that our formulation would be very effective. Experimental results show that for about 99 percent of real threading instances, the linear relaxations of their integer programs solve to integral optimal solutions directly. For the rest one percent of real instances, the integral solutions can be obtained with only several branch nodes. Experimental results also show that no special template or sequence features result in more possibilities of fractional solutions. This indicates that extra effort to seek for cutting planes to strengthen the existing formulation is unnecessary.     

A branch-and-price algorithm for production routing problems with carbon cap-and-trade

This study presents a model for a pollution production-routing problem under carbon cap-and-trade. The aim is to incorporate carbon emissions into production inventory and routing decisions. The model is characterized by an additional flow-related cost structure, which generalizes models for pollution-routing problems and production inventory and routing problems. Correspondingly, we develop a branch-and-price heuristic by incorporating a column-generation formulation based on the Dantzig–Wolfe decomposition. In addition, we design an ad hoc label-setting algorithm to deal with time-slice networks in pricing subproblems. Computational results allow us to provide managerial insights concerning reduction of carbon emissions in supply chains. We prove that the model has the potential to reduce emission levels of carbon dioxide and operational costs.     

Commercial territory design planning with realignment and disjoint assignment requirements

A territory design problem motivated by a bottled beverage distribution company is addressed. The problem consists of finding a partition of the entire set of city blocks into a given number of territories subject to several planning criteria. Each unit has three measurable activities associated to it, namely, number of customers, product demand, and workload. The plan must satisfy planning criteria such as territory compactness, territory balancing with respect to each of the block activity measures, and territory connectivity, meaning that there must exist a path between any pair of units in a territory totally contained in it. In addition, there are some disjoint assignment requirements establishing that some specified units must be assigned to different territories, and a similarity with existing plan requirement. An optimal design is one that minimizes a measure of territory dispersion and similarity with existing design. A mixed-integer linear programming model is presented. This model is unique in the commercial territory design literature as it incorporates the disjoint assignment requirements and similarity with existing plan. Previous methods developed for related commercial districting problems are not applicable. A solution procedure based on an iterative cut generation strategy within a branch-and-bound framework is proposed. The procedure aims at solving large-scale instances by incorporating several algorithmic strategies that helped reduce the problem size. These strategies are evaluated and tested on some real-world instances of 5000 and 10,000 basic units. The empirical results show the effectiveness of the proposed method and strategies in finding near optimal solutions to these very large instances at a reasonably small computational effort.     

Minimum cost network design in strategic alliances

Strategic alliances are established between firms to improve their competitiveness in markets and generally appear in the form of joint ventures. Such collaborative efforts require centralized planning, and the survival of the alliance largely depends on the success of joint planning processes. In this regard, we investigate the opportunities that centralized collaboration can offer to firms when designing their service networks. Apart from the classical fixed and variable costs associated with the network design, we also consider transaction costs induced by the formation of the alliance, which can broadly be defined as cost components related to the coordination and monitoring of the people, efforts and resources. We concentrate on bilateral alliances and develop alternative models for solving their associated network design problem. We also adopt a state-of-the-art heuristic to solve large-scale instances. Our findings confirm that accounting for the transaction cost in network design is vital for the alliance. These transaction costs can be high enough to even render the collaboration unattractive. Hence, careful data collection and model treatment are required before deciding whether to form an alliance.     

Data relaying with constraints in hierarchical sensor networks

In this paper we present and discuss several optimisation problems that arise in the management of data flow in wireless sensor networks (WSNets). We consider a hierarchical architecture for WSNets composed of sensors, relays, and relay gateways. Sensors send data they generate at a known average bit rate to relays in one hop. The relay nodes use a multi-hop mechanism to reach a set of assigned gateways which then forward the data directly to the base station. We are concerned with finding an assignment of relay gateways to relays so that certain constraints are satisfied. We define a unified model in which constraints such as lifetime, data delay, and data flow splitting are formulated in terms of four optimisation problem in graphs.