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.     

Using branch-and-price approach to solve the directed network design problem with relays

We present node-arc and arc-path formulations, and develop a branch-and-price approach for the directed network design problem with relays (DNDR). The DNDR problem can be used to model many network design problems in transportation, service, and telecommunication system, where relay points are necessary. The DNDR problem consists of introducing a subset of arcs and locating relays on a subset of nodes such that in the resulting network, the total cost (arc cost plus relay cost) is minimized, and there exists a directed path linking the origin and destination of each commodity, in which the distances between the origin and the first relay, any two consecutive relays, and the last relay and the destination do not exceed a predefined distance limit. With the node-arc formulation, we can directly solve small DNDR instances using mixed integer programming solver. With the arc-path formulation, we design a branch-and-price approach, which is a variant of branch-and-bound with bounds provided by solving linear programs using column generation at each node of the branch-and-bound tree. We design two methods to efficiently price out columns and present computational results on a set of 290 generated instances. Results demonstrate that our proposed branch-and-price approach is a computationally efficient procedure for solving the DNDR problem.     

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.     

Approximate dynamic programming for the aeromedical evacuation dispatching problem: Value function approximation utilizing multiple level aggregation

Sequential resource allocation decision-making for the military medical evacuation of wartime casualties consists of identifying which available aeromedical evacuation (MEDEVAC) assets to dispatch in response to each casualty event. These sequential decisions are complicated due to uncertainty in casualty demand (i.e., severity, number, and location) and service times. In this research, we present a Markov decision process model solved using a hierarchical aggregation value function approximation scheme within an approximate policy iteration algorithmic framework. The model seeks to optimize this sequential resource allocation decision under uncertainty of how to best dispatch MEDEVAC assets to calls for service. The policies determined via our approximate dynamic programming (ADP) approach are compared to optimal military MEDEVAC dispatching policies for two small-scale problem instances and are compared to a closest-available MEDEVAC dispatching policy that is typically implemented in practice for a large-scale problem instance. Results indicate that our proposed approximation scheme provides high-quality, scalable dispatching policies that are more easily employed by military medical planners in the field. The identified ADP policies attain 99.8% and 99.5% optimal for the 6- and 12-zone problem instances investigated, as well as 9.6%, 9.2%, and 12.4% improvement over the closest-MEDEVAC policy for the 6-, 12-, and 34-zone problem instances investigated.     

A sustainable supply chain network considering lot sizing with quantity discounts under disruption risks: centralized and decentralized models

This study proposes a framework for the main parties of a sustainable supply chain network considering lot-sizing impact with quantity discounts under disruption risk among the first studies. The proposed problem differs from most studies considering supplier selection and order allocation in this area. First, regarding the concept of the triple bottom line, total cost, environmental emissions, and job opportunities are considered to cover the criteria of sustainability. Second, the application of this supply chain network is transformer production. Third, applying an economic order quantity model lets our model have a smart inventory plan to control the uncertainties. Most significantly, we present both centralized and decentralized optimization models to cope with the considered problem. The proposed centralized model focuses on pricing and inventory decisions of a supply chain network with a focus on supplier selection and order allocation parts. This model is formulated by a scenario-based stochastic mixed-integer non-linear programming approach. Our second model focuses on the competition of suppliers based on the price of products with regard to sustainability. In this regard, a Stackelberg game model is developed. Based on this comparison, we can see that the sum of the costs for both levels is lower than the cost without the bi-level approach. However, the computational time for the bi-level approach is more than for the centralized model. This means that the proposed optimization model can better solve our problem to achieve a better solution than the centralized optimization model. However, obtaining this better answer also requires more processing time. To address both optimization models, a hybrid bio-inspired metaheuristic as the hybrid of imperialist competitive algorithm (ICA) and particle swarm optimization (PSO) is utilized. The proposed algorithm is compared with its individuals. All employed optimizers have been tuned by the Taguchi method and validated by an exact solver in small sizes. Numerical results show that striking similarities are observed between the results of the algorithms, but the standard deviations of PSO and ICA–PSO show better behavior. Furthermore, while PSO consumes less time among the metaheuristics, the proposed hybrid metaheuristic named ICA–PSO shows more time computations in all small instances. Finally, the provided results confirm the efficiency and the performance of the proposed framework and the proposed hybrid metaheuristic algorithm.

     

Multi-echelon supply chain network design in agile manufacturing

In this paper, we consider a supply chain network design problem in an agile manufacturing scenario with multiple echelons and multiple periods under a situation where multiple customers have heavy demands. Decisions in our supply chain design problem include selection of one or more companies in each echelon, production, inventory, and transportation. We formulate the problem integrating all decisions to minimize the total operational costs including fixed alliance costs between two companies, production, raw material holding, finished products holding, and transportation costs under production and transportation capacity limits. A Lagrangian heuristic is proposed in this paper. Optimizing a Lagrangian relaxation problem provides a lower bound, while a feasible solution is generated by adjustment techniques based on the solution of subproblems at each iteration. Computational results indicate the high quality solutions with less than 5% optimality gap are provided quickly by the approach in this paper. Further, compared to initiative managerial alternatives, an improvement of 15% to 25% is not unusual in certain cases for the proposed approach.     

Multi-echelon supply chain network design in agile manufacturing

In this paper, we consider a supply chain network design problem in an agile manufacturing scenario with multiple echelons and multiple periods under a situation where multiple customers have heavy demands. Decisions in our supply chain design problem include selection of one or more companies in each echelon, production, inventory, and transportation. We formulate the problem integrating all decisions to minimize the total operational costs including fixed alliance costs between two companies, production, raw material holding, finished products holding, and transportation costs under production and transportation capacity limits. A Lagrangian heuristic is proposed in this paper. Optimizing a Lagrangian relaxation problem provides a lower bound, while a feasible solution is generated by adjustment techniques based on the solution of subproblems at each iteration. Computational results indicate the high quality solutions with less than 5% optimality gap are provided quickly by the approach in this paper. Further, compared to initiative managerial alternatives, an improvement of 15% to 25% is not unusual in certain cases for the proposed approach.     

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.     

Revised GRASP with path-relinking for the linear ordering problem

The linear ordering problem (LOP) is an NP\mathcal{NP}-hard combinatorial optimization problem with a wide range of applications in economics, archaeology, the social sciences, scheduling, and biology. It has, however, drawn little attention compared to other closely related problems such as the quadratic assignment problem and the traveling salesman problem. Due to its computational complexity, it is essential in practice to develop solution approaches to rapidly search for solution of high-quality. In this paper we propose a new algorithm based on a greedy randomized adaptive search procedure (GRASP) to efficiently solve the LOP. The algorithm is integrated with a Path-Relinking (PR) procedure and a new local search scheme. We tested our implementation on the set of 49 real-world instances of input-output tables (LOLIB instances) proposed in Reinelt (Linear ordering library (LOLIB) 2002). In addition, we tested a set of 30 large randomly-generated instances proposed in Mitchell (Computational experience with an interior point cutting plane algorithm, Tech. rep., Mathematical Sciences, Rensellaer Polytechnic Institute, Troy, NY 12180-3590, USA 1997). Most of the LOLIB instances were solved to optimality within 0.87 seconds on average. The average gap for the randomly-generated instances was 0.0173% with an average running time of 21.98 seconds. The results indicate the efficiency and high-quality of the proposed heuristic procedure.     

A decision support approach for two-stage multi-objective index tracking using improved lagrangian decomposition

We present a decision support approach for a network structured stochastic multi-objective index tracking problem in this paper. Due to the non-convexity of this problem, the developed network is modeled as a Stochastic Mixed Integer Linear Program (SMILP). We also propose an optimization-based approach to scenario generation to protect against the risk of parameter estimation for the SMILP. Progressive Hedging (PH), an improved Lagrangian scheme, is designed to decompose the general model into scenario-based sub-problems. Furthermore, we innovatively combine tabu search and the sub-gradient method into PH to enhance the tracking capabilities of the model. We show the robustness of the algorithm through effectively solving a large number of numerical instances.     

Planning of a decentralized distribution network using bilevel optimization

This paper proposes a bilevel optimization problem to model the planning of a distribution network that allows us to take into account how decisions made at the distribution stage of the supply chain can affect and be affected by decisions made at the manufacturing stage. Usually, the distribution network design problem decides on the opening of depots and the distribution from the depots to customers only and pays no attention to the manufacturing process itself. By way of example, the paper discusses the implications of formulating a bilevel model to integrate distribution and manufacturing, maintaining the hierarchy existing in the decision process. The resulting model is a bilevel mixed integer optimization problem. Hence, only small instances can be optimally solved in an acceptable computing time. In order to be able to solve the optimization model for realistic large systems, a metaheuristic approach based on evolutionary algorithms is developed. The algorithm combines the use of an evolutionary algorithm to control the supply of depots with optimization techniques to determine the delivery from depots to customers and the supply from manufacturing plants to depots. A computational experiment is carried out to assess the efficiency and robustness of the algorithm.     

A heuristic framework for the bi-objective enhanced index tracking problem

The index tracking problem is the problem of determining a portfolio of assets whose performance replicates, as closely as possible, that of a financial market index chosen as benchmark. In the enhanced index tracking problem the portfolio is expected to outperform the benchmark with minimal additional risk. In this paper, we study the bi-objective enhanced index tracking problem where two competing objectives, i.e., the expected excess return of the portfolio over the benchmark and the tracking error, are taken into consideration. A bi-objective Mixed Integer Linear Programming formulation for the problem is proposed. Computational results on a set of benchmark instances are given, along with a detailed out-of-sample analysis of the performance of the optimal portfolios selected by the proposed model. Then, a heuristic procedure is designed to build an approximation of the set of Pareto optimal solutions. We test the proposed procedure on a reference set of Pareto optimal solutions. Computational results show that the procedure is significantly faster than the exact computation and provides an extremely accurate approximation.     

A robust branch-and-cut approach for the minimum-energy symmetric network connectivity problem

This paper considers the minimum-energy symmetric network connectivity problem (MESNC) in wireless sensor networks. The aim of the MESNC is to assign transmission power to each sensor node such that the resulting network, using only bidirectional links, is connected and the total energy consumption is minimized. We first present two new models of this problem and then propose new branch-and-cut algorithms. Based on an existing formulation, we present the first model by introducing additional constraints. These additional constraints allow us to relax certain binary variables to continuous ones and thus to reduce significantly the number of binary variables. Our second model strengthens the first one by adding an exponential number of lifted directed-connectivity constraints. We present two branch-and-cut procedures based on these proposed improvements. The computational results are reported and show that our approaches, using the proposed formulations, can efficiently solve instances with up to 120 nodes, which significantly improve our ability to solve much larger instances in comparison with other exact algorithms in the literature.     

Logic-based Benders decomposition for an inventory-location problem with service constraints

We study an integrated inventory-location problem with service requirements faced by an aerospace company in designing its service parts logistics network. Customer demand is Poisson distributed and the service levels are time-based leading to highly non-linear, stochastic service constraints and a nonlinear, mixed-integer optimization problem. Unlike previous work in the literature, which propose approximations for the nonlinear constraints, we present an exact solution methodology using logic-based Benders decomposition. We decompose the problem to separate the location decisions in the master problem from the inventory decisions in the subproblem. We propose a new family of valid cuts and prove that the algorithm is guaranteed to converge to optimality. This is the first attempt to solve this type of problem exactly. Then, we present a new restrict-and-decompose scheme to further decompose the Benders master problem by part. We test on industry instances as well as random instances. Using the exact algorithm and restrict-and-decompose scheme we are able to solve industry instances with up to 60 parts within reasonable time, while the maximum number of parts attempted in the literature is 5.     

A flexible model for the pricing of perishable assets

We present a flexible and versatile model which addresses the problem of assigning optimal prices to assets whose value becomes zero after a fixed expiry date. (Such assets include the important example of seats on airline flights.) Our model is broad in scope, in particular encompassing the ability to deal with arrivals of customers in groups. It is highly adaptable and can be adjusted to deal with a very extensive set of circumstances.Our approach to the problem is based on elementary and intuitively appealing ideas. We model the arrival of customers (or groups of customers) according to an inhomogeneous Poisson process. We incorporate into the model time dependent price sensitivity (which may also be described as “time dependent elasticity of demand”). In this setting the solution to the asset pricing problem is achieved by setting up coupled systems of differential equations which are readily amenable to numerical solution via (for instance) a vectorised Runge-Kutta procedure. An attractive feature of our approach is that it unifies the treatment of discrete and continuous prices for the assets.     

Separator-based data reduction for signed graph balancing

Polynomial-time data reduction is a classical approach to hard graph problems. Typically, particular small subgraphs are replaced by smaller gadgets. We generalize this approach to handle any small subgraph that has a small separator connecting it to the rest of the graph. The problem we study is the NP-hard Balanced Subgraph problem, which asks for a 2-coloring of a graph that minimizes the inconsistencies with given edge labels. It has applications in social networks, systems biology, and integrated circuit design. The data reduction scheme unifies and generalizes a number of previously known data reductions, and can be applied to a large number of graph problems where a coloring or a subset of the vertices is sought. To solve the instances that remain after reduction, we use a fixed-parameter algorithm based on iterative compression with a very effective heuristic speedup. Our implementation can solve biological real-world instances exactly for which previously only approximations were known. In addition, we present experimental results for financial networks and random networks.     

Management of school locations allowing for free school choice

Nearly without exception, we find in literature (school) location models with exogenously given demand. Indeed, we know from a large number of empirical studies that this assumption is unrealistic. Therefore, we propose a discrete location model for school network planning with free school choice that is based on simulated utility values for a large average sample. The objective is to maximize the standardized expected utility of all students taking into account capacity constraints and a given budget for the school network. The utility values of each student for the schools are derived from a random utility model (RUM). The proposed approach is general in terms of the RUM used. Moreover, we do not have to make assumptions about the functional form of the demand function. Our approach, which combines econometric and mathematical methods, is a linear 0–1 program although we consider endogenous demand by a highly non-linear function. The proposed program enables practicing managers to consider student demand adequately within their decision making. By a numerical investigation we show that this approach enables us to solve instances of real size optimally – or at least close to optimality – within few minutes using GAMS/Cplex.     

考虑差异化服务时间的多车型电动汽车路径优化与充电策略研究

在政府政策大力支持以及社会环境意识不断增长的背景下,电动汽车在物流配送行业快速普及。电动汽车参与的物流配送服务需要物流专员、电动汽车和顾客三方协作完成。因此,在传统车辆配送路径优化的基础上,车辆的多样性、充电策略、人车的匹配以及服务时间差异化等因素都会影响物流运营成本。本文提出了考虑差异化服务成本的多车型电动汽车路径优化与充电策略问题并建立了该问题的整数规划数学模型。其次,提出了混合启发式算法MCWGATS,并通过多组算例验证了算法的有效性。最后,采用多组算例分析了多车型和差异化服务时间对运营成本的影响。实验结果表明,该模型有助于物流企业提高人员、物流车辆、服务时间等资源的利用效率,降低运营成本。     

Reduced costs propagation in an efficient implicit enumeration for the 01 multidimensional knapsack problem

In a previous work we proposed a variable fixing heuristics for the 0-1 Multidimensional knapsack problem (01MDK). This approach uses fractional optima calculated in hyperplanes which contain the binary optimum. This algorithm obtained best lower bounds on the OR-Library benchmarks. Although it is very attractive in terms of results, this method does not prove the optimality of the solutions found and may fix variables to a non-optimal value. In this paper, we propose an implicit enumeration based on a reduced costs analysis which tends to fix non-basic variables to their exact values. The combination of two specific constraint propagations based on reduced costs and an efficient enumeration framework enable us to fix variables on the one hand and to prune significantly the search tree on the other hand. Experimentally, our work provides two main contributions: (1) we obtain several new optimal solutions on hard instances of the OR-Library and (2) we reduce the bounds of the number of items at the optimum on several harder instances.     

On greedy and strategic evaders in sequential interdiction settings with incomplete information

We consider a class of sequential network interdiction problem settings where the interdictor has incomplete initial information about the network while the evader has complete knowledge of the network including its structure and arc costs. In each decision epoch, the interdictor can block (for the duration of the epoch) at most k arcs known to him/her. By observing the evader’s actions, the interdictor learns about the network structure and costs and thus, can adjust his/her actions in subsequent decision epochs. It is known from the literature that if the evader is greedy (i.e., the shortest available path is used in each decision epochs), then under some assumptions the greedy interdiction policies that block k-most vital arcs in each epoch are efficient and have a finite regret. In this paper, we consider the evader’s perspective and explore deterministic “strategic” evasion policies under the assumption that the interdictor is greedy. We first study the theoretical computational complexity of the evader’s problem. Then we derive basic constructive properties of optimal evasion policies for two decision epochs when the interdictor has no initial information about the network structure. These properties are then exploited for the design of a heuristic algorithm for a strategic evader in a general setting with an arbitrary time horizon and any initial information available to the interdictor. Our computational experiments demonstrate that the proposed heuristic outperforms the greedy evasion policy on several classes of synthetic network instances under either perfect or noisy information feedback. Finally, some interesting insights from our theoretical and computational results conclude the paper.