Credibility-based fuzzy mathematical programming model for green logistics design under uncertainty

Measuring and controlling emissions across the logistics network is an important challenge for today’s firms according to increasing concern about the environmental impact of business activities. This paper proposes a bi-objective credibility-based fuzzy mathematical programming model for designing the strategic configuration of a green logistics network under uncertain conditions. The model aims to minimize the environmental impacts and the total costs of network establishment simultaneously for the sake of providing a sensible balance between them. A popular but credible environmental impact assessment index, i.e., CO₂ equivalent index is used to model the environmental impact across the concerned logistics network. Since transportation mode and production technology play important roles on the concerned objectives, the proposed model integrates their respective decisions with those of strategic network design ones. In addition, to solve the proposed bi-objective fuzzy optimization model, an interactive fuzzy solution approach based upon credibility measure is developed. An industrial case study is also provided to show the applicability of the proposed model as well as the usefulness of its solution method.     

A bi-objective approach for shortest-path network interdiction

In the literature, solution approaches to the shortest-path network interdiction problem have been developed for optimizing a single figure-of-merit of the network configuration when considering limited amount of resources available to interdict network links. This paper presents a newly developed evolutionary algorithm that allows approximating the optimal Pareto set of network interdiction strategies when considering bi-objective shortest path problems. Thus, the paper considers the concurrent optimization of two objectives: (1) maximization of shortest-path length and (2) minimization of interdiction strategy cost. Also, the paper considers the transformation of the first objective into the minimization of the most reliable path reliability. To solve these multi-objective optimization problems, an evolutionary algorithm has been developed. This algorithm is based on Monte Carlo simulation, to generate potential network interdiction strategies, graph theory to analyze strategies’ shortest path or most reliable path and, an evolutionary search driven by the probability that a link will appear in the optimal Pareto set. Examples for different sizes of networks and network behavior are used throughout the paper to illustrate and validate the approach.     

Hierarchical facility location problem: Models,classifications, techniques,and applications

The primary objective in a typical hierarchical facility location problem is to determine the location of facilities in a multi-level network in a way to serve the customers at the lowest level of hierarchy both efficiently (cost minimization objective) and effectively (service availability maximization objective). This paper presents a comprehensive review of over 40 years of hierarchical facility location modeling efforts. Published models are classified based on multiple characteristics including the type of flow pattern, service availability, spatial configuration, objective function, coverage, network levels, time element, parameters, facilities, capacity, and real world application. A second classification is also presented on the basis of solution methods adopted to solve various hierarchical facility location problems. The paper finally identifies the gaps in the current literature and suggests directions for future modeling efforts.     

Location based treatment activities for end of life products network design under uncertainty by a robust multi-objective memetic-based heuristic approach

Rapid growth in world population and recourse limitations necessitate remanufacturing of products and their parts/modules. Managing these processes requires special activities such as inspection, disassembly, and sorting activities known as treatment activities. This paper proposes a capacitated multi-echelon, multi-product reverse logistic network design with fuzzy returned products in which both locations of the treatment activities and facilities are decision variables. As the obtained nonlinear mixed integer programming model is a combinatorial problem, a memetic-based heuristic approach is presented to solve the resulted model. To validate the proposed memetic-based heuristic method, the obtained results are compared with the results of the linear approximation of the model, which is obtained by a commercial optimization package. Moreover, due to inherent uncertainty in return products, demands of these products are considered as uncertain parameters and therefore a fuzzy approach is employed to tackle this matter. In order to deal with the uncertainty, a stochastic simulation approach is employed to defuzzify the demands, where extra costs due to opening new centers or extra transportation costs may be imposed to the system. These costs are considered as penalty in the objective function. To minimize the resulting penalties during simulation's iterations, the average of penalties is added to the objective function of the deterministic model considered as the primary objective function and variance of penalties are considered as the secondary objective function to make a robust solution. The resulted bi-objective model is solved through goal programming method to minimizing the objectives, simultaneously.     

流线网络的物流组织优化模型研究

通过分析流线网络建设与运营的基本特征,构建了流线网络的抽象成本函数,为了降低物流成本和提高物流效率,建立以能力供给为约束,以网络建设和运营成本最小为目标的优化模型。将模型转化为相应的变分不等式,证明变分不等式与优化模型解的等价性,通过解变分不等式得到最优物流组织方案,算例验证了模型合理性和可行性,为企业对物流网络的经营提供理论支持。     

CLPS-GA: A case library and Pareto solution-based hybrid genetic algorithm for energy-aware cloud service scheduling

Since the appearance of cloud computing, computing capacity has been charged as a service through the network. The optimal scheduling of computing resources (OSCR) over the network is a core part for a cloud service center. With the coming of virtualization, the OSCR problem has become more complex than ever. Previous work, either on model building or scheduling algorithms, can no longer offer us a satisfactory resolution. In this paper, a more comprehensive and accurate model for OSCR is formulated. In this model, the cloud computing environment is considered to be highly heterogeneous with processors of uncertain loading information. Along with makespan, the energy consumption is considered as one of the optimization objectives from both economic and ecological perspectives. To provide more attentive services, the model seeks to find Pareto solutions for this bi-objective optimization problem. On the basis of classic multi-objective genetic algorithm, a case library and Pareto solution based hybrid Genetic Algorithm (CLPS-GA) is proposed to solve the model. The major components of CLPS-GA include a multi-parent crossover operator (MPCO), a two-stage algorithm structure, and a case library. Experimental results have verified the effectiveness of CLPS-GA in terms of convergence, stability, and solution diversity.     

Strategic Network Restoration

For any networked infrastructure, damage to arcs and/or nodes and associated disruption of network services is inevitable. To reestablish service in a damaged network, affected components must be repaired or reconfigured, a process that can be time consuming and costly, so care must be taken to identify network restoration strategies that reestablish service most efficiently. A strategic goal of service restoration, therefore, is to ensure that facility restoration is prioritized so that system performance is maximized over a planning horizon within budgetary restrictions. To address this problem, this paper proposes a multi-objective optimization approach for network restoration during disaster recovery. The proposed model permits tradeoffs between two objectives, minimization of system cost and maximization of system flow, to be evaluated. A telecommunication application illustrates the significance of the developed approach.     

区间不确定性需求下的D-LFLP模型及算法

考虑物流网络需求的不确定性,运用区间分析理念以区间数度量不确定性变量与参数,建立区间需求模式下的物流网络设计的混合整数规划模型,定义风险系数与最大约束偏差,对模型进行目标函数与约束条件的确定性转化,设计问题求解的区间递阶优化遗传算法,对不同情景状态下目标函数的区间最优解与节点决策方案进行运算。算例测试表明该算法可操作性更强,求解结果具有区间最优解与情景决策的优越性。     

The $Q$ -Norm Complexity Measure and the Minimum Gradient Method: A Novel Approach to the Machine Learning Structural Risk Minimization Problem

This paper presents a novel approach for dealing with the structural risk minimization (SRM) applied to a general setting of the machine learning problem. The formulation is based on the fundamental concept that supervised learning is a bi-objective optimization problem in which two conflicting objectives should be minimized. The objectives are related to the empirical training error and the machine complexity. In this paper, one general $Q$-norm method to compute the machine complexity is presented, and, as a particular practical case, the minimum gradient method (MGM) is derived relying on the definition of the fat-shattering dimension. A practical mechanism for parallel layer perceptron (PLP) network training, involving only quasi-convex functions, is generated using the aforementioned definitions. Experimental results on 15 different benchmarks are presented, which show the potential of the proposed ideas.      

集成整车物流系统的网络规划问题研究

综合考虑运输、库存、设施、服务质量等决策因素，建立了整车物流网络规划集成优化模型，针对由工厂、集货中心和分销中心构成的基本物流网络，提出了用于运输路径优化的流预测算法，并嵌入到遗传算法，解决了适应值的计算难点，给出了基于流预测的遗传算法求解框架．通过实例分析了运输规模效应、库存控制策略、服务质量指标等因素对物流网络结构设计方案的影响。     

A bi-objective optimization of supply chain design and distribution operations using non-dominated sorting algorithm: A case study

This paper considers simultaneous optimization of strategic design and distribution decisions for three-echelon supply chain architecture consisting of following three players; suppliers, production plants, and distribution centers (DCs). The key design decisions considered are: the number and location of plants in the system, the flow of raw materials from suppliers to plants, the quantity of products to be shipped from plants to distribution centers, so as to minimize the combined facility location, production, inventory, and shipment costs and maximize fill rate. To achieve this, three-echelon network model is mathematically represented and solved using swarm intelligence based Multi-objective Hybrid Particle Swarm Optimization algorithm (MOHPSO). This heuristic incorporates non-dominated sorting (NDS) procedure to achieve bi-objective optimization of two conflicting objectives. The applicability of proposed optimization algorithm was then tested by applying it to standard test problems found in literature. On achieving comparable results, the approach was applied to actual data of a pump manufacturing industry. The results show that the proposed solution approach performs efficiently.     

Optimizing a bi-objective multi-product EPQ model with defective items,rework and limited orders: NSGA-II and MOPSO algorithms

In this paper, a bi-objective multi-products economic production quantity (EPQ) model is developed, in which the number of orders is limited and imperfect items that are re-workable are produced. The objectives of the problem are minimization of the total inventory costs as well as minimizing the required warehouse space. The model is shown to be of a bi-objective nonlinear programming type, and in order to solve it two meta-heuristic algorithms namely, the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) algorithm, are proposed. To verify the solution obtained and to evaluate the performance of proposed algorithms, two-sample t-tests are employed to compare the means of the first objective value, the means of the second objective values, and the mean required CPU time of solving the problem using two algorithms. The results show while both algorithms are efficient to solve the model and the solution qualities of the two algorithms do not differ significantly, the computational CPU time of MOPSO is considerably lower than that of NSGA-II.     

基于遗传模拟退火算法的多层设施选址方法

逆向物流网络是逆向物流系统高效运作的基础和前提,而设施的选址定位是逆向物流网络设计的核心问题.为此,提出一个多层设施选址模型,旨在构建由回收点、回收中心和生产点相结合的最佳逆向物流回收网络.根据模型特点,提出基于遗传模拟退火算法的求解方法,个体采用二进制十进制混合编码;提出基于Metropolis准则的特定遗传进化操作;设计顾客对回收点、回收点对回收中心的两个子分配算法保证所有约束的满足性.最后通过仿真实验,得到满意的设施选址方案.可见,选址模型和算法是一种有效的设施选址方法,具有一定的应用前景.     

Genetic programming through bi-objective genetic algorithms with a study of a simulated moving bed process involving multiple objectives

A new bi-objective genetic programming (BioGP) technique has been developed for meta-modeling and applied in a chromatographic separation process using a simulated moving bed (SMB) process. The BioGP technique initially minimizes training error through a single objective optimization procedure and then a trade-off between complexity and accuracy is worked out through a genetic algorithm based bi-objective optimization strategy. A benefit of the BioGP approach is that an expert user or a decision maker (DM) can flexibly select the mathematical operations involved to construct a meta-model of desired complexity or accuracy. It is also designed to combat bloat – a perennial problem in genetic programming along with over fitting and under fitting problems. In this study the meta-models constructed for SMB reactors were compared with those obtained from an evolutionary neural network (EvoNN) developed earlier and also with a polynomial regression model. Both BioGP and EvoNN were compared for subsequent constrained bi-objective optimization studies for the SMB reactor involving four objectives. The results were also compared with the previous work in the literature. The BioGP technique produced acceptable results and is now ready for data-driven modeling and optimization studies at large.     

Hybrid simulation-analytical modeling approaches for the reverse logistics network design of a third-party logistics provider

In this study, we consider a manufacturer that has strategically decided to outsource the company specific reverse logistics (RL) activities to a third-party logistics (3PL) service provider. Given the locations of the collection centers and reprocessing facilities, the RL network design of the 3PL involves finding the number and places of the test centers under supply uncertainty associated with the quantity of the returns. Hybrid simulation-analytical modeling, which iteratively uses mixed integer programming models and simulation, is a suitable framework for handling the uncertainties in the stochastic RL network design problem. We present two hybrid simulation-analytical modeling approaches for the RL network design of the 3PL. The first one is an adaptation of a problem-specific approach proposed in the literature for the design of a distribution network design of a 3PL. The second one involves the development of a generic approach based on a recently proposed novel solution methodology. In the generic approach instead of exchanging problem-specific parameters between the analytical and simulation model, the interaction is governed by reflecting the impact of uncertainty obtained via simulation to the objective function of the analytical model. The results obtained from the two approaches under different scenario and parameter settings are discussed.     

A hybrid optimization/simulation approach for a distribution network design of 3PLS

Third party logistics service providers (3PLs) are playing an increasing role in the management of supply chains. Especially in warehousing and transportation services, a number of clients expect for 3PLs to improve lead times, fill rates, inventory levels, etc. Hence, these 3PLs are under pressure to meet various clients’ service requirements in a dynamic and uncertain business environment. As a result, 3PLs should maintain an efficient distribution system of high performance competitive advantages. In this paper, we propose a hybrid optimization/simulation approach to design a distribution network for 3PLs in consideration of the performance of the warehouses. The optimization model uses a genetic algorithm to determine dynamic distribution network structures. Subsequently, the simulation model is applied to capture the uncertainty in clients’ demands, order-picking time, and travel time for the capacity plans of the warehouses based on service time. The approach is applied to an example problem for examining its validity.     

考虑道路扩建的区域物流网络设计优化模型

通过对区域物流网络中边、点上费用、容量、流量等的分析,结合实际问题中对道路扩建和物流设施容量设计决策的需要,构建基于物流时间需求的区域物流网络设计数学模型。模型以最小化物流网络构建成本、初期运营成本和物流时间需求惩罚成本为目标,基于网络中物流量的特征给出了约束条件,分析模型的特点开发了改进的拉格朗日松弛算法并予以求解。计算机软件对模型和算法的仿真给出了物流网络构建中各项成本之间的关系,验证了模型和算法的有效性和实用性。     

Reverse logistics network design for a biogas plant: An approach based on MILP optimization and Analytical Hierarchical Process (AHP)

Among sustainable energy production processes, methanation (anaerobic co-digestion) has a high potential to valorize organic residual waste by exploiting its energetic capacities in the form of biogas. Nevertheless, at the early stage of the project, decisions must be made concerning the network used to supply biomass to the anaerobic co-digestion facility. However, these decisions involve complex hierarchical processes, taking into account the best compromise to be found among diverse factors and actors (economic, social, environmental, etc.). In this article a systematic approach integrating Mixed Integer Linear Programming (MILP) optimization and Analytical Hierarchical Process is proposed. It will allow project managers to evaluate possible scenarios for the implementation of an anaerobic co-digestion logistics network in order to facilitate the integration of the preferences of the stakeholders involved in the project. The approach proposed is then illustrated by the design of a municipal biogas facility in Nancy, France.     

Pareto set analysis: local measures of objective coupling in multiobjective design optimization

Multiobjective optimization focuses on the explicit trade-offs between competing criteria. A particular case is the study of combined optimal design and optimal control, or co-design, of smart artifacts where the artifact design and controller design objectives compete. In the system-level co-design problem, the objective is often the weighted sum of these two objectives. A frequently referenced practice is to solve co-design problems in a sequential manner: design first, control next. The success of this approach depends on the form of coupling between the two subproblems. In this paper, the coupling vector derived for a system problem with unidirectional coupling is shown to be related to the alignment of competing objectives, as measured by the polar cone of objective gradients, in the bi-objective programming formulation. Further, it is shown that a measure describing the case where a range of objective weighting values for the system objective result in identical design solutions can be normalized when the system problem is considered as a bi-objective one. Changes to the mathematical structure and input parameter values of a bi-objective programming problem can lead to changes in the shape of the attainable set and its Pareto boundary. We illustrate the link between the coupling and alignment measures and the outcomes of the Pareto set. Systematically studying changes to coupling and alignment measures due to changes to the multiobjective formulation can yield deeper insights into the system-level design problem. Two examples illustrate these results.     

Bi-objective vibration damping optimization for congested location–pricing problem

This paper presents a bi-objective mathematical programming model for the restricted facility location problem, under a congestion and pricing policy. Motivated by various applications such as locating server on internet mirror sites and communication networks, this research investigates congested systems with immobile servers and stochastic demand as M/M/m/k queues. For this problem, we consider two simultaneous perspectives; (1) customers who desire to limit waiting time for service and (2) service providers who intend to increase profits. We formulate a bi-objective facility location problem with two objective functions: (i) maximizing total profit of the whole system and (ii) minimizing the sum of waiting time in queues; the model type is mixed-integer nonlinear. Then, a multi-objective optimization algorithm based on vibration theory (so-called multi-objective vibration damping optimization (MOVDO)), is developed to solve the model. Moreover, the Taguchi method is also implemented, using a response metric to tune the parameters. The results are analyzed and compared with a non-dominated sorting genetic algorithm (NSGA-II) as a well-developed multi-objective evolutionary optimization algorithm. Computational results demonstrate the efficiency of the proposed MOVDO to solve large-scale problems.