A Barzilai-Borwein-based heuristic algorithm for locating multiple facilities with regional demand

We are interested in locations of multiple facilities in the plane with the aim of minimizing the sum of weighted distance between these facilities and regional customers, where the distance between a facility and a regional customer is evaluated by the farthest distance from this facility to the demand region. By applying the well-known location-allocation heuristic, the main task for solving such a problem turns out to solve a number of constrained Weber problems (CWPs). This paper focuses on the computational contribution in this topic by developing a variant of the classical Barzilai-Borwein (BB) gradient method to solve the reduced CWPs. Consequently, a hybrid Cooper type method is developed to solve the problem under consideration. Preliminary numerical results are reported to verify the evident effectiveness of the new method.     

Continuous allocation problems

Some mathematical aspects are studied for a wide class of problems called continuous allocation problems: Find a mapping, from one given continuous set onto another, to minimize a given function on these sets. Many problems of assortments, catalogs, scheduling, location-allocation, search, etc., fall in this class. Theorems on existence, uniqueness, and continuity of solution are given. A solution technique is given for then-dimensional generalized location-allocation problem, and it is shown to converge on a solution. Finally, an expression is found for the facility density in multiple-facility location-allocation problems when the range of the mapping is continuous (as the number of facilities tends to infinity).The work reported in this paper is part of a study sponsored by the National Research Council of Canada.     

考虑应急设施中断风险与防御的可靠性选址模型研究

为提高应急设施运行的可靠性和抵御中断风险的能力, 研究中断情境下的应急设施选址-分配决策问题。扩展传统无容量限制的固定费用选址模型, 从抵御设施中断的视角和提高服务质量的视角建立选址布局网络的双目标优化模型, 以应急设施的建立成本和抵御设施中断的加固成本最小为目标, 以最大化覆盖服务质量水平为目标, 在加固预算有限及最大最小容量限制约束下, 构建中断情境下应急设施的可靠性选址决策优化模型。针对所构建模型的特性利用非支配排序多目标遗传算法(NSGA-Ⅱ)求解该模型, 得到多目标的Pareto前沿解集。以不同的算例分析和验证模型和算法的可行性。在获得Pareto前沿的同时对不同中断概率进行灵敏度分析, 给出Pareto最优解集的分布及应急设施选址布局网络的拓扑结构。     

Integrated location and two-echelon inventory network design under uncertainty

In this paper, we propose a two-stage stochastic model to address the design of an integrated location and two-echelon inventory network under uncertainty. The central issue in this problem is to design and operate an effective and efficient multi-echelon supply chain distribution network and to minimize the expected system-wide cost of warehouse location, the allocation of warehouses to retailers, transportation, and two-echelon inventory over an infinite planning horizon. We structure this problem as a two-stage nonlinear discrete optimization problem. The first stage decides the warehouses to open and the second decides the warehouse-retailer assignments and two-echelon inventory replenishment strategies. Our modeling strategy incorporates various probable scenarios in the integrated multi-echelon supply chain distribution network design to identify solutions that minimize the first stage costs plus the expected second stage costs. The two-echelon inventory cost considerations result in a nonlinear objective which we linearize with an exponential number of variables. We solve the problem using column generation. Our computational study indicates that our approach can solve practical problems of moderate-size with up to twenty warehouse candidate locations, eighty retailers, and ten scenarios efficiently.     

带批次和临时库存的越库配送车辆路径问题研究

从零售业供应链整合入手,构建供应商、配送中心和零售点构成的协同配送网络,研究带批次和临时库存的越库配送车辆路径问题.将越库过程分为取货、分拣和配货三个阶段,考虑配送中心分拣能力,分批次设置车辆协同到达配送中心的服务时刻,据此建立以最小化车辆运输成本、临时库存成本和固定成本为目标的数学模型.考虑问题特征,设计一种混合变邻域搜索粒子群算法求解,并将结果进行横纵向比较.结果表明,所提算法有效且可靠,能够为带批次和临时库存的越库配送问题提供解决方案.     

Network location problems with continuous link demands: p-medians on a chain and 2-medians on a tree

This paper is concerned with minisum location-allocation problems on undirected networks in which demands can occur on links with uniform probability distributions. Two types of networks are considered. The first type considered is simply a chain graph. It is shown that except for the 1-median case, the problem is generally non-convex. However, for the p-median case, a discrete set of potential optimal facility locations may be identified, and hence it is shown that all local and global minima to the problem may be discovered by solving a series of trivial linear programming problems. This analysis is then extended to prescribe an algorithm for the 2-median location-allocation problem on a tree network involving uniform continuous demands on links. Some localization theorems are presented in the spirit of the work done on discrete nodal demand problems.     

A dynamic inventory model with supplier selection in a serial supply chain structure

Considering the inherent connection between supplier selection and inventory management in supply chain networks, this article presents a multi-period inventory lot-sizing model for a single product in a serial supply chain, where raw materials are purchased from multiple suppliers at the first stage and external demand occurs at the last stage. The demand is known and may change from period to period. The stages of this production–distribution serial structure correspond to inventory locations. The first two stages stand for storage areas for raw materials and finished products in a manufacturing facility, and the remaining stages symbolize distribution centers or warehouses that take the product closer to customers. The problem is modeled as a time-expanded transshipment network, which is defined by the nodes and arcs that can be reached by feasible material flows. A mixed integer nonlinear programming model is developed to determine an optimal inventory policy that coordinates the transfer of materials between consecutive stages of the supply chain from period to period while properly placing purchasing orders to selected suppliers and satisfying customer demand on time. The proposed model minimizes the total variable cost, including purchasing, production, inventory, and transportation costs. The model can be linearized for certain types of cost structures. In addition, two continuous and concave approximations of the transportation cost function are provided to simplify the model and reduce its computational time.     

The \alpha -cost minimization model for capacitated facility location-allocation problem with uncertain demands

Facility location-allocation problem aims at determining the locations of some facilities to serve a set of spatially distributed customers and the allocation of each customer to the facilities such that the total transportation cost is minimized. In real life, the facility location-allocation problem often comes with uncertainty for lack of the information about the customers’ demands. Within the framework of uncertainty theory, this paper proposes an uncertain facility location-allocation model by means of chance-constraints, in which the customers’ demands are assumed to be uncertain variables. An equivalent crisp model is obtained via the \(\alpha \) -optimistic criterion of the total transportation cost. Besides, a hybrid intelligent algorithm is designed to solve the uncertain facility location-allocation problem, and its viability and effectiveness are illustrated by a numerical example.     

考虑设施中断情景的震后救援初期应急物流网络优化设计

在震后救援初期,构建合理的应急物流网络,对于快速有效供应应急物资、减轻灾情具有重大价值。在传统可靠性选址问题与应急设施选址-分配问题的基础上,考虑震后救援初期的阶段性特征、设施中断情景、多品种模糊需求、设施能力限制等因素,建立了一个适用于震后救援初期的应急设施选址-分配模型。通过三角模糊数的期望值公式将模糊需求去模糊化。在此基础上,考虑模型特点,设计了一种整数编码的混合遗传算法。最后,以5·12汶川地震为背景,构造算例进行数值仿真。验证了所提模型和算法。结果表明:考虑设施中断情景后,即使系统中的部分设施失效,整个网络仍能较好运行,且优化结果更具可靠性和稳健性。     

基于时间的随机需求二级分销网络物流系统集成优化研究

分销网络设计包括设施选址、库存控制、运输等方面的设计与优化,但以往只是从战略层、战术层、运作层来分别进行各自的研究。实际上,这三个层次的决策要素之间存在着复杂的互动关系,并存在着广泛的效益悖反关系,这些在变化的环境下显得尤为突出。本文充分考虑时间因素的重要性,从物流系统的集成优化高度出发,研究建立需求随机的多分销中心多顾客的设施选址———运输路线安排———库存控制问题(ILRIP)的模型,对此设计了一个两层粒子群优化(PSO)算法,并给出了计算实例。研究结果有助于供应链分销网络的集成优化,缩短商品流转周期,提高顾客服务水平,提升竞争力。     

Designing two-echelon supply networks

A modern distribution network design model needs to deal with the trade-offs between a variety of factors, including (1) location and associated (fixed) operating cost of distribution centers (DCs), (2) total transportation costs, and (3) storage holding and replenishment costs at DCs and retail outlets. In addition, network design models should account for factors such as (4) stockouts, by setting appropriate levels of safety stocks, or (5) capacity concerns, which may affect operating costs in the form of congestion costs. The difficulty of making such trade-offs is compounded by the fact that even finding the optimal two-echelon inventory policy in a fixed and uncapacitated distribution network is already a hard problem. In this paper, we propose a generic modeling framework to address these issues that continues and extends a recent stream of research aimed at integrating insights from modern inventory theory into the supply chain network design domain. Our approach is flexible and general enough to incorporate a variety of important side constraints into the problem.     

Characterization of facility assignment costs for a location-inventory model under truckload distribution

We consider a two-stage distribution system, where the first stage consists of potential distribution centres (DCs) and the second stage consists of geographically dispersed existing retailers. Our goal is to determine the set of open DCs and assignment of open DCs to retailers simultaneously with inventory decisions of retailers. In addition to the DC-specific fixed facility location costs, we explicitly model the inventory replenishment and holding costs at the retailers and truckload transportation costs between the DCs and the retailers. The transportation costs are subject to truck/cargo capacity, leading to an integrated location-inventory problem with explicit cargo costs. We develop a mixed-integer nonlinear model and analyse its structural properties leading to exact expressions for the so-called implied facility assignment costs and imputed per-unit per-mile transportation costs. These expressions analytically demonstrate the interplay between strategic location and tactical inventory/transportation decisions in terms of resulting operational costs. Although both the theory and practice of integrated logistics have recognized the fact that strategic and tactical decisions are interrelated, to the best of our knowledge, our paper is the first to offer closed-form results demonstrating the relationship explicitly. We propose an efficient solution approach utilizing the implied facility assignment costs and we demonstrate that significant savings are realizable when the inventory decisions and cargo costs are modelled explicitly for facility location purposes.     

考虑共享不确定因素的应急设施最大覆盖选址模型

为提升应急设施的服务质量和抵御中断风险的能力,研究应急设施最大覆盖选址-分配决策问题。扩展无容量限制的固定费用的可靠性选址决策模型,建立考虑共享不确定因素的应急设施最大覆盖选址优化模型,通过在目标和约束中引入budget不确定集刻画共享不确定因素,基于Bertsimas和Sim鲁棒优化方法建立混合整数规划模型,并将非线性问题转化为易于求解的鲁棒等价模型,利用带混沌搜索策略的改进灰狼优化算法求解模型,并对不确定鲁棒水平和中断概率进行敏感性分析。最后通过案例及数据仿真结果的对比分析,验证了模型的合理性和有效性,并给出最优的选址分配布局。     

一类自由作业供应链排序的研究

本文研究一类集成工件生产和发送的排序模型.在该模型中,供应链的上游首先将工件安排在自由作业机器上加工,然后把加工完毕的工件分批发送给下游.问题是寻找生产和发送相连的排序,使得生产排序费用和发送费用总和最少.这里,生产排序费用是以工件带权送到时间和表示;发送费用由固定费用和与运输路径有关的变化费用组成.在指出问题的NP困难性后,本文用动态规划算法构造了一致条件下的多项式时间近似算法,并分析算法的性能比.本文最后还讨论了该问题的其它情形.     

Simulated N-Body: New Particle Physics-Based Heuristics for a Euclidean Location-Allocation Problem

The general facility location problem and its variants, including most location-allocation and P-median problems, are known to be NP-hard combinatorial optimization problems. Consequently, there is now a substantial body of literature on heuristic algorithms for a variety of location problems, among which can be found several versions of the well-known simulated annealing algorithm. This paper presents an optimization paradigm that, like simulated annealing, is based on a particle physics analogy but is markedly different from simulated annealing. Two heuristics based on this paradigm are presented and compared to simulated annealing for a capacitated facility location problem on Euclidean graphs. Experimental results based on randomly generated graphs suggest that one of the heuristics outperforms simulated annealing both in cost minimization as well as execution time. The particular version of location problem considered here, a location-allocation problem, involves determining locations and associated regions for a fixed number of facilities when the region sizes are given. Intended applications of this work include location problems with congestion costs as well as graph and network partitioning problems.     

An integrated framework for inventory management and transportation of refined petroleum products: Pipeline or marine?

We study the integrated problem of managing inventory of refined petroleum products, and their multi-modal (ships and pipeline) transportation between a refinery and the served distribution centers. It is important that the transportation decisions are driven not just by the inventory levels and customer demand, but also the environmental risks associated with different refined products. A bi-objective mixed integer linear programming optimization model (MILP) is proposed, where constituent components were independently developed and then interfaced to capture the complexity of the resulting integrated model. A time-based decomposition heuristic is also employed to solve the integrated problem. The proposed framework was used to study a number of problem instances generated using a realistic infrastructure in the United States, and the resulting analyses lead to the following inferences: pipeline is the preferred mode of transportation only when cost is the sole consideration; on the other hand, when environmental risks are considered marine is the preferred mode for most of the refined petroleum products, except for heavier oils; and, the proportion of traffic on the two modes is a function of the type and volume of products, and the number of vessels available at the start of the planning horizon.     

A genetic algorithm for a single product network design model with lead time and safety stock considerations

We consider a two-stage supply chain with a production facility that replenishes a single product at retailers. The objective is to locate distribution centers in the network such that the sum of facility location, pipeline inventory, and safety stock costs is minimized. We explicitly model the relationship between the flows in the network, lead times, and safety stock levels. We use genetic algorithms to solve the model and compare their performance to that of a Lagrangian heuristic developed in earlier work. A novel chromosome representation that combines binary vectors with random keys provides solutions of similar quality to those from the Lagrangian heuristic. The model is then extended to incorporate arbitrary demand variance at the retailers. This modification destroys the structure upon which the Lagrangian heuristic is based, but is easily incorporated into the genetic algorithm. The genetic algorithm yields significantly better solutions than a greedy heuristic for this modification and has reasonable computational requirements.     

电子商务环境下考虑退货的选址库存问题模型与算法

选址库存问题(location inventory problem, LIP)是物流系统集成的经典问题之一,也是企业需要面对的管理决策难题。本文考虑在电子商务环境下无质量缺陷的退货商品可简单再包装后重新进入销售市场这一现实情况,对设施选址和库存控制进行集成优化,构建随机需求下有退货的LIP模型。针对此问题求解的复杂性,设计了改进的自适应混合差分进化算法对模型进行整体求解。最后,通过多组算例验证了模型和算法的实用性和优越性,可为设施选址、库存控制和商品配送回收决策提供重要参考依据。     

Multi-location transshipment problem with capacitated transportation

We consider coordination among stocking locations through replenishment strategies that take explicitly into consideration transshipments, transfer of a product among locations at the same echelon level. We incorporate transportation capacity such that transshipment quantities between stocking locations are bounded due to transportation media or the location’s transshipment policy. We model different cases of transshipment capacity as a capacitated network flow problem embedded in a stochastic optimization problem. Under the assumption of instantaneous transshipments, we develop a solution procedure based on infinitesimal perturbation analysis to solve the stochastic optimization problem, where the objective is to find the policy that minimizes the expected total cost of inventory, shortage, and transshipments. Such a numerical approach provides the flexibility to solve complex problems. Investigating two problem settings, we show the impact of transshipment capacity between stocking locations on system behavior. We observe that transportation capacity constraints not only increase total cost, they also modify the inventory distribution throughout the network.     

Inventory sharing in integrated network design and inventory optimization with low-demand parts

Service Parts Logistics (SPL) problems induce strong interaction between network design and inventory stocking due to high costs and low demands of parts and response time based service requirements. These pressures motivate the inventory sharing practice among stocking facilities. We incorporate inventory sharing effects within a simplified version of the integrated SPL problem, capturing the sharing fill rates in 2-facility inventory sharing pools. The problem decides which facilities in which pools should be stocked and how the demand should be allocated to stocked facilities, given full inventory sharing between the facilities within each pool so as to minimize the total facility, inventory and transportation costs subject to a time-based service level constraint. Our analysis for the single pool problem leads us to model this otherwise non-linear integer optimization problem as a modified version of the binary knapsack problem. Our numerical results show that a greedy heuristic for a network of 100 facilities is on average within 0.12% of the optimal solution. Furthermore, we observe that a greater degree of sharing occurs when a large amount of customer demands are located in the area overlapping the time windows of both facilities in 2-facility pools.