The maximin gradual cover location problem

In this paper, we consider the multiple facility location problem with gradual cover. Gradual cover means that up to a certain distance from the facility a demand point is fully covered. Beyond another distance the demand point is not covered at all. Between these two distances the demand point is partially covered. When there are \(p\) facilities, the cover of each demand point can be calculated by a given formula. One objective in this setting is to find locations for \(p\) facilities that maximize the total cover. In this paper we consider another objective of maximizing the minimum cover of every demand point. This guarantees that every demand point is covered as much as possible and there are no demand points with low cover. The model is formulated and heuristic algorithms are proposed for its solution. We solved a real-life problem of locating cell phone towers in northern Orange County, California and demonstrated the solution approach on a set of 40 test problems.     

Locating capacitated facilities to maximize captured demand

We consider the problem of locating a set of facilities on a network to maximize the expected number of captured demand when customer demands are stochastic and congestion exists at facilities. Customers travel to their closest facility to obtain service. If the facility is full (no more space in the waiting room), they attempt to obtain service from the next-closest facility not yet visited from its current position on the network. A customer is lost either when the closest facility is located too far away or all facilities have been visited. After formulating the model, we propose two heuristic procedures. We combine the heuristics with an iterative calibration scheme to estimate the expected demand rate faced by the facilities: this is required for evaluating objective function values. Extensive computational results are presented.     

Satisfying partial demand in facilities location

In this paper we consider the location of new facilities which serve only a certain proportion of the demand. The total weighted distances of the served demand is minimized. We consider the problem in the plane for the location of one facility and on a network for the location of >m-facilities. Some computational experience with these models are reported.     

A large-scale hybrid simulated annealing algorithm for cyclic facility layout problems

The cyclic facility layout problem (CFLP) is a special case of the dynamic facility layout problem (DFLP) in which there are several production periods and the production cycle repeats itself by going to the first period after the last one because of the seasonal nature of products. In this article, a mixed integer programming formulation is developed for the CFLP. In the DFLP literature, department shapes are assumed to be given or fixed. However, this assumption does not hold in the case of the CFLP because the facility size is limited and the area requirements of the departments change significantly throughout the planning horizon. Therefore, department dimensions and sizes are considered as decision variables in the CFLP. A large-scale hybrid simulated annealing algorithm (LS-HSA) is proposed to solve the formulated problem and shown to be effective and versatile as it can be applied to various facility layout problems.     

Locating service facilities to reduce lost demand

We analyze the problem of locating a set of service facilities on a network when the demand for service is stochastic and congestion may arise at the facilities. We consider two potential sources of lost demand: (i) demand lost due to insufficient coverage; and (ii) demand lost due to congestion. Demand loss due to insufficient coverage arises when a facility is located too far away from customer locations. The amount of demand lost is modeled as an increasing function of the travel distance. The second source of lost demand arises when the queue at a facility becomes too long. It is modeled as the proportion of balking customers in a Markovian queue with a fixed buffer length. The objective is to find the minimum number of facilities, and their locations, so that the amount of demand lost from either source does not exceed certain pre-set levels. After formulating the model, we derive and investigate several different integer programming formulations, focusing in particular on alternative representations of closest assignment constraints. We also investigate a wide variety of heuristic approaches, ranging from simple greedy-type heuristics, to heuristics based on time-limited branch and bound, tabu search, and random adaptive search heuristics. The results of an extensive set of computational experiments are presented and discussed.     

A modeling framework for facility location of medical services for large-scale emergencies

Research on facility location is abundant. However, this research does not typically address the particular conditions that arise when locating facilities to service large-scale emergencies, such as earthquakes, terrorist attacks, etc. In this work we first survey general facility location problems and identify models used to address common emergency situations, such as house fires and regular health care needs. We then analyze the characteristics of large-scale emergencies and propose a general facility location model that is suited for large-scale emergencies. This general facility location model can be cast as a covering model, a P-median model or a P-center model, each suited for different needs in a large-scale emergency. Illustrative examples are given to show how the proposed model can be used to optimize the locations of facilities for medical supplies to address large-scale emergencies in the Los Angeles area. Furthermore, comparison of the solutions obtained by respectively using the proposed model and the traditional model is given to show the benefits of the proposed model in reducing loss of life and economic losses.     

The impact of client choice on preventive healthcare facility network design

In contrast with sick people who need urgent medical attention, the clientele of preventive healthcare have a choice in whether to participate in the programs offered in their region. In order to maximize the total participation to a preventive care program, it is important to incorporate how potential clients choose the facilities to patronize. We study the impact of client choice behavior on the configuration of a preventive care facility network and the resulting level of participation. To this end, we present two alternative models: in the “probabilistic-choice model” a client may patronize each facility with a certain probability, which increases with the attractiveness of the available facilities. In contrast, the “optimal-choice model” stipulates that each client will go to the most attractive facility. In this paper, we assume that the proximity to a facility is the only attractiveness attribute considered by clients. To ensure the quality of care, we impose a bound on the mean waiting time as well as a minimum workload requirement at each open facility. Subject to a total capacity limit, the number of open facilities as well as the location and the capacity (number of servers) of each open facility is the main determinant of the configuration of a facility network. Both models are formulated as a mixed-integer program. To solve the problems efficiently, we propose a probabilistic search algorithm and a genetic algorithm. Finally, we use the models to analyze the network of mammography centers in Montreal.     

Pricing and location decisions in multi-objective facility location problem with M/M/m/k queuing systems

This article presents a new multi-objective model for a facility location problem with congestion and pricing policies. This model considers situations in which immobile service facilities are congested by a stochastic demand following M/M/m/k queues. The presented model belongs to the class of mixed-integer nonlinear programming models and NP-hard problems. To solve such a hard model, a new multi-objective optimization algorithm based on a vibration theory, namely multi-objective vibration damping optimization (MOVDO), is developed. In order to tune the algorithms parameters, the Taguchi approach using a response metric is implemented. The computational results are compared with those of the non-dominated ranking genetic algorithm and non-dominated sorting genetic algorithm. The outputs demonstrate the robustness of the proposed MOVDO in large-sized problems.     

Applying genetic algorithm to a new location and routing model of hazardous materials

Nowadays – particularly in systems dealing with hazardous materials (HAZMAT) – in addition to minimising the cost of operations in facility location and routing problems, the risk of these operations is considered an important objective. In this paper, a new mathematical model for the location and routing in facilities and disposal sites is proposed. Also, the risk and cost of transporting goods from facilities to customers is considered. The model minimises weighted sum of the cost and risk by answering these questions: (1) where to open the facilities which produce HAZMAT; (2) where to open disposal sites; (3) to which facilities every customer should be assigned; (4) to which disposal site each facility should be assigned; (5) which route a facility should choose to serve the customers; and (6) which route a facility should choose to reach a disposal site. A novel GA is applied to solve the mathematical model. The results show the robustness of GA in terms of finding high-quality non-dominated solutions and running time.     

A heuristic approach on the facility layout problem based on game theory

Facility layout problems are related to the location of all facilities in a plant. Numerous research works related to facility layout have been published. The applicability of these various existing models may be limited by the fact that they all ignore competitive reactions to one's actions. In addition to external competitors, some internal problems of system such as material handling system design affect layout designs. For considering these effects, some researchers have investigated multi-objective approaches that in most cases lead to the optimisation of a weighted sum of score functions. The poor practicability of such an approach is due to the difficulty of normalising these functions and quantifying the weights. To the extent that competitors do react to a firm's actions and also the facility layout problem considers several conflicting objectives by distinct decision makers in the firm, the existing models may be oversimplifications of reality. In this paper, we modelled such a facility layout problem with conflicting objectives under a duopoly Bertrand competition as a game and solved it with a proposed simulated annealing meta-heuristic. Results obtained from solving some numerical examples confirm the effectiveness of the proposed model for the layout design.     

Multi-level supply chain network design with routing

Recently, the multi-level and multi-facility industrial problem in supply chain management (SCM) has been widely investigated. One of the key issues, central to this problem in the current SCM research area is the interdependence among the location of facilities, the allocation of facilities, and the vehicle routing for the supply of raw materials and products. This paper studies the supply chain network design problem, which involves the location of facilities, allocation of facilities, and routing decisions. The proposed problem has some practical applications. For example, it is necessary for third party logistics (3PL) companies to manage the design of the network and to operate vehicle transportation. The purpose of this study is to determine the optimal location, allocation, and routing with minimum cost to the supply chain network. The study proposes two mixed integer programming models, one without routing and one with routing, and a heuristic algorithm based on LP-relaxation in order to solve the model with routing. The results show that a developed heuristic algorithm is able to find a good solution in a reasonable time.     

The Uncapacitated Facility Location Problem With Primary and Secondary Facility Requirements

We consider the problem of locating uncapacitated facilities among a set of potential sites to minimize cost of serving a number of demand points each requiring service from two different facilities. This problem has many potential applications. One such application is location of emergency service facilities where it is desirable to have a primary and back-up service facility wthin a certain distance from every district An efficient solution procedure is developed. This procedure is tested on a number of problems and computational results are reported. It is compared to a state of the art commercial linear/integer programming package and found to be around two orders of magnitude faster than this package. It is also compared to a state of the art special purpose agorithm for the simple uncapacitated facility location problem to investigate the computational implications of introducing secondary service requirements. The model is used to illustrate the effect of considering secondary service on the spatial characteristics of the optimal set of locations. The model is further demonstrated on a “real life” example with 625 demand points and 30 potential facility locations.     

Facility location under uncertainty: a review

Plants, distribution centers, and other facilities generally function for years or decades, during which time the environment in which they operate may change substantially. Costs, demands, travel times, and other inputs to classical facility location models may be highly uncertain. This has made the development of models for facility location under uncertainty a high priority for researchers in both the logistics and stochastic/robust optimization communities. Indeed, a large number of the approaches that have been proposed for optimization under uncertainty have been applied to facility location problems. This paper reviews the literature on stochastic and robust facility location models. Our intent is to illustrate both the rich variety of approaches for optimization under uncertainty that have appeared in the literature and their application to facility location problems. In a few instances for which examples in facility location are not available, we provide examples from the more general logistics literature.     

Designing self-storage warehouses with customer choice

Self-storage warehousing is a rapidly growing industry where consumers or companies can rent storage space for personal or company use, over a certain horizon. This paper addresses the question of how to design the facilities so that revenue can be maximised over a finite horizon, considering multiple demand requirements with respect to size, pricing, location within the facility, climate control, security or outside access, among others. Using a customer choice model to specify the probability of purchase for each fare product as a function of the set of fare products offered, we propose methods to design self-storage warehouses while allowing different customer choice behaviours. We model the problem as a mixed-integer program and solve it using column generation and branch-and-price algorithms. In addition, we study the impact of re-layout and methods to modify facility layout, since self-storage facilities are relatively flexible in layout and individual storage compartments can be adapted to changes in demand. We validate our model using the data of four self-storage warehouses, and show our method can improve the expected revenue by nearly 11% on average for these cases.     

On the impact of spatial pattern,aggregation, and model parameters in planar Huff-type competitive location and design problems

A chain wants to set up a single new facility in a planar market where similar facilities of competitors, and possibly of its own chain, are already present. Fixed demand points split their demand probabilistically over all facilities in the market proportionally with their attraction to each facility, determined by the different perceived qualities of the facilities and the distances to them, through a gravitational or logit type model. Both the location and the quality (design) of the new facility are to be found so as to maximize the profit obtained for the chain. Several types of constraints and costs are considered. Applying an interval analysis based global optimization method on several spatial patterns in a quasi-real-world environment, the behaviour of optimal solutions is investigated when changes are made in the basic model parameters. The study yields valuable insight for modellers into the impact of spatial pattern and various model parameters of the model on the resulting location and design decision. Spatial patterns differ in distribution of demand, of own and/or competing facilities, and of facility qualities. Studied model parameters include push force effects, investment restrictions and aggregation of demand. An extended version of this paper including additional studies on model parameters and the exact data used in the computational experiments is available at Optimization Online (see Tóth et al. (2008)). This work has been supported by grants from the Ministry of Science and Innovation of Spain (TIN2008-01117, SEJ2005-06273/ECON and ECO2008-00667/ECON), Junta de Andalucía (P08-TIC-3518), and in part by the European Regional Development Fund (ERDF).     

Optimising the location of crossovers in conveyor-based automated material handling systems in semiconductor wafer fabs

This research presents several heuristics to optimise the location of crossovers in a conveyor-based automated material handling system (AMHS) for a semiconductor wafer fabrication facility. The objective is to determine the location of crossovers that minimises the total cost of the expected work-in-process on the conveyor and the cost of installing and operating the AMHS with the crossovers. The proposed heuristics are integrated with a queuing-based analytical model incorporating practical hardware considerations of the AMHS, such as turntables and crossovers. To illustrate the proposed heuristics’ practical application they are applied to SEMATECH's virtual wafer fabrication facility. Experimental results demonstrate that under a wide variety of operating conditions and cost scenarios the local improvement heuristic is able to identify the optimal solution and outperform other commonly used heuristics for layout design such as genetic algorithms.     

不确定环境下应急设施选址问题两阶段鲁棒优化模型

对于应急物流管理而言,应急物资集散中心选址是一个重要的决策要素。针对应急突发事件的不确定性特征,本文提出了一个应急设施选址问题两阶段鲁棒优化模型,以实现“预选址-重选址”两者的协同优化。第一阶段在需求和成本变动、设施损毁存在不确定因素的情况下,综合考虑选址策略在灾前规划、灾后反应、设施重建阶段的不同需求,建立了一种基于p-center的鲁棒“预选址”模型;第二阶段针对灾后新信息的获得,建立了一种基于反应式修复和调整策略的新建设施“重选址”模型。算例分析表明,本文模型对于应急设施选址问题比传统p-center模型更为合理有效     

考虑市场扩张和吞并的新设施竞争选址模型

连锁型企业新设施的选址在市场扩张中占有至关重要的地位.提出了连锁型企业新设施进入产生两个结果:带来市场需求的扩张和对企业内部已存设施的市场侵蚀,建立了使连锁企业市场份额最大和企业内已存设施市场吞并最小的新设施选址的双目标模型,并给出了求解模型的遗传算法和具体的案例.结果表明该模型和算法可以用于连锁型企业新设施选址决策中,并能够有效的得到问题的近似解.     

MULTI-HOPE: A tool for multiple floor layout problems

The objective of most facility layout problems is to minimize material handling cost, which is directly proportional to both the distance between the machines and the mix, as well as the volume of products handled. The mix and volume of products are dependent on the demand patterns, and the distance is dependent on the layout plan used for the facility. Because it is relatively difficult to change the demand patterns, and hence the mix and volume of products, the primary focus of most designers has been to deal with the distance attribute of the material handling costs. The limitations of available horizontal space create a need to explore vertical expansion of facilities. This brings up new aspects of vertical material handling and flow that need to be considered in the facility design problem. In this paper, we present a genetic algorithm-based heuristic for generating block layouts for multiple-floor layout problems. This approach produces better solutions than existing simulated annealing-based heuristics for all but one of five multiplefloor test problems available in the literature.