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Locating Facilities in the Presence of Disruptions and Incomplete Information
Abstract
ABSTRACT In this article, we analyze a location model where facilities may be subject to disruptions. Customers do not have advance information about whether a given facility is operational or not, and thus may have to visit several facilities before finding an operational one. The objective is to locate a set of facilities to minimize the total expected cost of customer travel. We decompose the total cost into travel, reliability, and information components. This decomposition allows us to put a value on the advance information about the states of facilities and compare it to the reliability and travel cost components, which allows a decision maker to evaluate which part of the system would benefit the most from improvements. The structure of optimal solutions is analyzed, with two interesting effects identified: facility centralization and co-location; both effects appear to be stronger than in the complete information case, where the status of each facility is known in advance.
... Most of these reliable facility location models assume that perfect information about all facility functioning states is available to customers in real time and thus they always know a proper facility to visit (e.g., the closest operating facility). However, because of institutional barriers (Birenbaum, 2009), technical constraints (Baillieul and Antsaklis, 2007), and customer unpreparedness (Berman et al., 2009), this assumption might not always reflect reality. Furthermore, because of likely communication and infrastructure disruptions, it is even more difficult to access real-time facility states in unexpected emergency scenarios (Hasan and Folient, 2015). ...
... Under imperfect information, customers do not know real-time states of facilities, thus they have to visit a series of pre-assigned facilities until they either find a functioning facility to get the service or abort the attempt, receiving a penalty instead. Only a few studies have investigated this type of location problems under imperfect information (Berman et al., 2009;Yun et al., 2015Yun et al., , 2017. These studies contributed to modeling reliable location design with imperfect information with a focus on outbound transportation cost (for a customer to reach the service from her home). ...
... Some researchers proposed a few models to deal with these reliable facility location problems. Berman et al. (2009) investigated the median location problem. This study considers that a customer always tries facilities according to their distances from this customer in any facility disruption scenario. ...
In this paper, we propose a discrete model to investigate reliable location design with round-trip transportation under imperfect information. The unique feature of this problem is that under each disruption scenario, a customer’s outbound and inbound trips are different when she travels to obtain a service. The discrete model is formulated as a compact non-linear integer programming problem and solved efficiently by a customized Lagrangian relaxation algorithm. Numerical experiments find that the discrete model performs well for small and medium-scale problem instances. Sensitivity analyses reveal the impacts of several parameters on both the cost components and the optimal facility layouts.
... earthquakes, floods, and hurricanes), terrorist attacks, labor strikes, political instability, power outages, sabotage or even equipment breakdowns. Some events such as the Severe Acute Respiratory Syndrome (SARS) outbreak in Asia, the September 11, 2001 terrorist attack, the hurricanes Katrina and Rita (2005), and more recent disasters like earthquake and Tsunami in Japan, 2011, highlighted the necessity to protect supply chains against disruption (Berman et al. 2009). ...
... In the study of Berman et al. (2009), the location of facilities is addressed in an environment that customers are not aware in advance about whether a given facility is operational or not, therefore they may go to several facilities to find an operational one. Seeking for automated teller machines (ATMs) is an example, where a customer may have to try several ATMs before finding one able to provide service, due to network disruptions, maintenance, etc. ...
This paper seeks to develop a reliable network of cross-docks by taking in to account disruption and reliability issues to hedge against heterogeneous risk of cross-docking failure. In real environments, applying a recovery policy can be a feasible strategy to handle disruptions. Hence, in this study, a recovery policy has been addressed in the form of reallocating suppliers to alternative cross-docks or altering the transportation strategy to move shipments. In addition to cross-dock location design, the optimum capacity of opened cross-docks will be determined considering the loads that will be served by each cross-docking center under regular and disruption conditions. A mixed integer nonlinear programming formulation is presented for the problem and is then linearized to present an efficient model. In order to solve it, two Lagrangian relaxation algorithms are designed and tested on 40 problem instances with different values of parameters. The results achieved by GAMS/CPLEX are compared with those of two algorithms and some analyses are performed on the solutions. Moreover, as the case study, the focus has been placed on logistic part of a car-manufacturing company with a vast supply chain network, containing more than 600 suppliers. The logistic strategies have been applied in order to reduce the transportation cost through the supply chain network and diminish the disruption subsequences in such a network. Based on the results, some managerial recommendations are presented.
... This "trial-and-error" visiting behavior further complicates quantification of associated operational costs. Only a few studies have been conducted for suitable reliable facility location design[15,16]under imperfect information. All these studies assume that all candidate facilities have the identical independent disruption probabilities, while site-dependent disruptions under imperfect information remain unaddressed probably due to modeling difficulties. ...
... On the other hand, a handful of studies investigated reliable location problems under imperfect information. Berman et.al[15]proposed the reliable p-median facility location model with imperfect information by assuming that the customer always visits the closest facility one by one in any facility disruption scenario. This assumption may yield a significantly higher cost compared to the true optimal sequence. ...
This paper proposes a reliable facility location design model under imperfect information with site-dependent disruptions; i.e., each facility is subject to a unique disruption probability that varies across the space. In the imperfect information contexts, customers adopt a realistic “trial-and-error” strategy to visit facilities; i.e., they visit a number of pre-assigned facilities sequentially until they arrive at the first operational facility or give up looking for the service. This proposed model aims to balance initial facility investment and expected long-term operational cost by finding the optimal facility locations. A nonlinear integer programming model is proposed to describe this problem. We apply a linearization technique to reduce the difficulty of solving the proposed model. A number of problem instances are studied to illustrate the performance of the proposed model. The results indicate that our proposed model can reveal a number of interesting insights into the facility location design with site-dependent disruptions, including the benefit of backup facilities and system robustness against variation of the loss-of-service penalty.
... The assumption of uniform failure probabilities may seem too hard but in the location literature there are many cases of this application. Some examples in which all facilities fail with the same degree of probability are ATM's [3] and traffic surveillance sensors [15,16]. In both cases the common failure probability is obtained from past history performance statistics. ...
... Berman et al. [3] were the first in this field of research to introduce incomplete information to the problem. The authors analyze a multi-level reliability model with uniform failure probabilities and incomplete information. ...
The Reliability Fixed-Charge Location Problem is an extension of the Simple Plant Location Problem that considers that some facilities have a probability of failure. In this paper we reformulate the original mathematical programming model of the Reliability Fixed-Charge Location Problem as a set packing problem. We study certain aspects of its polyhedral properties, identifying all the clique facets. We also discuss how to obtain facets of the Reliability Fixed-Charge Location Problem from facets of the Simple Plant Location Problem. Subsequently, we study some conditions for optimal solutions. Finally, we propose an improved compact formulation for the problem and we check its performance by means of an extensive computational study.
... Among them, some considered the correlated probabilistic disruptions (Li & Ouyang, 2010; and the uncertain disruptions (Lu et al., 2015;Li et al., 2022). Several researches (Berman et al., 2009;Yun et al., 2014;Albareda-Sambola et al., 2015) investigated the case of incomplete information where the operational state of a facility is unknown before reaching it and thus customers should optimize the routing decision to find a functional facility efficiently. Some papers considered the option of facility hardening to prevent disruptions, in which the facilities to fortify should be selected and sometimes under a budget constraint (Lim et al., 2010;Afify et al., 2019). ...
This paper studies a framework of Reliable Capacitated Facility Location Problem with Single source constraint, which allows us to capture the mental account management problem for a bank under uncertain environment. In the problem, each facility, corresponding to a financial product, has limited capacity and may fail randomly, which represents that the product fails to reach the threshold level of return. Each customer, corresponding to a mental account, is served by a single primary facility or product, and its demands, or the setting goals, can be split on several backup facilities or alternative investments with redundant capacity. With the operation, a portion of the satisfaction can still be met by the backup facilities when the primary service of a customer fails. We formulate a mixed integer programming model for the problem and design a Lagrangian relaxation based solution algorithm, which sophisticatedly exploits the structure of the model and transfers the complicated relaxation problems into 0–1 knapsack problems to reduce the complexity. A local search procedure is also incorporated into the algorithm to enhance the accuracy of small- and large-scale computation. Finally, a real-life case of mental accounting is investigated to illustrate the application of the decision model.
... Considering multiple sourcing for outsourced items, backup suppliers, extra inventory, and recovery and protection plans for some of the suppliers are introduced by Torabi et al. (2015). Most of the previous studies consider only the disruption risks in the SCs facilities that cause them (suppliers, manufacturers, DCs, and connection links) complete or partial breakdown of service or inaccessibility (Lee, 2001;Snyder et al., 2006;Aryanezhad and Jabbarzadeh, 2009;Berman et al., 2009;Liu et al., 2010;Peng et al., 2011). Jabbarzadeh et al. (2012) studied the SCND problem under the risk of disruption at facilities. ...
Nowadays, sustainability has become an integral part of industries and supply chains, which are facing the risk of unpredictable disruptions. Therefore, the capability of the supply chains to thwart the harmful effects of disruptions using preventive and recovery policies cannot be neglected. In this respect, this study addresses bi-level programming to optimize a sustainable supply chain by considering resilience factors and pricing decisions. Moreover, it is defined how the governments can optimize and affect environmental and social responsibility by setting an emissions tax rate. In the developed model, Stackelberg game model is employed while the government is considered as the leader and the manufacturer as the follower. Furthermore, the results of the model are compared with the centralized one indicating that the centralized model will result in a better solution for both the manufacturer and the government. Moreover, the results express that keeping emergency stock strategy always is suggested but considering multiple suppliers and extra reserved capacity are not always preferable for mitigating the adverse effect of disruptions in the investigated case study. For highlighting the efficiency of the proposed model, it has been implemented in a real case, and the managerial insights ensuing from the results of the case study are provided.
... As a strategic decision in SCND models, appropriate location of facilities can reduce the impact of disruptions and empower the SCs to be reliable enough against disruption risks. The majority of research assumes that disruption in the facilities of SC (suppliers, manufacturers, distribution centers, etc.) makes them entirely or partially inaccessible or unreachable (Lee 2001;Snyder et al. 2006;Berman et al. 2009;Aryanezhad and Jabbarzadeh 2009;Liu et al. 2010;Diabat et al. 2019;Ghavamifar and Sabouhi 2018;Jabbarzadeh et al. 2018b;Peng et al. 2011). Most of researchers consider uncertainty in supply side (Shen and Daskin 2005;You and Grossmann 2008;Cardona-Valdés et al. 2011;Rezaee et al. 2015;Cardoso et al. 2015) whereas others assume it in demand side (Jabbarzadeh et al. 2015;Bode and Wagner 2015;Makui and Ghavamifar 2016). ...
This paper utilizes a Stackelberg game approach for designing resilient supply chains under price competition and facilities disruption. The impact of using resilience strategies, namely holding extra inventory at distribution centers and considering reliable distribution centers, was investigated on the supply chains competition. A two-phase bi-level mixed integer programming approach is utilized to model the assumed problem, and a decomposition-based approach is utilized to solve the resultant model. Then, the performance of the presented model and solution approach is examined through numerical experiments. Finally, some discussions are presented with a number of examples, and managerial insights are suggested for the conditions similar to the assumed problem. Our analysis focuses on exploring the advantages of considering resilience strategies in the competitive supply chain netwrok design problems.
... Hybrid metaheuristics and simple Lagrangian heuristics for generating the trade-off curve were developed and computationally tested. Further studies were devoted to similar formulations (Aboolian et al. 2013;Cui et al. 2010), including those where the probabilities of facility failure are not equal and design dependent (Berman et al. 2007;Zhang et al. 2016), disruptions are correlated with an uncertain joint distribution (Lu et al. 2015;Yu et al. 2017), there are incomplete information (Albareda-Sambola et al. 2015;Berman et al. 2009;Yun et al. 2015) and the means of facility fortification (Lim et al. 2010;Li et al. 2013). ...
We address a general fault-tolerant version of the k-median problem on a network. Unlike the original k-median, the objective is to find k nodes (medians or facilities) of a network, assign each non-median node (customer) to distinct medians, and each median nodes to other medians so as to minimize the overall assignment cost. The problem can be considered in context of the so-called reliable facility location, where facilities once located may be subject to failures. Hedging against possible disruptions, each customer is assigned to multiple distinct facilities. We propose a fast and effective heuristic rested upon consecutive searching for lower and upper bounds for the optimal value. The procedure for finding lower bounds is based on a Lagrangian relaxation and a specialized effective subgradient algorithm for solving the corresponding dual problem. The information on dual variables is then used by a core heuristic in order to determine a set of primal variables to be fixed. The effectiveness and efficiency of our approach are demonstrated in a computational experiment on large-scale problem instances taken from TSPLIB. We show that the proposed algorithm is able to fast find near-optimal solutions to problem instances with almost 625 million decision variables (on networks with up to 24978 vertices).
... Therefore, the optimal solution can be obtained (Table 1). In supply chain literature on reliable facility location, the estimation of disruption probability is usually assumed perfectly accurate while there has very limited discussion on the misestimating disruption probability [24,31,32]. However, as mentioned above, the uncertainty in dynamic environments or misestimating the disruption probability would definitely affect the optimal solution. ...
The classical location models implicitly assume that the facilities, once built, will always operate as planned. However, some of the facilities may become unavailable from time to time due to disruptions which highlight the urgent need to effectively manage supply chain disruptions in spite of their low probability of occurrence. Therefore, it is critical to take account of disruptions when designing a resilient supply chain network so that it performs well as a whole even after an accidental disruption. In this paper, a stylized facility location problem is considered in a continuous plane which is solved through an improved Voronoi-diagram-based algorithm under disruption risks. The research problem is to minimize the total cost in normal and failure scenarios. Furthermore, the impact of misestimating the disruption probability is also investigated. The results numerically show that although the estimated disruption probability has a significant impact on the facilities configuration, it has a minor impact on the total quantity of facilities and the expected total cost. Therefore, this paper proposes that the decision-maker should moderately overestimate disruption risk based on the “pessimistic principle”. Finally, the conclusion considers managerial insights and proposes potential areas for future research.
... Most of the previous studies considered only the disruption risks in the SCs facilities that cause them (suppliers, manufacturers, DCs, and connection links) complete or partial breakdown of service or inaccessibility (Lee, 2001;Snyder et al., 2006;Aryanezhad and Jabbarzadeh, 2009;Berman et al., 2009;Liu et al., 2010;Peng et al., 2011). Jabbarzadeh et al. (2012 studied the SCND problem under the risk of disruption at facilities. ...
We address an intra-supply chain competition where a producer and resellers competing to achieve their goals, while taking into consideration the uncertainties and disruption risks. We utilize a bi-level multi-objective programming approach for designing a competitive supply chain network. A hybrid solution approach, combining the compromise programming and Benders
decomposition methods, is developed to solve the model. Furthermore, an efficient inequality constraint is proposed to cope with the computational complexity of the bi-level model. To explore
the practical application of the model, a real-world case example is discussed. Finally, the scalability of the solution approach is illustrated for large-scale problems.
... In somewhat similar research to this paper, Averbakh and Berman (1997) studied a weighted p-center problem with uncertain node weights and were able to achieve an analytical solution. Berman et al. (2007Berman et al. ( , 2009) built on this work investigating centralizing resources and locating facilities in the presence of incomplete information. Lu and Sheu (2013) built on that work by investigating the placement of urgent relief centers as a robust p-center model using a heuristic method to solve the NP-hard problem. ...
Disaster recovery efforts are enhanced through the collection and dissemination of satellite data, which is downloaded from satellites to ground stations. The optimal ground station locations vary depending on the location of the disaster, but ground station construction occurs before the realization of a disaster. Thus, a stochastic optimization problem arises: decide the location of ground stations before disasters with uncertain locations. We use a stochastic programming approach to select the location of ground stations given a set of potential disaster scenarios. The objective is to maximize the expected amount of data downloaded. The problem formulation consists of a two-stage stochastic program where the first-stage determines the locations of the ground stations and the second-stage schedules the uploading and downloading of data. We solve the problem using the L-shaped method; we find that it significantly outperforms solving the deterministic equivalent problem directly. We also find that an alternate second-stage formulation significantly improves solution time. The optimized set of ground stations found by our algorithm is compared to the set of ground stations operated by the National Oceanic and Atmospheric Administration’s; results confirm that the current placement is effective and demonstrate the benefit in adding additional ground stations. © 2018 Springer Science+Business Media, LLC, part of Springer Nature
... Berman, Krass, and Menezes (2007) introduced a reliable model based on the different failure probabilities for various facilities. In another work, Berman, Krass, and Menezes (2009) considered location of unreliable facilities where a customer have incomplete information about the state of operating facilities. Cui, Ouyang, and Shen (2010) and Li and Ouyang (2010) developed continuum approximation models to analyze the reliable facility location problems. ...
Hub location problem (HLP) is one of the strategic problems encountered in designing transportation and telecommunication networks. Regardless of the considered objective in design of hub networks, such as cost minimization or service level maximization, the located hubs can be subject to natural or intentional disruptions after installation. In this paper, we address the multiple allocation p-hub median, p-hub maximal covering, and p-hub center problems under intentional disruptions. In each case, the problem is considered as a Stackelberg game where the leader locates p hubs to optimize his/her objective function, whereas the follower tries to identify and interdict r hubs that their loss would diminish the network performance the most. Bilevel and single level mathematical formulations are presented to model the problem from the leader's and the follower's perspectives. Furthermore, efficient Simulated Annealing (SA) heuristics are proposed for solving the problems. Extensive computational experiments show the capability of the proposed SA algorithms to obtain the optimal solutions in short computational times. Some managerial insights are also derived based on the obtained numerical results.
... The mathematical modeling of RFLDP is as follows [4]: ...
This paper proposes a model for reliable facility location with distribution protection. The proposed model utilizes site-dependent failure probabilities and random link disruptions. It uses both proactive and reactive measures when a customers primary facility fails. The proactive mitigation strategy is implemented for reliable distribution centers during the design phase. It uses single-level backup mechanism as reactive measure that will increase facility availability. It can simultaneously determine both optimal number and location of capacitated distribution centers. The formulation of proposed model uses the concept of cross decomposition approach. The proposed model is implemented in IBM CPLEX 12.6.3. It is tested on randomly generated datasets for 180 customers and 30 distribution centers. Experimental results reveal that the proposed model provides optimal solution in a reasonable time.
... In this direction, Wilson (2007) studied the effect of disruptions in transportation on the supply chain performance by comparing the vendor managed inventory and traditional supply chain. Berman et al. (2009) proposed a facility location model considering the reliability which in turns depends on the effect of natural or man-made disruptions on facility operations. Li et al. (2009) proposed a vehicle routing problem with time windows. ...
Natural or man-made disasters lead to disruptions across entire supply chain, hugely affecting the entire distribution system. Owing to disaster, the supply chain usually takes longer time to recover and eventually leads to loss in reputation and revenue. Therefore, business organizations are constantly focusing on making its distribution network of a supply chain resilient to either man-made or natural disasters in order to satisfy customer demand in time. The supply chain distribution network broadly comprises of two major decisions i.e. facility location and vehicle routing. The paper addresses these distribution decisions jointly as location-routing problem. The paper proposes Location-Routing Model with Time Windows using proactive and reactive approaches. In proactive approach, the risk factors are considered as preventive measure for disaster caused disruptions. The model is extended for reactive approach by considering the disruptions such as facility breakdowns, route block ages, and delivery delays with cost penalties. The case illustration is discussed for proactive approach. In case of disaster caused disruptions, the reactive approach is illustrated using three disruption case scenarios. Using both proactive and reactive approach, designing the distribution system can make the overall supply chain a disaster resilient supply chain.
... Also, by extending using site-specific failures. Berman et al. [12] study the reliable P-median problem on a network and propose several exact and heuristic algorithms, ultimately revealing that facilities become more centralized or even co-located as the failure probability increases. Shen et al. [13] propose a scenario-based stochastic program and a nonlinear integer program for the reliable facility location problem with heterogeneous failure probabilities. ...
The designing of reliable facility location is an important way to evade against unexpected facility disruptions. In this paper, a facility allocation for distribution supply chain is designed that intend to achieve the effectiveness of system under unexpected facility disruptions occur. This paper considers a distribution network having site dependent facility disruptions and develop a mathematical formulation of mixed-integer programming. The proposed model is able to minimize facility allocation and transportation cost. The proposed model can determine the optimal distribution center locations with respect to disruption in distribution chain design. The commercial optimization solver CPLEX 12.6.3 is used to implement the proposed model. The Lagrangian relaxation approach is used to solve the proposed mathematical model. It is compared with CPLEX solver on twenty test instances. The test instances are generated randomly. The performance gap and computational time is used to measure the performance of proposed model. The impact of different parameters on the model is analyzed. The failure probability of reliable and un-reliable facility is also investigated. The experimental results reveal that the proposed model has capability to generate an optimal solution.
... Snyder and Daskin (2005) study facility location in which some of cases with definite probability become unusable and assume that customers would be served by facilities which are not affected by disruption. Berman et al. (2009) and Shen et al. (2011) who are inspired by this model developed new location problem models with disruption consideration. They supposed that facilities are not completely reliable and customers do not have any information about a facility being operational or not and it is supposed that every facility may be non-operation by a definite probability. ...
The hub location problem (HLP) is one of the strategic planning problems encountered in different contexts such as supply chain management, passenger and cargo transportation industries, and telecommunications. In this paper, we consider a reliable uncapacitated multiple allocation hub location problem under hub disruptions. It is assumed that every open hub facility can fail during its use and in such a case, the customers originally assigned to that hub, are either reassigned to other operational hubs or they do not receive service in which case a penalty must be paid. The problem is modeled as two-stage stochastic program and a metaheuristic algorithm based on the adaptive large neighborhood search (ALNS) is proposed. Extensive computational experiments based on the CAB and TR data sets are conducted. Results show the high efficiency of the proposed solution method.
... Though this multi-level backup mechanism can improve the availability of facilities, it also increases the operational and managerial complexities because each customer must set up connections with multiple facilities and vice versa. A more complicated situation emerges when prior information on the operational states of facilities is unknown to a customer before reaching it; therefore, the customer may have to visit several disrupted facilities before finding an operational one [17][18][19]. ...
This paper studies a reliable facility location problem with facility protection that aims to hedge against random facility disruptions by both strategically protecting some facilities and using backup facilities for the demands. An Integer Programming model is proposed for this problem, in which the failure probabilities of facilities are site-specific. A solution approach combining Lagrangian Relaxation and local search is proposed and is demonstrated to be both effective and efficient based on computational experiments on random numerical examples with 49, 88, 150 and 263 nodes in the network. A real case study for a 100-city network in Hunan province, China, is presented, based on which the properties of the model are discussed and some managerial insights are analyzed.
... This approach uses nonlinear terms to calculate the probability that a customer is served by its rth closest facility. It is used by Berman et al. (2007Berman et al. ( , 2009Berman et al. ( , 2011Berman et al. ( , 2013, Zhan et al. (2008), Cui et al. (2010), Shen et al. (2011), and Aboolian et al. (2013). 3. Reliable backups. ...
... It is clear that optimal location patterns and optimal service costs may differ if customers do not have prior information about the state of the facilities and must travel to different facilities before they can receive service. The role of information in reliable facility design is analyzed in Berman et al. (2009) and Berman et al. (2013). ...
Facility systems may be vulnerable to a disaster, whether caused by intention, an accident, or by an act of nature. When disrupting events do occur, services may be degraded or even destroyed. This chapter addresses problems of disruption associated with facility based service systems. Three main questions often arise when dealing with a possible disaster: (1) how bad can it get? (2) is there a way in which we can protect our system from such an outcome? and (3) is there a way in which we can incorporate such issues in our future designs and plans? This chapter addresses each of these main questions with respect to several classic location problems. Specifically, it discusses recent location models under disaster events along three main streams of research: facility interdiction, facility protection, and resilient design.
... Within location-routing contexts, there exists a volume of literature that either addresses location problems where transportation is considered as a fixed input to the problem (Berman et al., 2007(Berman et al., , 2009Álvarez-Miranda et al., 2015;Ceder et al., 2015;Yun et al., 2015); or routing problems with a pre-defined location set (Badeau et al., 1997;Huang et al., 2013;Liu et al., 2003). ...
The first step in most location-routing projects involves bringing the primary stakeholders on board and securing funding for implementation of the required changes. To this end, practitioners often need a good feasible solution together with a lower bound on the cost of any solution to the problem at hand, rather than exact solutions based on detailed and accurate parameter estimates. In this article, we present a simple methodology for assessing the quality of the current distribution network as well as for identifying opportunities for improvement. We incorporate the potential use of different transportation technologies at different layers of the network. We demonstrate the versatility of the proposed rough-cut approach by means of two real life implementations: (i) redesigning the supply network of the Casino Group, a supermarket chain in southeast France, and (ii) redesigning the household material recycling network of the city of Calgary, in Canada.
... From a management perspective, having more charging facilities set up in the high demand areas, as suggested by the PMP model, may be beneficial in terms of power management of the electricity grids (Gurkaynak & Khaligh, 2009). This facility distribution scheme can better respond to the event of facility disruptions since a demand point is close to multi-charging stations simultaneously (Berman et al., 2009;Daskin, 1983;ReVelle & Hogan, 1989). The idea of centralized location has also been applied to the location-allocation problems of other public facilities. ...
In this paper, we present a case study on planning the locations of public electric vehicle (EV) charging stations in Beijing, China. Our objectives are to incorporate the local constraints of supply and demand on public EV charging stations into facility location models and to compare the optimal locations from three different location models. On the supply side, we analyse the institutional and spatial constraints in public charging infrastructure construction to select the potential sites. On the demand side, interviews with stakeholders are conducted and the ranking-type Delphi method is used when estimating the EV demand with aggregate data from municipal statistical yearbooks and the national census. With the estimated EV demand, we compare three classic facility location models – the set covering model, the maximal covering location model, and the p-median model – and we aim to provide policy-makers with a comprehensive analysis to better understand the effectiveness of these traditional models for locating EV charging facilities. Our results show that the p-median solutions are more effective than the other two models in the sense that the charging stations are closer to the communities with higher EV demand, and, therefore, the majority of EV users have more convenient access to the charging facilities. From the experiments of comparing only the p-median and the maximal covering location models, our results suggest that (1) the p-median model outperforms the maximal covering location model in terms of satisfying the other’s objective, and (2) when the number of charging stations to be built is large, or when minor change is required, the solutions to both models are more stable as p increases.
... They applied several exact and heuristic solution approaches, and analysed the impact of disruption probabilities on the centralisation and co-location of the facilities. Berman, Krass, and Menezes (2009) attempted to minimise the expected cost of customer travels under facility disruptions. In their model, customers do not have complete information about whether a facility is operational or non-operational. ...
Most of current logistics network design models in the literature typically assume that facilities are always available and absolutely reliable while in practice, they are always subject to several operational and disruption risks. This paper proposes a reliable closed-loop supply chain network design model, which accounts for both partial and complete facility disruptions as well as the uncertainty in the critical input data. The proposed model is of mixed integer possibilistic linear programming type that aims to minimise simultaneously the total cost of opening new facilities and the expected cost of disruption scenarios. An enhanced possibilistic programming approach is proposed to deal with the epistemic uncertainty in input data. Furthermore, the p-robustness criterion is used to limit the cost of disruption scenarios and protect the designed network against random facility disruptions. Several numerical experiments along with sensitivity analyses on uncertain parameters are conducted to illustrate the significance and applicability of the developed model as well as the effectiveness of the proposed solution approach. Our results demonstrate that operational and disruption risks considerably affect the whole structure of the designed network and they must be taken into account when designing a reliable closed-loop logistics network.
... For instance, in [7], a model where the customers may have to visit several facilities until finding an available one is analyzed to conclude that centralization and co-location are adequate strategies to locate centers in this case. More recently, the same authors try to explain in [6] how correlated failure probabilities and problem objective (median and center) affect the location decisions when information is available, and when it is not. On the other hand, using or not failure probabilities to include the possibility that facilities become unavailable defines a second classification. ...
This paper presents the p-next center problem, which aims to locate p out of n centers so as to minimize the maximum cost of allocating customers to backup centers. In this problem it is assumed that centers can fail and customers only realize that their closest (reference) center has failed upon arrival. When this happens, they move to their backup center, i.e., to the center that is closest to the reference center. Hence, minimizing the maximum travel distance from a customer to its backup center can be seen as an alternative approach to handle humanitarian logistics, that hedges customers against severe scenario deteriorations when a center fails.
This research addresses the location problem of congested facilities, assuming service interruptions and customer withdrawals. Service interruptions can occur as a result of events such as machine failures, power outages, and communication system disconnections. As long as no interruption occurs, each facility functions as a M/M/1 queuing system. Upon an interruption, the server stops working, and customers receiving service or waiting in line leave the queue before being served. Moreover, customers who visit the facility during the repair avoid entering the facility. The problem is first formulated as a mixed-integer nonlinear programming (MINLP) model, for which two piecewise mixed-integer linear programming (MILP) relaxations, an exact solution algorithm (the branch and bound algorithm), and a metaheuristic algorithm (the antlion algorithm), are then presented for solution. Numerical experiments indicate the efficiency of the branch and bound algorithm. The antlion algorithm also exhibits the proper convergence speed to obtain near-optimal solutions.
Continuous approximation is regarded as a scalable and insightful method for acquiring near-optimum solutions to various location problems. A continuous approximation solution is nonetheless only a continuous density function and a further discretization procedure is needed to obtain a discrete location solution for engineering practice. Inspired by the process of “crystal growth”, this paper proposes a constructive heuristic algorithm as an alternative to the classic meta-heuristic disk algorithm (Ouyang and Daganzo, 2006) in discretizing a continuous solution from a continuum approximation location model. The main idea of this algorithm is to rasterize the space into a set of small cells (either regular triangles or squares) and repeatedly grow a core cell into a full-service area according to a certain visiting sequence. Thus, it has only linear time complexity proportional to the number of cells in the space. Numerical examples are conducted to test the performance of the proposed algorithm. The results indicate that this algorithm can solve discrete facility locations more efficiently and exhibits robust performance compared with the disk algorithm.
The article summarizes the results of a detailed study of selected elements of critical infrastructure. Based on the interconnection of risk management and safety for technical installations and their selected critical elements and, above all, the lessons learned from the study of their accidents and failures, a ge-neric model for managing their safety during the operation is compiled. Its main parts are and described, e.g. a process of risk management towards safety; structure of safety management over time, the division of responsibilities for risk management and the way of safety management process documentation.
We consider conditional facility location problems with unreliable facilities that can fail with known probabilities. The demand is uniformly distributed over a convex polygon in the rectilinear plane where a number of facilities are already present, and it is required to optimally locate another facility. We analyze properties of the exponential family of incremental Voronoi diagrams associated with possible realizations of the set of operational facilities, and, based on this analysis, present polynomial algorithms for three conditional location problems. The approach can be extended to various other conditional location problems with continuous demand and unreliable facilities, under different probabilistic models including ones with correlated facility failures.
Supply chains, as vital systems to the well-being of countries and economies, require systematic approaches to reduce their vulnerability. In this paper, we propose a non linear optimisation model to determine an effective distribution of protective resources among facilities in service and supply systems so as to reduce the probability of failure to which facilities are exposed in case of external disruptions. The failure probability of protected assets depends on the level of protection investments and the ultimate goal is to minimise the expected facility-customer transport or travel costs to provide goods and services. A linear version of the model is obtained by exploiting a specialised network flow structure. Furthermore, an efficient GRASP solution algorithm is developed to benchmark the linearised model and resolve numerical difficulties. The applicability of the proposed model is demonstrated using the Toronto hospital network. Protection measures within this context correspond to capacity expansion investments and reduce the likelihood that hospitals are unable to satisfy patient demand during periods of high hospitalisation (e.g. during a pandemic). Managerial insights on the protection resource distribution are discussed and a comparison between probabilistic and worst-case disruptions is provided.
This research addresses the problem of locating facilities with immobile servers. The possibility of occurrence of congestion in the facilities and the risk of interruption in the servers are considered as the sources of uncertainty. As the stochastic process of interruption in servers stops the process of providing service, the customers leave the facility once the interruption occurs, while no customer enters the facility until the server is fixed. The proposed model specifies the number and the optimal locations of the facilities so that the profit obtained by serving customers is maximized on the one hand. On the other hand, the cost of the system, including those corresponding to the customers' travel and waiting time and locating the facilities, is minimized. Furthermore, two meta-heuristic algorithms, i.e., a genetic algorithm and an ant lion algorithm, are proposed to solve the complicated optimization problem. The results of running the proposed algorithms on standard test problems suggest their efficiency as compared to the results obtained by solving the mathematical model. Moreover, the ant lion algorithm exhibits a higher quality and convergence rate than the genetic algorithm.
Facility systems may be vulnerable to a disaster, whether caused by intention, an accident, or by an act of nature. When disrupting events do occur, services may be degraded or even destroyed. This chapter addresses problems of disruption associated with facility based service systems. Three main questions often arise when dealing with a possible disaster: (1) how bad can it get? (2) is there a way in which we can protect our system from such an outcome? and (3) is there a way in which we can incorporate such issues in our future designs and plans? The chapter addresses each of these main questions with respect to several classic location problems. Specifically, it discusses recent location models under disaster events along three main streams of research: facility interdiction, facility protection, and resilient design.
مسئلهی مکانیابی هاب، از مسائل مهم و پرکاربرد در طراحی شبکه به شمار میآید. هابهای مستقر شده در طول زمان به دلایل مختلفی از جمله بلایای طبیعی یا اختلالات عمدی میتوانند از کار بیفتند که در این صورت هزینههای گزافی به شرکتهای بهرهبردار تحمیل میشود. بنابراین لازم است برنامهریزی مناسب برای کاهش اثرات مخرب اختلال صورت گیرد. در این تحقیق مسئلهی مکانیابی
هاب تکتخصیصهی بدون ظرفیت تحت شرایط اختلال هابها در نظر گرفته شده است. هر هاب بعد از احداث ممکن است دچار اختلال شود؛ بنابراین باید متقاضیانی که به هاب خراب شده در شبکه متصل شدهاند به هابهای سالم شبکه تخصیص یابند که در صورت بالا بودن هزینه، جریمهیی به عنوان هزینهی عدم خدمت رسانی تقاضاها پرداخت شود. مسئله به صورت مدل ریاضی تصادفی دو مرحلهیی فرمولبندی شده و روش فراابتکاری ترکیبی جستجوی همسایگی بزرگ تطبیقیافته با شبیهسازی تبرید ارائه شده است. محاسبات انجام شده بر روی دو مجموعه داده نشان دهندهی کارایی و عملکرد بالای الگوریتم پیشنهادی است.
This paper investigates the design of reliable supply networks to make them resilient to unpredictable disruptions. We develop an optimization model that incorporates several features, including (1) partial failure of facilities (instead of complete shutdown) resulting in interrupted supply capacity, (2) the effect of disruption on customer demand, and (3) the possibility to use multistrategies to mitigate disruption. We formulate a mixed-integer linear programming model to determine the optimal location of facilities and assignment of customers to opened facilities. An accelerated Benders decomposition method with valid inequalities is proposed to solve the problem. We discuss the computational efficiency of this decomposition procedure using two case studies as well as randomized data. For medium- and large-sized instances, our approach can decrease computational times by as much as 60% on average. We analyze the effect of multimitigation policies on the optimal solution and the model performance. Compared with the existing single-mitigation strategy models, we find that our model reduces the need for redundancy by as much as 50% and improves the total cost by as much as 8% in our case studies.
Many real-world service facilities are subject to probabilistic disruptions. Such disruptions often exhibit correlations that arise from shared external hazards or direct interactions among these facilities. This paper builds an overarching methodological framework for reliable facility location design under correlated facility disruptions. We first incorporate and extend the concepts of supporting station structure and quasi-probability from Li et al. (2013) and Xie et al. (2015), such that any correlated facility disruptions (positive and/or negative) can be equivalently represented by independent failures of a layer of properly constructed supporting stations, which are virtually added to the original facility system for capturing the effect of correlations among facilities. We then develop a compact mixed-integer mathematical model to optimize the facility location and customer assignment decisions in order to strike a balance between system reliability and cost efficiency. Lagrangian relaxation based algorithms, including modules for obtaining upper bound and lower bounds of relaxed subproblems, are proposed to effectively solve the optimization model. Numerical case studies are carried out to demonstrate the methodology, to test the performance of the framework, and to draw managerial insights.
In service systems with natural or anthropogenic barriers (e.g., rivers, railroads), customers who intend to visit facilities for service must first pass through certain network access points (e.g., bridges, railway crossings). Possible blockage or disruptions of these access points could change the customer-facility assignments or even affect reachability of various facilities, and thus introduce facility reliability and correlation issues. This paper incorporates network access points and their probabilistic failures into a joint optimization framework. A layer of network access points are added and connected to facilities to imply the real-world connections between facilities and access points. The access points are assumed to be subject to disruptions with site-dependent probabilities. We then develop a compact mixed-integer mathematical model to optimize the facility location and customer assignment decisions for the service systems design. Lagrangian relaxation based algorithms are designed to effectively solve the proposed model. Multiple case studies are constructed to test the model and the algorithm, and to demonstrate their performance and applicability.
Due to the interdependency between multiple infrastructure systems, the performance of a facility may depend on the resources or supplies received from other facilities. However, cross-system interdependence has seldom been studied in the location design context, probably due to the lack of a concise model describing interdependence across heterogeneous systems. This paper proposes a new heterogeneous flow scheme to describe cross-system interdependence. This scheme has two features distinguished from existing models in describing an interdependent facility location problem. First, it is a simple linear model upon which a compact facility location model can be built. Secondly, it relaxes the need to maintain flow conservation between different systems and is suitable in describing heterogeneous systems that take in and output different resources or services. Built on this scheme, this paper proposes a reliable location design model for a nexus of interdependent infrastructure systems. This model aims to locate the optimal facility locations in multiple heterogeneous systems to balance the tradeoff between the facility investment and the expected nexus operation performance. Different from other reliable facility location models, this expected performance captures interdependence among heterogeneous systems due to the resource input-output relationships. The consideration of continuous partial capacity losses complements the reliable location literature that mainly focuses on binary disruptions. Two numerical examples are conducted for investigating features and applications of the proposed model. The results indicate that with a standard off-the-shelf integer programming solver, the proposed model is able to solve optimal facility location design for problem instances of realistic scales to the near-optimum solutions with optimality gap assurance. Sensitivity analyses of key parameters indicate that improving facility capacity and reducing interdependency between systems can mitigate impacts of facility capacity losses and reduce the overall system cost.
Supply chains evolve over time: they expand via planned construction and/or corporate mergers and acquisitions, and contract due to required facility closures, partnership terminations, and/or other cost-cutting decisions. In addition, businesses also operate in an uncertain world wherein network and other design decisions must be made despite the reality of unforeseen future events that can and often do disrupt or damage corporate supply chains. We present a multi-objective network design model and accompanying optimization-based decision support methodology for supply chain architects. Our methodology helps to evaluate the trade-off between total network cost minimization and maximizing overall supply chain network connectivity. Decision makers can evaluate a collection of solutions with different cost and connectivity values using our methodology and choose the network configuration that best serves the needs of their organization. Though our multi-objective network design model is applicable for individual companies looking to expand or contract their internal supply chains, we demonstrate our model's efficacy through the lens of a practically-motivated corporate merger and acquisition activity.
Shelter location and traffic allocation decisions are critical for an efficient evacuation plan. In this study, we propose a scenario-based two-stage stochastic evacuation planning model that optimally locates shelter sites and that assigns evacuees to nearest shelters and to shortest paths within a tolerance degree to minimize the expected total evacuation time. Our model considers the uncertainty in the evacuation demand and the disruption in the road network and shelter sites. We present a case study for a potential earthquake in Istanbul. We compare the performance of the stochastic programming solutions to solutions based on single scenarios and mean values.
This paper considers the design of an immobile service system in which each facility’s service process is subject to the risk of interruptions. The location-capacity decisions and allocations are simultaneously made to maximize the difference between the service provider’s profit and the sum of customers’ transportation and waiting costs. An efficient Lagrangian-based solution algorithm is developed, which solves large-sized instances with up to 50 service facilities and 500 customers in a few seconds. Several sensitivity analyses and managerial insights are presented. The model is also applied to a case study on a logistics network design problem in the zinc mining industry.
The goal of this paper is to introduce facility capacities into the Reliability Fixed-Charge Location Problem in a sensible way. To this end, we develop and compare different models, which represent a tradeoff between the extreme models currently available in the literature, where a priori assignments are either fixed, or can be fully modified after failures occur. In a series of computational experiments we analyze the obtained solutions and study the price of introducing capacity constraints according to the alternative models both, in terms of computational burden and of solution cost.
The p-center problem is one of the most important models in location theory. Its objective is to place a fixed number of facilities so that the maximum service distance for all customers is as small as possible. This article develops a reliable p-center problem that can account for system vulnerability and facility failure. A basic assumption is that located centers can fail with a given probability and a customer will fall back to the closest nonfailing center for service. The proposed model seeks to minimize the expected value of the maximum service distance for a service system. In addition, the proposed model is general and can be used to solve other fault-tolerant center location problems such as the (p, q)-center problem using appropriate assignment vectors. I present an integer programming formulation of the model and computational experiments, and then conclude with a summary of findings and point out possible future work.
Based on the classic uncapacitated fixed charge model, and considering simultaneously the system operation cost and reliability, this paper proposed a nonlinear mixed integer programming model taking into account the failure probability and the customer multi-level redistribution. The linear processing model was solved by using the optimized Lagrangian relaxation algorithm. The data case shows that Lagrangian relaxation algorithm is more effective for mid-size network location problem, and relative to multi-level reassignment of customers, the failure probability of facilities has more influence on it.
Infrastructure facilities may be subject to probabilistic disruptions that compromise individual facility functionality as well as overall system performance. Disruptions of distributed facilities often exhibit complex spatial correlations, and thus it is difficult to describe them with succinct mathematical models. This paper proposes a new methodological framework for analyzing and modeling facility disruptions with general correlations. This framework first proposes pairwise transformations that unify three probabilistic representations (i.e., based on conditional, marginal, and scenario probabilities) of generally correlated disruption profile among multiple distributed facilities. Then facilities with any of these disruption profile representations can be augmented into an equivalent network structure consisting of additional supporting stations that experience only independent failures. This decomposition scheme largely reduces the complexity associated with system evaluation and optimization. We prove analytical properties of the transformations and the decomposition scheme, and illustrate the proposed methodological framework using a set of numerical case studies and sensitivity analyses. Managerial insights are also drawn.
Supply chain risk management is of growing importance, as globalization extends supply chains and makes them more vulnerable to a wide range of disruptive events. Supply interruptions can be the result of large-scale natural diasters, terrorist attacks, plant fires, electrical blackouts, financial or political crises, and many other scenarios.
Although disruption risks may occur with a low probability in a supply chain network, they have negative financial impacts and also the recovery process from their destructive effects is very slow. This paper proposes a reliability model for an integrated forward-reverse logistics network design, which can cope with both partial and complete facility disruptions. The reliability model is formulated as a stochastic robust programming whose objective function is to minimise the fixed opening costs of facilities and the expected cost of disruption scenarios, including processing costs, transportation costs, and penalty costs for non-satisfied demands. For doing so, a recent robust optimisation approach is modified to protect the concerned network against partial and complete capacity disruptions. Furthermore, a stochastic programming is employed to account for all interested scenarios. Three numerical experiments are designed to study the effect of capacity disruptions on the concerned logistic network. Finally, the results of the proposed model are compared with the conventional robust optimisation models.
This paper deals with a discrete facility location model where service is provided at the facility sites. It is assumed that facilities can fail and customers do not have information on failures before reaching them. As a consequence, they may need to visit more than one facility, following an optimized search scheme, in order to get service. The goal of the problem is to locate p facilities in order to minimize the expected total travel cost. The paper presents two alternative mathematical programming formulations for this problem and proposes a matheuristic based on a network flow model to provide solutions to it. The computational burden of the presented formulations is tested and compared on a test-bed of instances.
Solutions for facility location problems are numerous. As the problem is NP hard, continuous efforts have been made to find more efficient techniques. The nature of the facility adds to its variety. A popular approach has been based on geometric solutions. Other methods have also been tried; one of them is based on density applied for large databases as in Spatial Data Mining and Geographic Information Systems. A novel approach is evolved using density in the work presented in this paper wherein two stage solution is proposed for Uncapacitated Facility Location Problem. Experiments are conducted for urban public facility on standard data set of houses and roads to establish the superiority of the technique.
This paper presents game-theoretical models based on a continuous approximation (CA) scheme to optimize service facility location design under spatial competition and facility disruption risks. The share of customer demand in a market depends on the functionality of service facilities and the presence of nearby competitors, as customers normally seek the nearest functioning facility for service. Our game-theoretical models incorporate these complicating factors into an integrated framework, and use continuous and differentiable density functions to represent discrete location decisions. We first analyze the existence of Nash equilibria in a symmetric two-company competition case. Then we build a leader–follower Stackelberg competition model to derive the optimal facility location design when one of the companies has the first mover advantage over its competitor. Both models are solved effectively, and closed-form analytical solutions can be obtained for special cases. Numerical experiments (with hypothetical and empirical data) are conducted to show the impacts of competition, facility disruption risks and transportation cost metrics on the optimal design. Properties of the models are analyzed to cast interesting managerial insights.
As companies increasingly adopt global sourcing and supply chain management practices, they are discovering both opportunities and challenges. On the one hand, global sourcing is lowering purchase prices and expanding market access. On the other hand, operating a global distribution channel increases the level of supply chain risk—there's an increase both in the potential for product and service flow disruptions and in the magnitude of those disruptions. Top executives must now manage supply chain risks, just as aggressively as they manage other risks that affect business performance. In fact, a recent survey by insurance company FM Global and market research firm Harris Interactive found that 69 percent of chief financial officers, treasurers, and risk managers at Global 1000 companies in North America and Europe considered property-related hazards and supply chain disruptions as major threats to top revenue sources. 1 Recent studies also have shown that supply chain disruptions can be very costly and have the same magnitude as other types of corporate crises. 2,3 Managing supply chain risks is challenging because disruptions can occur for a wide variety of reasons such as industrial plant fires, transportation delays, work slowdowns or stoppages, or natural disasters. Yet, companies running lean operations no longer have the inventory or excess capacity to make up for production losses caused by such disruptions. As a result, material-flow problems can rapidly escalate to wide-scale network disruptions. Customers, however, don't care why or where the disruption occurred; they still expect the final product or service to be delivered at the right time and price. To maintain customer satisfaction, it falls on operations to handle these disruptions in real time.
On the morning of September 11th, 2001, the United States and the Western world entered into a new era - one in which large scale terrorist acts are to be expected. The impacts of the new era will challenge supply chain managers to adjust relations with suppliers and customers, contend with transportation difficulties and amend inventory management strategies. This paper looks at the twin corporate challenges of (i) preparing to deal with the aftermath of terrorist attacks and (ii) operating under heightened security. The first challenge involves setting certain operational redundancies. The second means less reliable lead times and less certain demand scenarios. In addition, the paper looks at how companies should organize to meet those challenges efficiently and suggests a new public-private partnership. While the paper is focused on the US, it has worldwide implications.
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.
Abstract Classical facility location models like the P-median problem (PMP) and the uncapacitated flxed-charge location problem (UFLP) implicitly assume that once constructed, the facilities chosen will always operate as planned. In reality, however, facilities \fail" from time to time due to poor weather, labor actions, changes of ownership, or other factors. Such failures may lead to excessive transportation costs as customers must be served from facilities much farther than their regularly assigned facilities. In this paper, we present models for choosing facility locations to minimize cost while also taking into account the expected transportation cost after failures of facilities. The goal is to choose facility locations that are both inexpensive under traditional objective functions and also reliable. This reliability approach is new in the facility location literature. We formulate reliability models based on both the PMP and the UFLP and present an optimal Lagrangian relaxation algorithm to solve them. We discuss how to use these models to generate a tradeofi curve between the day-to-day operating cost and the expected cost taking failures into account, and use these tradeofi curves to demonstrate empirically that substantial improvements in reliability are often possible with minimal increases in operating cost. 1 1 INTRODUCTION,2
This paper extends S. L. Hakimi's one-median problem by embedding it in a general queueing context. Demands for service arise solely on the nodes of a network G and occur in time as a Poisson process. A single mobile server resides at a facility located on G. The server, when available, is dispatched immediately to any demand that occurs. When a demand finds the server busy with a previous demand, it is either rejected (Model 1) or entered into a queue that is depleted in a first-come, first-served manner (Model 2). Service time for each demand comprises travel time to the scene, on-scene time, travel time back to the facility and possibly additional off-scene time.
A greedy randomized adaptive search procedure (GRASP) is a metaheuristic for combinatorial optimization. It is a multi-start or iterative process, in which each GRASP iteration consists of two phases, a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Since 1989, numerous papers on the basic aspects of GRASP, as well as enhancements to the basic metaheuristic have appeared in the literature. GRASP has been applied to a wide range of combinatorial optimization problems, ranging from scheduling and routing to drawing and turbine balancing. This paper is an annotated bibliography of the GRASP literature from 1989 to 2001.
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.
In this paper, we analyze a facility location model where facilities may be subject to disruptions, causing customers to seek service from the operating facilities. We generalize the classical p-median problem on a network to explicitly include the failure probabilities, and analyze structural and algorithmic aspects of the resulting model. The optimal location patterns are seen to be strongly dependent on the probability of facility failure, with facilities becoming more centralized, or even co-located, as the failure probability grows. Several exact and heuristic solution approaches are developed. Results of numerical experiments are reported.
The median problem has been generalized to include queueing-like congestion of facilities (which are assumed to have finite numbers of servers). In one statement of the generalizations, a closest available server is assumed to handle each service request. More general server assignment policies are admissable. The objective is to minimize the steady state expected travel time associated with a random service request. It is shown that, under suitable conditions, at least one set of optimal locations exists solely on the nodes of the network. It is also shown that this result has a direct relationship to the hypercube queueing model.
In this paper, the p-median and p-centre problems are generalized by considering the possibility that one or more of the facilities may become inactive. The unreliable p-median problem is defined by introducing the probability that a facility becomes inactive. The (p, q)-centre problem is defined when p facilities need to be located but up to q of them may become unavailable at the same time. An heuristic procedure is presented for each problem. A rigorous procedure is discussed for the (p, q)-centre problem. Computational results are presented.
The general problem is that of locating a central facility in a network so as to minimize the sum of its distances from the sources of flow to it, each distance being appropriately weighted to reflect the associated flow volume and/or cost. In this paper, simple one-pass solution algorithms are given for two classes of topologically simple networks, namely those which are either acyclic or contain exactly one cycle. The first algorithm is based on a reduction procedure that may also yield useful simplification of problems involving general networks.
It is shown that the problem of finding a p-median of a network is an NP-hard problem even when the network has a simple structure (e. g. , planar graph of maximum vertex degree 3). However, results leading to efficient algorithms are presented when the network is a tree: in particular, it is first shown that a l-median of a tree is identical to its w-centroid, and obtain A. J. Goldman's O(n) algorithm for finding a 1-median of a tree out of more general considerations. Then an algorithm is presented which finds a p-median of a tree (for p greater than 1) in time O(n**2 multiplied by (times) p**2).
Problems of finding p-centers and dominating sets of radius r in networks are discussed. Let n be the number of vertices and vertical E vertical be the number of edges of a network. With the assumption that the distance-matrix of the network is available, there are designed an O( vertical E vertical multiplied by (times) n multiplied by (times) lg n) algorithm for finding an absolute l-center of a vertex-weighted network and an O( vertical E vertical multiplied by (times) n plus n**2 multiplied by (times) lg n) algorithm for finding an absolute 1-center of a vertex-unweighted network. It is shown that the problem of finding a (vertex or absolute) p-center (for 1 less than p less than n) of a (vertex-weighted or vertex-unweighted) network, and the problem of finding a dominating set of radius r are NP-hard even in the case where the network has a simple structure.
A greedy randomized adaptive search procedure (GRASP) is a metaheuristic for combinatorial optimization. It is a multi-start or iterative process, in which each GRASP iteration consists of two phases, a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Since 1989, numerous papers on the basic aspects of GRASP, as well as enhancements to the basic metaheuristic, have appeared in the literature. GRASP has been applied to a wide range of combinatorial optimization problems, ranging from scheduling and routing to drawing and turbine balancing. This is the second of two papers with an annotated bibliography of the GRASP literature from 1989 to 2008. In the companion paper, algorithmic aspects of GRASP are surveyed. In this paper, we cover the literature where GRASP is applied to scheduling, routing, logic, partitioning, location, graph theory, assignment, manufacturing, transportation, telecommunications, biology and related fields, automatic drawing, power systems, and VLSI design.
The concepts of the “center” and the “median vertex” of a graph are generalized to the “absolute center” and the “absolute median” of a weighted graph (a graph with weights attached to its vertices as well as to its branches). These results are used to find the optimum location of a “switching center” in a communication network and to locate the best place to build a “police station” in a highway system. It is shown that the optimum location of a switching center is always at a vertex of the communication network while the best location for the police station is not necessarily at an intersection. Procedures for finding these locations are given.
Unmade in America: The true cost of a global assembly line
- B C Lynn
Lynn, B. C. (2002). Unmade in America: The true cost of a global assembly line.
Harper's, 304, 33-41.
Ambulance deverted each minute
- D Witlin
Witlin, D. (2006). Ambulance deverted each minute. Boston Herald, February 17.