Resilient facility location against the risk of disruptions

Given facility disruptions and uncertainties after disasters, we propose a hybrid multi-period scenario-based robust model (HMSR) to optimize emergency response. This model aims to select appropriate facility locations, organize casualty evacuation, and coordinate relief supply distribution, while minimizing both deprivation cost and operational cost. We utilize the scenario-based robust method to reduce the impact caused by the risks of facility disruptions, and the interval robust method to handle the uncertainty of casualty numbers. In addition, we examine the performance of this model through case studies based on the 2008 Wenchuan earthquake. The proposed model demonstrates its advantages by comparing it with a single-period model, a model that addresses multiple disruption scenarios using stochastic programming, and a model that does not account for the uncertainty in casualty numbers. The sensitivity analysis results indicate that the proposed model can improve rescue efficiency during disasters and reduce deprivation costs to some extent.

The facility location problem is a classical combinatorial optimization problem with extensive applications spanning communication technology, economic management, traffic governance, and public services. The facility location problem is to assign a set of clients to a set of facilities such that each client connects to a facility and the total cost (open cost and connection cost) is as low as possible. Among its various models, the uncapacitated facility location (UFL) problem is the most fundamental and widely studied. However, in real-world scenarios, resource constraints often make the UFL problem insufficient, necessitating more generalized models. This investigation primarily focuses on the universal facility location (Uni-FL) problem, a generalized framework encompassing both capacitated facility location problems (with hard and soft capacity constraints) and the UFL problem. Through a systematic analysis, we examine the Uni-FL problem alongside its specialized variants: the hard capacitated facility location (HCFL) problem and soft capacitated facility location (SCFL) problem. A comprehensive survey is conducted of existing approximation algorithms and theoretical results. The relevant results of their important variants are also discussed. In addition, we propose some open questions and future research directions for this problem based on existing research.

In recent years, various kinds of carbon dioxide capture, utilization and storage supply chain network design (CCUS SCND) problems have been extensively studied by scholars from the supply chain management community and other fields. The existing works mainly focus on the various deterministic or uncertainty problems; few works consider the CCUS SCND resilience problem in the context of utilization/storage facility disruptions due to unexpected natural disasters or other geological anomaly events. This paper aims to study the CCUS SCND resilience problem under utilization/storage facility capacity disruption risk. We propose a stochastic mixed-integer linear programming model for the considered problem. In the considered problem, the main decisions related to the following areas are taken into account: supply chain design and planning; facility disruption risk handling, including the optimal determination of facility locations and the matching of carbon dioxide emission sources and utilization/storage facilities; carbon dioxide normal transportation planning; and transshipment planning for various disruption scenarios. Finally, an experimental study comprising a case study from China is conducted to validate the effectiveness and performance of our proposed model. The obtained results show that the supply chain networks for the case study obtained by our proposed model are efficient, cost-effective and resilient in mitigating various kinds of utilization/storage facility disruption scenarios, showing the model can be applied to large-scale CCUS projects to help managers effectively deal with disruption risks. Future research should consider multiple disruption events and propose multiple effective resilience strategies.

This paper offers a credibility-constrained programming model for reliable design of an integrated forward–reverse logistics network with hybrid facilities under uncertainty and random facility disruptions. To tackle with this problem, a novel mathematical model is first developed that integrates the network design decisions in both forward and reverse flows and utilises reliability concepts to deal with facility disruptions. Then, the developed model is enhanced based on the credibility-constrained programing to cope with the epistemic uncertainties embedded in the model parameters. Since the hybrid distribution-collection facilities play an important role in both forward and reverse flows, it is supposed that they might be randomly disrupted. Several effective reliability strategies are considered to hedge against random facility disruptions. First, locating two types of hybrid facilities, namely, reliable and unreliable, is taken into account in the concerned logistics network when disruptions strike. Second, unreliable hybrid facilities are allowed to be partially disrupted, and thus a percentage of their capacities may be lost. However, they can still serve their customers with their remaining capacities. To compensate the lost capacity at unreliable hybrid facilities, a sharing strategy is also considered, in which goods can be shipped from reliable hybrid facilities to unreliable ones. Finally, several numerical experiments along with a sensitivity analysis are conducted to illustrate the significance and applicability of the developed model as well as the effectiveness of the credibility-based solution approach.

PurposeThe purpose of this paper is to propose a new casualty scheduling optimisation problem and to effectively treat casualties in the early stage of post-earthquake relief.Design/methodology/approachDifferent from previous studies, some new characteristics of this stage are considered, such as the grey uncertainty information of casualty numbers, the injury deterioration and the facility disruption scenarios. Considering these new characteristics, we propose a novel casualty scheduling optimisation model based on grey chance-constrained programming (GCCP). The model is formulated as a 0–1 mixed-integer nonlinear programming (MINP) model. An improved particle swarm optimisation (PSO) algorithm embedded in a grey simulation technique is proposed to solve the model.FindingsA case study of the Lushan earthquake in China is given to verify the effectiveness of the model and algorithm. The results show that (1) considering the facility disruption in advance can improve the system reliability, (2) the grey simulation technology is more suitable for dealing with the grey uncertain information with a wider fluctuation than the equal-weight whitening method and (3) the authors' proposed PSO is superior to the genetic algorithm and immune algorithm.Research limitations/implicationsThe casualty scheduling problem in the emergency recovery stage of post-earthquake relief could be integrated with our study to further enhance the research value of this paper.Practical implicationsConsidering the facility disruption in advance is beneficial to treat more patients. Considering the facility disruption in the design stage of the emergency logistics network can improve the reliability of the system.Originality/value(1) The authors propose a new casualty scheduling optimisation problem based on GCCP in the early stage of post-earthquake relief. The proposed problem considers many new characteristics in this stage. To the best of the authors' knowledge, the authors are the first to use the GCCP to study the casualty scheduling problem under the grey information. (2) A MINP model is established to formulate the proposed problem. (3) An improved integer-encoded particle swarm optimisation (PSO) algorithm embedded grey simulation technique is designed in this paper.

Risk-averse supplier selection and order allocation in the centralized supply chains under disruption risks

Design of Supply Chains under the Risk of Facility Disruptions

The uncapacitated facility location problem (UFLP) involves locating an undetermined number of facilities to minimize the sum of the (annualized) fixed setup costs and the variable costs of serving the market demand from these facilities. UFLP is also known as the “simple” facility location problem SFLP, where both the alternative facility locations and the customer zones are considered discrete points on a plane or a road network. This assumes that the alternative sites have been predetermined and the demand in each customer zone is concentrated at the point representing that region. UFLP focuses on the production and distribution of a single commodity over a single time period (e.g., one year that is representative of the firm’s long-run demand and cost structure), during which the demand is assumed to be known with certainty. The distinguishing feature of this basic discrete location problem, however, is the decision maker’s ability to determine the size of each facility without any budgetary, technological, or physical restrictions. Krarup and Pruzan (1983) provided a comprehensive survey of the early literature on UFLP, including its solution properties. By demonstrating the relationships between UFLP and the set packing-covering-partitioning problems, they established its NP-completeness.

The uncapacitated facility location problem (UFLP) is a well-known combinatorial optimization problem having single-objective function. The objective of UFLP is to find a subset of facilities from a given set of potential facility locations such that the sum of the opening costs of the opened facilities and the service cost to serve all the customers is minimized. In traditional UFLP, customers are served by their nearest facilities. In this article, we have proposed a multi-objective UFLP where each customer has a preference for each facility. Hence, the objective of the multi-objective UFLP with customers’ preferences (MOUFLPCP) is to open a subset of facilities to serve all the customers such that the sum of the opening cost and service cost is minimized and the sum of the preferences is maximized. In this article, the elitist non-dominated sorting genetic algorithm II (NSGA-II), a popular Pareto-based GA, is employed to solve this problem. Moreover, a weighted sum genetic algorithm (WSGA)-based approach is proposed to solve MOUFLPCP where conflicting two objectives of the problem are aggregated to a single quality measure. For experimental purposes, new test instances of MOUFLPCP are created from the existing UFLP benchmark instances and the experimental results obtained using NSGA-II and WSGA-based approaches are demonstrated and compared for these newly created test instances.

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.

This paper studies a supply chain design problem with the risk of disruptions at facilities. At any point of time, the facilities are subject to various types of disruptions caused by natural disasters, man‐made defections, and equipment breakdowns. We formulate the problem as a mixed‐integer nonlinear program which maximizes the total profit for the whole system. The model simultaneously determines the number and location of facilities, the subset of customers to serve, the assignment of customers to facilities, and the cycle‐order quantities at facilities. In order to obtain near‐optimal solutions with reasonable computational requirements for large problem instances, two solution methods based on Lagrangian relaxation and genetic algorithm are developed. The effectiveness of the proposed solution approaches is shown using numerical experiments. The computational results, in addition, demonstrate that the benefits of considering disruptions in the supply chain design model can be significant.

In this paper, the performance of the recently developed Pastoralist Optimization Algorithm (POA) on classical uncapacitated Facility Location problem (UFLP) was investigated. POA is a culture-inspired metaheuristic motivated by the herding schemes of Nomadic Pastoralist (NP). The NP seek optimal herding location for their livestock using some well-defined and robust strategies. UFLP is an NP-hard problem from which many facility location and real-world problems are built around. In this paper, five UFLP datasets were used for the experiments each comprising of five cities and seven, fifteen, thirty, fifty and one hundred cities respectively. The performance of POA was compared and validated with some popular and similar metaheuristic algorithms such as ABC, BBO and PSO. The results obtained proves POA competiveness and superiority in obtaining the lowest allocation cost and convergence rate as the data size increases.

The Uncapacitated Facility Location Problem (UFLP) is a fundamental optimization problem involving the selection of locations at which facilities supplying the same service are to be placed. Since it has been shown that the UFLP is NP‐hard, it has generally been thought that there is no hope of finding a polynomial time algorithm by which an optimal solution is always obtained. In this paper, we propose a genetic algorithm for solving the UFLP. In the UFLP, according to the ratio of the cost of facility placement and the cost to users of the facility, the number of facility locations can be roughly estimated. Therefore, partial solution spaces that are likely to contain a good solution can be predicted to some extent on the basis of the classification index. By using mutation with the operation that searches the solution space that is likely to contain a good solution, the proposed method can search the whole space of solutions efficiently. Its effectiveness is shown by a numerical experiment in which our method is compared with existing methods. © 2011 Wiley Periodicals, Inc. Electron Comm Jpn, 94(5): 47–54, 2011; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/ecj.10180

The Uncapacitated Facility Location Problem (UFLP) is considered in this paper. Given a set of customers and a set of potential facility locations, the objective of UFLP is to open a subset of facilities to satisfy the demands of all the customers such that the sum of the opening cost for the opened facilities and the service cost is minimized. UFLP is a well-known combinatorial optimization problem which is also NP-hard. So, a metaheuristic algorithm for solving this problem is natural choice. In this paper, a relatively new swarm intelligence-based algorithm known as the Monkey Algorithm (MA) is applied to solve UFLP. To validate the efficiency of the proposed binary MA-based algorithm, experiments are carried out with various data instances of UFLP taken from the OR-Library and the results are compared with those of the Firefly Algorithm (FA) and the Artificial Bee Colony (ABC) algorithm.

We obtain a 1.5-approximation algorithm for the metric uncapacitated facility location (UFL) problem, which improves on the previously best known 1.52-approximation algorithm by Mahdian, Ye, and Zhang. Note that the approximability lower bound by Guha and Khuller is $1.463\dots$. An algorithm is a ($\lambda_f$,$\lambda_c$)-approximation algorithm if the solution it produces has total cost at most $\lambda_f\cdot F^*+\lambda_c\cdot C^*$, where $F^*$ and $C^*$ are the facility and the connection cost of an optimal solution. Our new algorithm, which is a modification of the $(1+2/e)$-approximation algorithm of Chudak and Shmoys, is a $(1.6774,1.3738)$-approximation algorithm for the UFL problem and is the first one that touches the approximability limit curve $(\gamma_f,1+2e^{-\gamma_f})$ established by Jain, Mahdian, and Saberi. As a consequence, we obtain the first optimal approximation algorithm for instances dominated by connection costs. When combined with a $(1.11,1.7764)$-approximation algorithm proposed by Jain et al., and later analyzed by Mahdian et al., we obtain the overall approximation guarantee of 1.5 for the metric UFL problem. We also describe how to use our algorithm to improve the approximation ratio for the 3-level version of UFL.