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When designing an optimization model for use in a mass casualty event response, it is common to encounter the heavy and considerable demand of injured patients and inadequate resources and personnel to provide patients with care. The purpose of this study is to create a model that is more practical in the real world. So the concept of “predicting the resource and personnel shortages” has been used in this research. Their model helps to predict the resource and personnel shortages during a mass casualty event. In this paper, to deal with the shortages, some temporary emergency operation centers near the hospitals have been created, and extra patients have been allocated to the operation center nearest to the hospitals with the purpose of improving the performance of the hospitals, reducing congestion in the hospitals and considering the welfare of the applicants.

The authors research will focus on where to locate health-care facilities and how to allocate the patients to multiple hospitals to take into view that in some cases of emergency situations, the patients may exceed the resource and personnel capacity of hospitals to provide conventional standards of care.

In view of the fact that the problem is high degree of complexity, two multi-objective meta-heuristic algorithms, including non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA), were proposed to solve the model where their performances were compared in terms of four multi-objective metrics including maximum spread index (MSI), spacing (S), number of Pareto solution (NPS) and CPU run-time values. For comparison purpose, paired t-test was used. The results of 15 numerical examples showed that there is no significant difference based on MSI, S and NPS metrics, and NRGA significantly works better than NSGA-II in terms of CPU time, and the technique for the order of preference by similarity to ideal solution results showed that NRGA is a better procedure than NSGA-II.

The planning horizon and time variable have not been considered in the model, for example, the length of patients’ hospitalization at hospitals.

Presenting an effective strategy to respond to a mass casualty event (natural and man-made) is the main goal of the authors’ research.

This paper strategy is used in all of the health-care centers, such as hospitals, clinics and emergency centers when dealing with disasters and encountering with the heavy and considerable demands of injured patients and inadequate resources and personnel to provide patients with care.

This paper attempts to shed light onto the formulation and the solution of a three-objective optimization model. The first part of the objective function attempts to maximize the covered population of injured patients, the second objective minimizes the distance between hospitals and temporary emergency operation centers and the third objective minimizes the distance between the warehouses and temporary centers.

The aim of this research is to improve the responsiveness of the healthcare network of a large city to a major earthquake, by applying a combined methodology to reduce human suffering and death.

Scenario analysis, a non-linear programming (NLP) model, and the analytical network process are sequentially applied to find the “best location pattern”.

When considering the occurrence of major earthquakes in cities with high population density, as a rule of thumb, the location of healthcare facilities should prioritize areas characteristically overcrowded and/or that were built based on poor standards of seismic resistance.

The proposed research design does not include a cost criterion in the set of decision variables involved. Furthermore, the results derived from the NLP-model are restricted by the input simulation data.

The performance of the “best location pattern” is compared with the current location of healthcare facilities in terms of their distances to the affected zones. Metropolis areas worldwide with similar conditions to the city under consideration could be benefited from applying the general methodology for relocation of healthcare facilities described in this research.

This research implements a diverse combination of methodologies to examine the problem of relocating of healthcare facilities in a large city in the wake of an assumed earthquake. In addition, to the best of authors' knowledge, this is the first study of its kind that proposes improvements in the responsiveness of the healthcare facilities' network in the city in question.

Waste production is one of the most important problems that humankind faces. Human-based activities generate diverse waste types that have to be treated and disposed differently. This results in the need to build more facilities to manage the waste and to avoid further environmental damage. Colombia established a successful policy to close open dumps and to control pollution. Notwithstanding the advances that have been made in final disposal, it is necessary to extend the life of the final disposal sites and increase the closure of open landfills. Valle del Cauca is the third most populated Colombian province, and it is also considered the third province that generates more waste. This chapter addresses the problem of locating solid waste disposal centers in Valle del Cauca by applying the analytic hierarchy process (AHP) with fuzzy logic, a multicriteria method that compares opinions of a decision-making group. Additionally, each potential location area is characterized by considering industrial and environmental issues, societal dynamics, infrastructure and topography, costs, and taxes. After applying a variant of AHP, the decision-making group was able to find that Jamundi is the best location to open the disposal center. The method shows strong potential to identify and prioritize alternative locations for a diverse group of stakeholders. Most importantly, the methodology lets us structure better qualitative and quantitative data, as well as to link multiple levels to avoid choosing locations that will affect society, environment, and other stakeholders, without considering the trade-offs among diverse criteria considering benefits, opportunities, costs, and risks (BOCR).

Increasing public consciousness and demand for sustainable environment make selection of a safe location for effective disposal of healthcare waste (HCW) a challenging issue. This problem becomes more complicated due to involvement of multiple decision makers having varying knowledge and interest, conflicting quantitative and qualitative evaluation criteria, and presence of several alternative locations.

To efficiently resolve the problem, the past researchers have already coupled different multi-criteria decision-making tools with uncertainty models and criteria weight measurement techniques, which are time-consuming and highly computationally complex. Based on involvement of a group of experts expressing their opinions with respect to relative importance of criteria and performance of alternative locations against each criterion, this paper proposes application of ordinal priority approach (OPA) integrated with grey numbers to solve an HCW disposal location selection problem.

The grey OPA can simultaneously estimate weights of the experts, criteria and locations relieving the decision makers from complicated computational steps. The potentiality of grey OPA in solving an HCW disposal location selection problem is demonstrated here using an illustrative example consisting of three experts, six criteria and four alternative locations.

The derived results show that it can be employed to deal with real-time HCW disposal location selection problems in uncertain environment providing acceptable and robust decisions. It relieves the experts from pair-wise comparisons of criteria, normalization of data, identification of ideal and anti-ideal solutions, aggregation of information and so on, while arriving at the most consistent decision with minimum computational effort.

There have been numerous extensions of the maximum covering location problem that has been developed in the last decade to deal with facility location. Most of the research, however, addresses a single attribute or objective. In the case when a single criterion such as minimizing average response time to access a service facility is insufficient to address the interests of the decision maker, multiple objectives must be employed. Qualitative factors like customer service and market demand as well as quantitative factors like distribution and operating costs need to be appropriately weighted and used in a mathematical programming model. We develop a multi‐objective model for a service facility location problem that simultaneously sites facilities and allocates demand for products from different customer zones. We apply this model to “real‐world” data and show the practical advantages of using this model to solve capacitated service logistics problems.

This paper aims to propose an innovative building information modelling (BIM)-based framework for multi-objective and dynamic temporary construction site layout design (SLD), which uses a hybrid approach of systematic layout planning (SLP) and mathematical modelling.

The hybrid approach, which follows a step-by-step process for site layout planning, is designed to facilitate both qualitative and quantitative data collection and processing. BIM platform is usedto facilitate the determination of the required quantitative data, while the qualitative data are generated through knowledge-based rules.

The multi-objective layout model represents two important aspects: layout cost and adjacency score. The result shows that the model meets construction managers’ requirements in not only saving cost but also assuring the preferences of temporary facility relationships. This implies that the integration of SLP and mathematical layout modelling is an appropriate approach to deliver practical multi-objective SLD solutions.

The proposed framework is expected to serve as a solution, for practical application, which takes the advantage of technologies in data collection and processing. Besides, this paper demonstrates, by using numerical experimentation and applying Microsoft Excel Solver for site layout optimisation, how to reduce the complexity in mathematical programming for construction managers.

The original contribution of this paper is the attempt of developing a framework in which all data used for the site layout modelling are collected and processed using a systematic approach, instead of being predetermined, as in many previous studies.

The paper aims at the bi‐objective optimization of a two‐echelon distribution network model for facility location and capacity allocation where in a set of customer locations with demands and a set of candidate facility locations will be known in advance. The problem is to find the locations of the facilities and the shipment pattern between the facilities and the distribution centers (DCs) to minimize the combined facility location and shipment costs subject to a requirement that maximum customer demands be met.

To optimize the two objectives simultaneously, the location and distribution two‐echelon network model is mathematically represented in this paper considering the associated constraints, capacity, production and shipment costs and solved using hybrid multi‐objective particle swarm optimization (MOPSO) algorithm.

This paper shows that the heuristic based hybrid MOPSO algorithm can be used as an optimizer for characterizing the Pareto optimal front by computing well‐distributed non‐dominated solutions. These aolutions represent trade‐off solutions out of which an appropriate solution can be chosen according to industrial requirement.

Very few applications of hybrid MOPSO are mentioned in literature in the area of supply chain management. This paper addresses one of such applications.

The purpose of this paper is to develop a mathematical model that determines the location of temporary logistics hubs (TLHs) for disaster response and proposes a new method to determine weights of the objectives in a multi-objective optimization problem. The research is motivated by the importance of TLHs and the complexity that surrounds the determination of their location.

A multi-period multi-objective model with multi-sourcing is developed to determine the location of the TLHs. A fuzzy factor rating system (FFRS) under the group decision-making (GDM) condition is then proposed to determine the weights of the objectives when multiple decision makers exist.

The interview with decision makers shows the heterogeneity of decision opinions, thus substantiating the importance of GDM. The optimization results provide useful managerial insights for decision makers by considering the trade-off between two non-commensurable objectives.

In this study, decision makers are considered to be homogeneous, which might not be the case in reality. This study does not consider the stochastic nature of relief demand.

The outcomes of this study are valuable to decision makers for relief distribution planning. The proposed FFRS approach reveals the importance of involving multiple decision makers to enhance sense of ownership of established TLHs.

A mathematical model highlighting the importance of multi-sourcing and short operational horizon of TLHs is developed. A new method is proposed and implemented to determine the weights of the objectives. To the best of the authors’ knowledge, the multi-actor and multi-objective aspects of the TLH location problem have not thus far been considered simultaneously for one particular problem in humanitarian logistics.

The purpose of this paper is to realize a multi‐objective location‐routing network optimization in reverse logistics using particle swarm optimization based on grey relational analysis with entropy weight.

Real world network design problems are often characterized by multi‐objective in reverse logistics. This has recently been considered as an additional objective for facility location problem or vehicle routing problem in reverse logistics network design. Both of them are shown to be NP‐hard. Hence, location‐routing problem (LRP) with multi‐objective is more complicated integrated problem, and it is NP‐hard too. Due to the fact that NP‐hard model cannot be solved directly, grey relational analysis and entropy weight were added to particle swarm optimization to decision among the objectives. Then, a mathematics model about multi‐objective LRP of reverse logistics has been constructed, and a proposed hybrid particle swarm optimization with grey relational analysis and entropy weight has been developed to resolve it. An example is also computed in the last part of the paper.

The results are convincing: not only that particle swarm optimization and grey relational analysis can be used to resolve multi‐objective location‐routing model, but also that entropy and grey relational analysis can be combined to decide weights of objectives.

The method exposed in the paper can be used to deal with multi‐objective LRP in reverse logistics, and multi‐objective network optimization result could be helpful for logistics efficiency and practicability.

The paper succeeds in realising both a constructed multi‐objective model about location‐routing of reverse logistics and a multi‐objective solution algorithm about particle swarm optimization and future stage by using one of the newest developed theories: grey relational analysis.

The purpose of this paper is to review, evaluate and classify the academic research that has been published in facility layout problems (FLPs) and to analyse how researches and practices on FLPs are.

The review is based on 166 papers published from 1953 to 2021 in international peer-reviewed journals. The literature review on FLPs is presented under broader headings of discrete space and continuous space FLPs. The important formulations of FLPs under static and dynamic environments represented in the discrete and continuous space are presented. The articles reported in the literature on various representations of facilities for the continuous space Unequal Area Facility Layout Problems (UA-FLPs) are summarized. Discussed and commented on adaptive and robust approaches for dynamic environment FLPs. Highlighted the application of meta-heuristic solution methods for FLPs of a larger size.

It is found that most of the earlier research adopted the discrete space for the formulation of FLPs. This type of space representation for FLPs mostly assumes an equal area for all facilities. UA-FLPs represented in discrete space yield irregular shape facilities. It is also observed that the recent works consider the UA-FLPs in continuous space. The solution of continuous space UA-FLPs is more accurate and realistic. Some of the recent works on UA-FLPs consider the flexible bay structure (FBS) due to its advantages over the other representations. FBS helps the proper design of aisle structure in the detailed layout plan. Further, the recent articles reported in the literature consider the dynamic environment for both equal and unequal area FLPs to cope with the changing market environment. It is also found that FLPs are Non-deterministic Polynomial-complete problems, and hence, they set the challenges to researchers to develop efficient meta-heuristic methods to solve the bigger size FLPs in a reasonable time.

Due to the extremely large number of papers on FLPs, a few papers may have inadvertently been missed. The facility layout design research domain is extremely vast which covers other areas such as cellular layouts, pick and drop points and aisle structure design. This research review on FLPs did not consider the papers published on cellular layouts, pick and drop points and aisle structure design. Despite the possibility of not being all-inclusive, the authors firmly believe that most of the papers published on FLPs are covered and the general picture presented on various approaches and parameters of FLPs in this paper are precise and trustworthy.

To the best of the authors’ knowledge, this paper reviews and classifies the literature on FLPs for the first time under the broader headings of discrete space and continuous space representations. Many important formulations of FLPs under static and dynamic environments represented in the discrete and continuous space are presented. This paper also provides the observations from the literature review and identifies the prospective future directions.