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The purpose of the paper is to present an integrated model for the location of warehouse, the allocation of retailers to warehouses, and finding the number of vehicles to deliver the demand and the required vehicle routing in order to minimize total transportation costs, fixed and operating costs, and routing costs.

The model assumes that the number of plants has already been determined and answers the following questions: what is the number of warehouses to open? How warehouse are allocated to plants? How retailers are allocated to warehouses? Who are the retailers that will be visited and in what order? How many vehicles are required for each route? What are the total minimum costs?

The model was formulated as a mixed integer linear programming model and solved using Lagrange relaxation and sub‐gradient search for the location/allocation module and a traveling salesman heuristic for the routing module. The results for the randomly selected problems show that the deviation in objective function value ranges between 0.29 and 2.05 percent from the optimum value. Also, from the CPU time point of view, the performance was very good.

An attempt is made to integrate location, allocation, and routing decisions in the design of a supply chain network.

Finding efficient disaster recovery center location-allocation-routing (DRCLAR) network schemes play a vital role in the disaster recovery logistics network (DRLN) design. The purpose of this paper is to propose and demonstrate how to design efficient DRCLAR network schemes under the risk of facility disruptions as a part of the disaster relief activities.

A goal programming (GP) model is formulated to consider four performance measures simultaneously for the DRCLAR design. The cross-evaluation based-super efficiency data envelopment analysis (DEA) approach is applied to better evaluate the DRCLAR network schemes generated by solving the GP model so that more efficient network schemes can be identified.

The proposed approach identifies more efficient DRCLAR network schemes consistently among various network schemes generated by GP. We find that combining these two methods compensates for each method's weaknesses and enhances the discriminating power of the DEA method for effectively identifying and ranking the network schemes.

This study presents how to generate balanced DRCLAR network schemes and how to evaluate various network schemes for identifying efficient ones. The proposed procedure of developing and evaluating them could be extended for designing some disaster recovery/relief supply chain systems with conflicting performance measures.

Today’s, supply chain production and distribution of products to improve the customer satisfaction in the shortest possible time by paying the minimum cost, has become the most important challenge in global market. On the other hand, minimizing the total cost of the transportation and distribution is one of the critical items for companies. To handle this challenge, this paper aims to present a multi-objective multi-facility model of green closed-loop supply chain (GCLSC) under uncertain environment. In this model, the proposed GCLSC considers three classes in case of the leading chain and three classes in terms of the recursive chain. The objectives are to maximize the total profit of the GCLSC, satisfaction of demand, the satisfactions of the customers and getting to the proper cost of the consumers, distribution centers and recursive centers.

Then, this model is designed by considering several products under several periods regarding the recovery possibility of products. Finally, to evaluate the proposed model, several numerical examples are randomly designed and then solved using non-dominated sorting genetic algorithm and non-dominated ranking genetic algorithm. Then, they are ranked by TOPSIS along with analytical hierarchy process so-called analytic hierarchy process-technique for order of preference by similarity to ideal solution (AHP-TOPSIS).

The results indicated that non-dominated ranked genetic algorithm (NRGA) algorithm outperforms non-dominated sorting genetic algorithm (NSGA-II) algorithm in terms of computation times. However, in other metrics, any significant difference was not seen. At the end, to rank the algorithms, a multi-criterion decision technique was used. The obtained results of this method indicated that NSGA-II had better performance than ones obtained by NRGA.

This study is motivated by the need of integrating the leading supply chain and retrogressive supply chain. In short, the highlights of the differences of this research with the mentioned studies are as follows: developing multi-objective multi-facility model of fuzzy GCLSC under uncertain environment and integrating the leading supply chain and retrogressive supply chain.

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.

Fortification-interdiction models provide system designers with a broader perspective to identify and protect vital components. Based on this concept, the authors examine how disruptions impact critical supply systems and propose the most effective protection strategies based on three levels of decision-makers. This paper aims to investigate location and fortification decisions at the first level. Moreover, a redesign problem is presented in the third level to locate backup facilities and reallocate undisrupted facilities following the realization of the disruptive agent decisions at the second level.

To address this problem, the authors develop a tri-level planner-attacker-defender optimization model. The model minimizes investment and demand satisfaction costs and alleviates maximal post-disruption costs. While decisions are decentralized at different levels, the authors develop an integrated solution algorithm to solve the model using the column-and-constraint generation (CCG) method.

The model and the solution approach are tested on a real supply system consisting of several hospitals and demand areas in a region in Iran. Results indicate that incorporating redesign decisions at the third level reduces maximum disruption costs.

The paper makes the following contributions: presenting a novel tri-level optimization model to formulate facility location and interdiction problems simultaneously, considering corrective measures at the third level to reconfigure the system after interdiction, creating a resilient supply system that can fulfill all demands after disruptions, employing a nested CCG method to solve the model.

Previously use of drones as a relief distribution vehicle was studied in several studies where required number of drones and the best locations for the relief centers were investigated. The maximum travel distance of drones without a need to recharge is limited by their endurance. Recharge stations can be used to extend the coverage area of the drones. The purpose of this paper is to find the best topology for both relief centers and recharge stations to cover a large-scale area with minimum and feasible incurred costs and waiting times.

A multi-level facility location problem (FLP) is utilized to find the optimum number of relief centers and refuel stations and their locations. It is supposed that the demand occurs according to Poisson distribution. The allocation of the demand is based on nearest neighborhood method. A hybrid genetic algorithm is proposed to solve the model. The performance of the algorithm is examined through a case study.

The proposed method delivers increased efficiency and responsiveness of the humanitarian relief system. The coverage area of the drones is extended by refuel stations, total costs of the system are reduced and the time to respond an emergency, which is an important factor in survival rate, is significantly decreased.

This study proposes a multi-level FLP to simultaneously account for recharge stations, relief centers and the number of required drones to cover all the demand for relief in a post-disaster period.

A growing body of evidence points to the influence of location and allocation decisions on the structure of healthcare networks. The authors introduced a three-level hierarchical facility location model to minimize travel time in the healthcare system under uncertainty.

Most healthcare networks are hierarchical and, as a result, the linkage between their levels makes it difficult to specify the location of the facilities. In this article, the authors present a hybrid approach according to data envelopment analysis and robust programming to design a healthcare network. In the first phase, the efficiency of each potential location is calculated based on the non-radial range-adjusted measure considering desirable and undesirable outputs based on a number of criteria such as the target area's population, proximity to earthquake faults, quality of urban life, urban decrepitude, etc. The locations deemed suitable are then used as candidate locations in the mathematical model. In the second phase, based on the proposed robust optimization model, called light robustness, the location and allocation decisions are adopted.

The developed model is evaluated using an actual-world case study in District 1 of Tehran, Iran and relevant results and different sensitivity analyses were presented as well. When the percentage of referral parameters changes, the value of the robust model's objective function increases.

The contributions of this article are listed as follows: Considering desirable and undesirable criteria to selecting candidate locations, providing a robust programming model for building a service network and applying the developed model to an actual-world case study.

The purpose of this paper is to investigate the economic feasibility of a three-echelon Halal Meat Supply Chain (HMSC) network that is monitored by a proposed radio frequency identification (RFID)-based management system for enhancing the integrity traceability of Halal meat products and to maximize the average integrity number of Halal meat products, maximize the return of investment (ROI), maximize the capacity utilization of facilities and minimize the total investment cost of the proposed RFID-monitoring system. The location-allocation problem of facilities needs also to be resolved in conjunction with the quantity flow of Halal meat products from farms to abattoirs and from abattoirs to retailers.

First, a deterministic multi-objective mixed integer linear programming model was developed and used for optimizing the proposed RFID-based HMSC network toward a comprised solution based on four conflicting objectives as described above. Second, a stochastic programming model was developed and used for examining the impact on the number of Halal meat products by altering the value of integrity percentage. The ε-constraint approach and the modified weighted sum approach were proposed for acquisition of non-inferior solutions obtained from the developed models. Furthermore, the Max-Min approach was used for selecting the best solution among them.

The research outcome shows the applicability of the developed models using a real case study. Based on the computational results, a reasonable ROI can be achievable by implementing RFID into the HMSC network.

This work addresses interesting avenues for further research on exploring the HMSC network design under different types of uncertainties and transportation means. Also, environmentalism has been becoming increasingly a significant global problem in the present century. Thus, the presented model could be extended to include the environmental aspects as an objective function.

The model can be utilized for food supply chain designers. Also, it could be applied to realistic problems in the field of supply chain management.

Although there were a few studies focusing on the configuration of a number of HMSC networks, this area is overlooked by researchers. The study shows the developed methodology can be a useful tool for designers to determine a cost-effective design of food supply chain networks.

In emergency services, maximizing population coverage with the lowest cost at the peak of the demand is important. In addition, due to the nature of services in emergency centers, including hospitals, the number of servers and beds is actually considered as the capacity of the system. Hence, the purpose of this paper is to propose a multi-objective maximal covering facility location model for emergency service centers within an M _(t)/M/m/m queuing system considering different levels of service and periodic demand rate.

The process of serving patients is modeled according to queuing theory and mathematical programming. To cope with multi-objectiveness of the proposed model, an augmented ε-constraint method has been used within GAMS software. Since the computational time ascends exponentially as the problem size increases, the GAMS software is not able to solve large-scale problems. Thus, a NSGA-II algorithm has been proposed to solve this category of problems and results have been compared with GAMS through random generated sample problems. In addition, the applicability of the proposed model in real situations has been examined within a case study in Iran.

Results obtained from the random generated sample problems illustrated while both the GAMS software and NSGA-II almost share the same quality of solution, the CPU execution time of the proposed NSGA-II algorithm is lower than GAMS significantly. Furthermore, the results of solving the model for case study approve that the model is able to determine the location of the required facilities and allocate demand areas to them appropriately.

In the most of previous works on emergency services, maximal coverage with the minimum cost were the main objectives. Hereby, it seems that minimizing the number of waiting patients for receiving services have been neglected. To the best of the authors’ knowledge, it is the first time that a maximal covering problem is formulated within an M _(t)/M/m/m queuing system. This novel formulation will lead to more satisfaction for injured people by minimizing the average number of injured people who are waiting in the queue for receiving services.

The research in competitive facility location (CFL) is quite dynamic, both from a problem formulation and an algorithmic point of view. Research direction has changed immensely over the years to address various competitive challenges. This study aims to explore CFL literature to highlight these research trends, important issues and future research opportunities.

This study utilises the Scopus database to search for related CFL models and adopts a five-step systematic approach for the review process. The five steps involve (1) Article Identification and keyword selection, (2) Selection criteria, (3) Literature review, (4) Literature analysis and (5) Research studies.

The paper presents a comprehensive review of CFL modelling efforts from 1981 to 2021 to provide a depth study of the research evolution in this area. The published articles are classified based on multiple characteristics, including the type of problem, type of competition, game-theoretical approaches, customer behaviour, decision space, type of demand, number of facilities, capacity and budget limitations. The review also highlights the popular problem areas and dedicated research in the respective domain. In addition, a second classification is also provided based on solution methods adopted to solve various CFL models and real-world case studies.

The paper covers 40 years of CFL literature from the perspective of the problem area, CFL characteristics and the solution approach. Additionally, it introduces characteristics such as capacity limit and budget constraint for the first time for classification purposes.