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Ambulance response time is an important factor in saving lives and is highly linked with the ambulance location problem. The Maximum Expected Covering Location Problem (MEXCLP), introduced by Daskin (1983), is one of the most used ambulance location models that maximize the probability of stratifying demands for emergency medical service (EMS) centers. Due to huge increase in the operational costs of EMS centers, ambulance location models must consider the cost of coverage and the opportunity to use other companies’ private ambulances to answer emergency calls. The paper aims to discuss these issues.

In this paper, the authors propose to extend the MEXCLP to a bi-objective optimization problem where the cost of satisfying emergency calls is minimized.

The proposed model is tested using data retrieved from the Lebanese Red Cross (LRC) in Beirut capital of Lebanon. The reported findings show significant enhancements in the results where the LRC can fully satisfy the perceived demands from all areas in Beirut within 9 min with an affordable cost.

The model is a first attempt to reduce operational costs of EMS centers while constraining the response time to satisfy emergency calls at an acceptable rate.

This paper aims to minimize the mean-risk cost of sustainable and resilient supplier selection, order allocation and production scheduling (SS,OA&PS) problem under uncertainty of disruptions. The authors use conditional value at risk (CVaR) as a risk measure in optimizing the combined objective function of the total expected value and CVaR cost. A sustainable supply chain can create significant competitive advantages for companies through social justice, human rights and environmental progress. To control disruptions, the authors applied (proactive and reactive) resilient strategies. In this study, the authors combine resilience and social responsibility issues that lead to synergy in supply chain activities.

The present paper proposes a risk-averse two-stage mixed-integer stochastic programming model for sustainable and resilient SS,OA&PS problem under supply disruptions. In this decision-making process, determining the primary supplier portfolio according to the minimum sustainable-resilient score establishes the first-stage decisions. The recourse or second-stage decisions are: determining the amount of order allocation and scheduling of parts by each supplier, determining the reactive risk management strategies, determining the amount of order allocation and scheduling by each of reaction strategies and determining the number of products and scheduling of products on the planning time horizon. Uncertain parameters of this study are the start time of disruption, remaining capacity rate of suppliers and lead times associated with each reactive strategy.

In this paper, several numerical examples along with different sensitivity analyses (on risk parameters, minimum sustainable-resilience score of suppliers and shortage costs) were presented to evaluate the applicability of the proposed model. The results showed that the two-stage risk-averse stochastic mixed-integer programming model for designing the SS,OA&PS problem by considering economic and social aspects and resilience strategies is an effective and flexible tool and leads to optimal decisions with the least cost. In addition, the managerial insights obtained from this study are extracted and stated in Section 4.6.

This work proposes a risk-averse stochastic programming approach for a new multi-product sustainable and resilient SS,OA&PS problem. The planning horizon includes three periods before the disruption, during the disruption period and the recovery period. Other contributions of this work are: selecting the main supply portfolio based on the minimum score of sustainable-resilient criteria of suppliers, allocating and scheduling suppliers orders before and after disruptions, considering the balance constraint in receiving parts and using proactive and reactive risk management strategies simultaneously. Also, the scheduling of reactive strategies in different investment modes is applied to this problem.

Introduction Operations research, i.e. the application of scientific methodology to operational problems in the search for improved understanding and control, can be said to have started with the application of mathematical tools to military problems of supply bombing and strategy, during the Second World War. Post‐war these tools were applied to business problems, particularly production scheduling, inventory control and physical distribution because of the acute shortages of goods and the numerical aspects of these problems.

Supplier selection problem is the key process in decision making of supply chain management. An effective selection of vendors is heavily responsible for the success of any organization. Vendor selection problem (VSP) reflects a more practical view when the decision makers involved in the problem are present on different levels. Moreover, vendor selection consists of various random parameters to be dealt with in real life. The purpose of this paper is to present a decentralized bi-level VSP where demand and supply are normal random variables and objectives are fuzzy in nature. Decision makers are present at two levels and are called as leader and follower. As the next purpose, this paper extends and presents a solution approach for fuzzy bi-level multi-objective decision-making model with stochastic constraints. Different scenarios have been developed within a real-life case study based on different sets of controlling factors under the control of leader.

This study uses chance-constrained programming and fuzzy set theory to generate the results. Stochastic constraints are converted into deterministic constraints using chance-constrained programming. Decision variables in the bi-level VSP are partitioned between the two levels and considered as controlling factors. Membership functions based on fuzzy set theory are created for the goals and controlling factors and are used to obtain the overall satisfactory solutions. The model is tested on a real-life case study of a textile industry and different scenarios are constructed based on the choice of leader’s controlling factors.

Results showed that the approach is quite helpful as it generates efficient results producing a good level of satisfaction for the decision makers of both the levels. Results showed that on choosing the vendors that are associated with worst values in terms of associated costs, vendor ratings and quota flexibilities as controlling factors by the leaders, the level of satisfaction achieved is highest. The level of satisfaction of solution is lowest for the scenario when the leader chooses to control the decision variables associated with vendors that are profiled with minimum vendor ratings. Results also showed that higher availability of materials and budget with vendors proved helpful in obtaining quota allocations. Different scenarios generate different results along with different values of satisfaction degrees and objective values which shows the flexible feature of the approach based on leader’s choice of controlling factors. Numerical results showed that the leader’s control can be effectively incorporated maintaining satisfaction levels of the followers under various scenarios or conditions.

The paper makes a certain contribution toward the study of vendor selection existing in a hierarchical manner under uncertain environment. A wide set of data of different factors is needed which can be seen as a limitation when the available time is short for the supplier selection process.

VSP which is generally adopted by most of the large organizations is characterized with hierarchical decision making. Moreover, dealing with the real-life concern, the data available for some of the parameters are not complete, representing an uncertainty of parameters. This study is quite helpful for decentralized VSP under uncertain environment to reduce the costs, improve profit margins and to create long-term relationships with selected vendors. The proposed model also provides an avenue to explore the decision making when the leader has control over some of the decision variables.

Reviewing the literature available, this is the first attempt to present a multi-objective VSP where the decision makers are at hierarchical levels considering uncertain parameters such as demand and supply as per the best knowledge of authors. This research further provides an approach to construct scenarios or different cases based on the choice of leader’s choice of controlling factors.

In this paper, vendor selection and order allocation problem is considered for a buyer dealing in multiple products to be supplied by multiple vendors. Each product has an associated lead time with stochastic demand having stochastic capacity for each vendor across entire time period. Uncertainties related to costs which are further influenced by the periodically changing incremental quantity discounts offered by various vendors. The purpose of this paper is to find an optimal trade-off of vendor selection and order allocation in the presence of uncertainties involving multiple conflicting objectives such as cost minimization, service level/quality level maximization and delivery lead time minimization concurrently.

Vendor selection problem considered here has a multi-objective optimization design subject to a set of demand, capacity and quantity discount based constraints. These constraints as well as uncertainty related to lead time have been handled using chance constraint approach. The problem is titled as “integrated dynamic vendor selection problem (IDVSP).” The proposed multi-objective IDVSP is solved using both non-pre-emptive goal programming (GP) and weighted sum aggregate objective function (AOF) technique.

Findings indicate goal achievement for different objectives from both non-pre-emptive GP and AOF procedure. While the goals are satisfactorily achieved as per the target values for cost and lead time, quality/service level was somewhat compromised in order to find an appropriate trade off.

The research work is original as it integrates dynamic as well as stochastic (uncertain) nature of supply chain simultaneously coupled with the concept of incremental quantity discounts on lot sizes.

Globalization of markets and pace of technological change have caused the growing importance of paying attention to supplier selection problem. Therefore, this study aims to choose the best suppliers by providing a mathematical model for the supplier selection problem considering the green factors and stochastic parameters. This paper aims to propose a multi-objective model to identify optimal suppliers for a green supply chain network under uncertainty.

The objective of this model is to select suppliers considering total cost, total quality parts and total greenhouse gas emissions. Also, uncertainty is tackled by stochastic programming, and the multi-objective model is solved as a single-objective model by the LP-metric method.

Twelve numerical examples are provided, and a sensitivity analysis is conducted to demonstrate the effectiveness of the developed mathematical model. Results indicate that with increasing market numbers and final product numbers, the total objective function value and run time increase. In case that decision-makers are willing to deal with uncertainty with higher reliability, they should consider whole environmental conditions as input parameters. Therefore, when the number of scenarios increases, the total objective function value increases. Besides, the trade-off between cost function and other objective functions is studied. Also, the benefit of the stochastic programming approach is proved. To show the applicability of the proposed model, different modes are defined and compared with the proposed model, and the results demonstrate that the increasing use of recyclable parts and application of the recycling strategy yield more economic savings and less costs.

This paper aims to present a more comprehensive model based on real-world conditions for the supplier selection problem in green supply chain under uncertainty. In addition to economic issue, environmental issue is considered from different aspects such as selecting the environment-friendly suppliers, purchasing from them and taking the probability of defective finished products and goods from suppliers into account.

This paper proposes a two-level supply chain including suppliers and manufacturers. The purpose of this paper is to design a resilient fuzzy risk-averse supply portfolio selection approach with lead-time sensitive manufacturers under partial and complete supply facility disruption in addition to the operational risk of imprecise demand to minimize the mean-risk costs. This problem is analyzed for a risk-averse decision maker, and the authors use the conditional value-at-risk (CVaR) as a risk measure, which has particular applications in financial engineering.

The methodology of the current research includes two phases of conceptual model and mathematical model. In the conceptual model phase, a new supply portfolio selection problem is presented under disruption and operational risks for lead-time sensitive manufacturers and considers resilience strategies for risk-averse decision makers. In the mathematical model phase, the stages of risk-averse two-stage fuzzy-stochastic programming model are formulated according to the above conceptual model, which minimizes the mean-CVaR costs.

In this paper, several computational experiments were conducted with sensitivity analysis by GAMS (General algebraic modeling system) software to determine the efficiency and significance of the developed model. Results show that the sensitivity of manufacturers to the lead time as well as the occurrence of disruption and operational risks, significantly affect the structure of the supply portfolio selection; hence, manufacturers should be taken into account in the design of this problem.

The study proposes a new two-stage fuzzy-stochastic scenario-based mathematical programming model for the resilient supply portfolio selection for risk-averse decision-makers under disruption and operational risks. This model assumes that the manufacturers are sensitive to lead time, so the demand of manufacturers depends on the suppliers who provide them with services. To manage risks, this model also considers proactive (supplier fortification, pre-positioned emergency inventory) and reactive (revision of allocation decisions) resilience strategies.

This study aims to minimize the expected arrival time of relief vehicles to the affected areas, considering the destruction of potential routes and disruptions due to disasters. In relief operations, required relief items in each affected area and disrupted routes are considered as uncertain parameters. Additionally, for a more realistic consideration of the situations, it is assumed that the demand of each affected area could be met by multiple vehicles and distribution centers (DCs) and vehicles have limited capacity.

The current study developed a two-stage stochastic programming model for the distribution of relief items from DCs to the affected areas. Locating the DCs was the first-stage decisions in the introduced model. The second-stage decisions consisted of routing and scheduling of the vehicles to reach the affected areas.

In this paper, 7th district of Tehran was selected as a case study to assess the applicability of the model, and related results and different sensitivity analyses were presented as well. By carrying out a simultaneous sensitivity analysis on the capacity of vehicles and the maximum number of DCs that can be opened, optimal values for these parameters were determined, that would help making optimal decisions upon the occurrence of a disaster to decrease total relief time and to maximize the exploitation of available facilities.

The contributions of this paper are as below: presenting an integrated model for the distribution of relief items among affected areas in the response phase of a disaster, using a two-stage stochastic programming approach to cope with route disruptions and uncertain demands for relief items, determining location of the DCs and routing and scheduling of vehicles to relief operations and considering a heterogeneous fleet of capacitated relief vehicles and DCs with limited capacity and fulfilling the demand of each affected area by more than one vehicle to represent more realistic situations.

Logistics is the part of the supply chain (SC) that plans, executes and handles forward and reverse movement and storage of products, services and related information, in order to respond to customers' needs effectively and efficiently. The main concern for logistics is to ensure that the correct product is placed at the right time. This paper introduces a linear model of shipping focused on decision-making, which includes configuration of shipping network, choosing of transport means and transfer of individual customer shipments through a particular transport system.

In this study, authors try to address the problem of supply chain network (SCN) where the primary goal is to determine the appropriate order allocation of products from different sources to different destinations. They also seek to minimize total transportation cost and inventory cost by simultaneously determining optimal locations, flows and shipment composition. The formulated problem of getting optimal allocation turns out to be a problem of multi-objective programming, and it is solved by using the max-addition fuzzy goal programming approach, for obtaining optimal order allocation of products. Furthermore, the problem demand and supply parameters have been considered random in nature, and the maximum likelihood estimation approach has been used to assess the unknown probabilistic distribution parameters with a specified probability level (SPL).

A case study has also been applied for examining the effectiveness and applicability of the developed multi-objective model and the proposed solution methods. Results of this study are very relevant for the manufacturing sector in particular, for those facing logistics issues in SCN. It enables researchers and managers to cope with various types of uncertainty and logistics risks associated with SCN.

The principal contribution of the proposed model is the improved modelling of transportation and inventory, which are affected by different characteristics of SCN. To demonstrate computational information of the suggested methods and proposed model, a case illustration of SCN is provided. Also, environmentalism is increasingly becoming a significant global concern. Hence, the concept proposed could be extended to include environmental aspects as an objective function or constraint.

Efficient integration of logistical cost components, such as transportation costs, inventory costs, with mathematical programming models is an important open issue in logistics optimization. This study expands conventional facility location models to incorporate a range of logistic system elements such as transportation cost and different types of inventory cost, in a multi-product, multi-site network. The research is original and is focused on case studies of real life.

The adverse interactions between disruptions can increase the supply chain's vulnerability. Accordingly, establishing supply chain resilience to deal with disruptions and employing business continuity planning to preserve risk management achievements is of considerable importance. The aforementioned idea is discussed in this study.

This study proposes a multi-objective optimization model for employing business continuity management and organizational resilience in a supply chain for responding to multiple interrelated disruptions. The improved augmented e-constraint and the scenario-based robust optimization methods are adopted for multi-objective programming and dealing with uncertainty, respectively. A case study of the automotive battery manufacturing industry is also considered to ensure real-world conformity of the model.

The results indicate that interactions between disruptions remarkably increase the supply chain's vulnerability. Choosing a higher fortification level for the supply chain and foreign suppliers reduces disruption impacts on resources and improves the supply chain's resilience and business continuity. Facilities dispersion, fortification of facilities, lateral transshipment, order deferral policy, dynamic capacity planning and direct transportation of products to markets are the most efficient resilience strategies in the under-study industry.

Applying resource allocation planning and portfolio selection to adopt preventive and reactive resilience strategies simultaneously to manage multiple interrelated disruptions in a real-world automotive battery manufacturing industry, maintaining the long-term achievements of supply chain resilience using business continuity management and dynamic capacity planning are the main contributions of the presented paper.