The COVID-19 pandemic, which is still spreading its new mutations all around the world, is considered a healthcare challenge around the world. The best approach to forestall this pandemic is to avoid exposure to the virus. Therefore, medical protective equipment is essential for fighting this pandemic. This underlines the chief role of having a sustainable supply chain network (SCN) for producing and distributing personal protective equipment to avoid shortage and augmenting costs. The reality, however, is that the COVID-19 pandemic leads to many developments in countries and this study is another step for these purposes. This research develops a multi-period, multi-objective, multi-echelon, and multi-product medical protective equipment sustainable SCN considering the production, distribution, allocation, and inventory with “risk pooling” strategy effect with the aim of filling the existing gaps in health SCN research during the COVID-19 pandemic. By applying the risk pooling strategy, lower inventory levels or higher service levels can be achieved without increasing inventory costs. This model explores the possibility of lateral transshipments between distribution centers, as a way to increase the reliability of SCN performance. We model a new production, inventory, distribution, location, and allocation problem and consider four objectives for our suggested model (i) minimizing total SCN costs, (ii) minimizing environmental effects , (iii) minimizing social impacts, and (iv) maximizing the reliability of demand delivery. The proposed model simultaneously examines all three dimensions of sustainability (economic, environmental, and social) as well as the reliability of demand delivery. Considering all of these decisions and assumptions brings the studied problem closer to reality. We employ various algorithms for solving our developed model with different sizes: the improved version of the augmented ε-constraint (AUGMECON2) algorithm for small and medium-sized problems and two meta -heuristic algorithms, i.e., Multi-Objective Whale Optimization Algorithm (MOWOA) and Multi-Objective Variable Neighborhood Search (MOVNS) algorithm, for large-sized ones. The Taguchi approach is used to tune the parameters of meta -heuristic algorithms, and a comparison is performed using four evaluation metrics: Mean Ideal Distance (MID), Number of Pareto Solutions (NPS), Maximum Spread (MS), and Spread of Non-Dominance Solution (SNS). Proposed solving methods for the studied problem and making comparisons between them are another innovation of this study. A couple of numerical examples are provided to illustrate the applicability of the presented solution methods. Finally, sensitivity analysis for problem parameters is performed to validate our suggested model. Our study reveals the superiority of the MOWOA over the other algorithms.

Adopting various pricing policies has been highly regarded in recent years for setting prices and increasing firms' profits. One of the most common steps in pricing is to identify costs. Since a significant part of costs is related to the corresponding supply chain, many researchers in different fields have used decision-making for simultaneous pricing and network design. However, there is no such approach in the field of healthcare. This paper tries to fill this gap by formulating a mixed-integer nonlinear bi-level programming model examining the interaction of hospitals and their medicines suppliers. At the upper level, there is a competitive market where a new firm (entrant) intends to enter the market and faces the challenge of pricing medicines and making network design decisions. At the lower level, there is a private hospital competing with a public hospital, and it also struggles with healthcare services pricing and supplier selection. A comprehensive utility function that considers healthcare services prices, quality, waiting time, health insurance, readmission rate, and referral rate is extended at this level. Three novel meta-heuristic algorithms are recommended, including bi-level, improved fruit fly, jellyfish optimization, and forensic-based investigation optimization algorithms to solve the presented complex mathematical problem.

Abstract The concept of sustainability consists of three main dimensions: environmental, techno‐economic, and social. Measuring the sustainability status of a system or technology is a significant challenge, especially when it needs to consider a large number of attributes in each dimension of sustainability. In this study, we first propose a hybrid approach, involving data envelopment analysis (DEA) and a multi‐attribute decision making (MADM) methodologies, for computing an index for each dimension of sustainability, and then we define the overall sustainability index as the mean of the three measured indexes. Towards this end, we define new concepts of efficiency and cross‐efficiency of order (p, q) where p and q are the number of inputs and outputs, respectively. For a given (p, q), we address the problem of finding efficiency of order (p, q) by developing a novel DEA‐based selecting method. Finally, we define the sustainability index as a weighted sum of all possible cross‐efficiencies of order (p, q). Form a computational viewpoint, the proposed selecting model significantly decreases the computational burden in comparison with the successive solving of traditional DEA models. A case study of the electricity‐generation technologies in the United Kingdom is taken as a real‐world example to illustrate the potential application of our method.

All models in data envelopment analysis (DEA) have been built on the foundation of performance factors. Performance factors in DEA are divided conventionally into the input and output measures. In some positions, we confront with dual-role factors which can play simultaneously input and output roles. Traditionally, all performance factors are considered as precise values, while in some real-world problems they characterized as imprecise values. In this paper, we evaluate the performance of 18 third-party reverse logistics (3PL) providers in the presence of dual-role factors and under uncertainty. We illustrate the superiority of the employed DEA approach over a suggested approach in the literature.

Finding and classifying all efficient solutions for a Bi-Objective Integer Linear Programming (BOILP) problem is one of the controversial issues in Multi-Criteria Decision Making problems. The main aim of this study is to utilize the well-known Data Envelopment Analysis (DEA) methodology to tackle this issue. Toward this end, we first state some propositions to clarify the relationships between the efficient solutions of a BOILP and efficient Decision Making Units (DMUs) in DEA and next design a new two-stage approach to find and classify a set of efficient solutions. Stage I formulates a two-phase Mixed Integer Linear Programming (MILP) model, based on the Free Disposal Hull (FDH) model in DEA, to gain a Minimal Complete Set of efficient solutions. Stage II uses a variable returns to scale DEA model to classify the obtained efficient solutions from Stage I as supported and non-supported. A BOILP model containing 6 integer variables and 4 constraints is solved as an example to illustrate the applicability of the proposed approach.