Solid waste generation continuously puts tremendous pressure on human health, socio-economic and environmental protection, and many regions are transitioning to the circular economy using waste recycling to advance sustainable development. A more practical and integrated solid waste recycling network (SWRN) design is essential for solid waste recycling management, which can be complex and uncertain. Therefore, this paper focuses on the design of a robust SWRN that aims to optimize the construction of sorting centers (SCs) while robustly operating with waste recycling allocation. This approach often involves two main challenges related to the uncertainty of unknown distribution information and the bi-level structure of decision making. To address these challenges, we first present two pairs of uncertainty sets to capture the separation rate and transportation cost in the case of free distribution information. Then, we develop a bi-level framework that integrates SC construction locations and waste operation allocation. For this purpose, a globalized robust optimization bi-level model is developed and reformulated into a mixed integer linear programming. We apply this methodology to the case of Baoding, China to demonstrate its validity. The main numerical achievements show that: (1) the proposed model can hedge the uncertainty in the separation rate and transportation cost with a small price of robustness and provide a robust recovery scheme; (2) the average operating cost of our model for a single period is approximately 19.4% lower than that of the classical robust model; and (3) by adjusting several parameters based on the preferences of waste recycling managers, a balance between operating costs and robustness can be achieved. Finally, some managerial insights are obtained to assist waste recycling managers in solid waste recycling management transition to the circular economy.
In real-world counterterrorism activities, it is usually difficult for the defender and the attacker to accurately know the private information of the each other such as valuations of targets. Instead, players may only know the relative preference on the target valuations from the adversary. In the conflict analysis, graph model is a powerful tool for dealing with relative preferences. This paper studies the defensive resource allocation in terrorism conflict management with incomplete information by establishing a graph model. To solve the model, we divide the conflict states into two types and discuss the conditions under which these two types of states are at equilibrium. Furthermore, we study how the defender should optimally allocate the resource to achieve two goals: (i) achieving a certain Nash equilibrium state desired by the defender; and (ii) minimizing the total loss from an attack in equilibrium. Subsequently, we conduct several numerical analyses: (i) analyzing the effects of both players' investment effectiveness on the optimal defense loss; (ii) comparing our model's results with those obtained using three classical decision methods, revealing that the defense loss in our model is lower; and (iii) presenting a case study to illustrate the applicability of the proposed model. This paper provides novel insights on how to efficiently allocate defensive resource when the defender and attacker know only the relative preference of the adversary on target valuations.
To address the residency training performance and further explore its determinants, with the help of a unique dataset, our study calculated the efficiency of residency training and health outcomes in 18 Chinese tertiary hospitals from 2020 to 2021 using a two-stage data envelopment analysis (DEA) model given the two-stage characteristics of vocational training and clinical practice of residents. The results showed that the efficiency of the sample hospitals in both residency training and medical service provision was high, there are approximately 1/3 hospitals of sub-efficient in each stage, but the number of efficient units for assessing the residency training performance was slightly less than that for assessing the health outcome performance. All the decision-making units (DMUs) were clustered into four groups through K-means cluster analysis according to efficiency results. The results showed that there was an obvious inconsistency between the teaching goals and the health outcome goals of Chinese public hospitals. In some hospitals, the low residency pass rate resulted in the low efficiency in stage 1, while the redundant inputs in beds resulted in the low efficiency in stage 2. Residency training hospitals should strengthen their synergistic management in programs of residency training and health outcomes.