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AbstractIn this article, we propose a branch‐and‐price‐and‐cut (BPC) algorithm to exactly solve the manpower routing problem with synchronization constraints (MRPSC). Compared with the classical vehicle routing problems (VRPs), the defining characteristic of the MRPSC is that multiple workers are required to work together and start at the same time to carry out a job, that is, the routes of the scheduling subjects are dependent. The incorporation of the synchronization constraints increases the difficulty of the MRPSC significantly and makes the existing VRP exact algorithm inapplicable. Although there are many types of valid inequalities for the VRP or its variants, so far we can only adapt the infeasible path elimination inequality and the weak clique inequality to handle the synchronization constraints in our BPC algorithm. The experimental results at the root node of the branch‐and‐bound tree show that the employed inequalities can effectively improve the lower bound of the problem. Compared with ILOG CPLEX, our BPC algorithm managed to find optimal solutions for more test instances within 1 hour. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 138–171, 2016

Xiang Li,1,2,* Shu-Jie An,3,* Xiao-Ling Liu,1,* Ai-Ling Ji,4 Yi Cao,5 Ying Xiang,1 Xiang-Yu Ma,1 Qin Hu,1 Zhi-Quan Yuan,1 Ya-Fei Li,1 Yuan-Gang Lu,2 Tong-Jian Cai1 1Department of Epidemiology, College of Preventive Medicine, Army Medical University (Third Military Medical University), Chongqing, People's Republic of China; 2Department of Plastic & Cosmetic Surgery, Daping Hospital, Army Medical University (Third Military Medical University), Chongqing, People's Republic of China; 3Medical Department, Xijing Hospital, Air Force Medical University (Fourth Military Medical University), Xi'an, People's Republic of China; 4Department of Preventive Medicine & Chongqing Engineering Research Center of Pharmaceutical Sciences, Chongqing Medical and Pharmaceutical College, Chongqing, People's Republic of China; 5Department of Health Economics Management, Xijing Hospital, Air Force Medical University (Fourth Military Medical University), Xi'an, People's Republic of China*These authors contributed equally to this workCorrespondence: Yuan-Gang LuDepartment of Plastic & Cosmetic Surgery, Daping Hospital, Army Medical University, 10 Changjiang Branch Road, Daping, Chongqing, 400042, People's Republic of ChinaTel +86-23-68757597Fax +86-23-68757596Email skin515@163.comTong-Jian Cai Email ctjcsl@fmmu.edu.cnBackground: Post-adolescent acne is a common skin disease faced by adults. However, whether air pollution (AP) serves as a risk factor for post-adolescent acne remains elusive.Aim: To determine the relationship between short-term AP exposure (within 7 days) and outpatient visits for post-adolescent acne.Methods: Daily outpatient visit data for post-adolescent acne and routinely AP data between 2010 and 2013 were collected from Xi'an, China. A generalized additive regression model was used to analyze the relationship between outpatient visits for post-adolescent acne and short-term ambient AP exposure. The gender-specific analyses were conducted as well.Results: Totally, 27,190 outpatient visits for post-adolescent acne were included. The results revealed that a 10 μg/m3 increase in PM10, SO2, and NO2 at lag 0– 7 day was associated with the increase of outpatient visits for post-adolescent acne at 0.84% (95% CI: 0.53%, 1.16%), 1.61% (95% CI: 0.12%, 3.10%), and 3.50% (95% CI: 1.60%, 5.40%), respectively. The significant positive associations of PM10, SO2, and NO2 were found at both single-lag models and moving average models. The gender-specific analyses showed that the effect estimates of PM10 was stronger for females than for males, while there was no observed gender difference in the effects of SO2 and NO2.Conclusion: Short-term exposure to AP was associated with increased outpatient visits for post-adolescent acne, especially for females in the effects of PM10.Keywords: short-term, air pollution, post-adolescent acne, adult acne, time-series analysis