A robust periodic capacitated arc routing problem for urban waste collection considering drivers and crew’s working time Erfan Babaee Tirkolaee a,⇑ , Iraj Mahdavi a , Mir Mehdi Seyyed Esfahani b a Department of Industrial Engineering, Mazandaran University of Science & Technology, Babol, Iran b Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran article info Article history: Received 3 December 2017 Revised 7 March 2018 Accepted 8 March 2018 Available online xxxx Keywords: Waste collection Capacitated arc routing problem Working time Simulated annealing Robust optimization abstract In this paper, a novel mathematical model is developed for robust periodic capacitated arc routing problem (PCARP) considering multiple trips and drivers and crew’s working time to study the uncertain nature of demand parameter. The objective function of the proposed model aims to minimize total tra- versed distance and total usage cost of vehicles over a planning period. To solve the problem, an improved hybrid simulated annealing algorithm (SA) is developed based on a heuristic algorithm and an efficient cooling equation. It has been proved that the performance of the proposed algorithm is acceptable in comparison with the exact solution method. Finally, the results have shown the effects of different uncertainty level of the demand parameter on the problem to be considered as a managerial overview in decision making process under uncertainty. Ó 2018 Elsevier Ltd. All rights reserved. 1. Introduction Nowadays, generating different types of solid wastes and man- ifestation of their associated social, economic and environmental inconsistencies create numerous complications for urban service management in regard to the collection, transportation, processing and disposal of such wastes. An optimal planning in collecting, management, and disposal of urban waste are one of the most important strategies that can yield multiple improvements in both total cost and health. Due to the fact that 60–80 percent of costs of solid wastes man- agement are related to collecting and transporting them (Lifset, 1992), the evaluation of underlying collection and transportation system plays a significant role in reducing and solving the prob- lems of urban service management (Golden et al., 2002). The wastes should be collected, transported and disposed in the least time, through the best method, and directly from household areas to disposal sites. Based on the above discussions, the significance of an optimal system of waste collection becomes more highlighted. Therefore, selection of optimal policy of waste collection has a significant impact on reducing costs. In routing problems related to the urban wastes collection, two categories of problems are defined (Golden et al., 2002). In the first category, there is a predefined node series with positive demand and the objective is to find the best tours which cover all nodes-Capacitated Vehicle Routing Problem (CVRP). In the second category, a series of predefined edges is existed with positive or zero demand and the objective is to find the best tours covering all required edges (edges with positive demand)-Capacitated Arc Routing Problem (CARP). Although VRP has been studied widely in the literature with numerous applications (Tirkolaee et al., 2017; Mirmohammadi et al., 2017; Alinaghian et al., 2014), the CARP has more appropri- ate application in studying waste collection and its routing prob- lems (Babaee Tirkolaee et al., 2016). So, the second category is the problem being studied in this research. In this problem, wastes are along the edges (i.e. streets or alleys with demands). In addi- tion, the capacity of vehicles is limited and when vehicles traverse the required edges, their remained capacities decrease. Drivers and crew’s working time is another important parameter which has a great impact on determining the number of required vehicles besides the capacity constraints. The objective is defined to deter- mine the optimal routes of serving the required edges based on a daily planning in a week. In the following, important research in the literature of CARP for urban waste collection has been reviewed and described. Chu et al. (2005) introduced a periodic capacitated arc routing problem (PCARP) in order to provide a weekly planning horizon. They proposed a mathematical model based on a mixed integer linear programming (MILP) and solved the problem through two innovative methods. The objective was to assign a set of service https://doi.org/10.1016/j.wasman.2018.03.015 0956-053X/Ó 2018 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: e.babaee@in.iut.ac.ir (E.B. Tirkolaee). Waste Management xxx (2018) xxx–xxx Contents lists available at ScienceDirect Waste Management journal homepage: www.elsevier.com/locate/wasman Please cite this article in press as: Tirkolaee, E.B., et al. A robust periodic capacitated arc routing problem for urban waste collection considering drivers and crew’s working time. Waste Management (2018), https://doi.org/10.1016/j.wasman.2018.03.015