Abstract
This paper studies a multi-trip vehicle routing problem with time windows specifically related to urban waste collection. Urban waste collection is one of the municipal activities with large costs and has many practical difficulties. In other words, waste collection and disposal is a costly task due to high operating expenses (fuel, maintenance, recycling, manpower, etc.) and small improvements in this field can result in tremendous savings on municipal expenditure. In the raised problem, the goal is to minimize total cost including traversing cost, vehicle employment cost, and exit penalty from permissible time windows. In this problem, the waste is deposited at the points indicating the demand nodes, in which each demand shows the volume of generated waste. Considering multiple trips for vehicles and time windows are the most critical features of the problem, so that the priorities of serving some specific places such as hospitals can be observed. Since vehicle routing problems (VRP) belongs to NP-hard problems, an efficient simulated annealing (SA) is proposed to solve the problem. The computational results show that our proposed algorithm has a great performance in a short computational time in comparison with the CPLEX solver. Finally, in order to demonstrate the applicability of the model, a case study is analyzed in Iran, and the optimal policies are presented.
Highlights
The world population has grown dramatically in the last 10 years, with annual growth rates of 1.1%
Optimal routing and vehicle allocating are one of the important decisions of organizations such as municipalities in the urban waste collection, since optimal vehicles’ allocation and their optimal routing can lead to a significant percentage reduction of related costs
A mixed-integer linear programming (MILP) model is proposed for heterogeneous multi-trip vehicle routing problem with time windows specific to the urban waste collection, which aims to determine the optimal service routes and the optimal number of the used vehicles
Summary
The world population has grown dramatically in the last 10 years, with annual growth rates of 1.1%. 1. Developing a novel waste collection model for the real-world applications by considering a maximum available time for vehicles in addition to the possibility of having multiple trips – hard and soft time windows for covering all demand nodes according to the priorities of service, and separate locations for the disposal site and the depot. In the following: the proposed mathematical model is presented in the second section; in the third section, the proposed solution method is introduced; in the fourth section, the numerical results from the implementation of the algorithm are presented; and the conclusions and suggestions for future works are given in the fifth section This problem involves obtaining the optimal number of used vehicles and the optimal routes of each vehicle in order to minimize the total cost, which includes the usage cost of vehicles, traversing cost through network edges, and violating penalty cost from the permissible time windows of services. Cost of the traversing edge (i , j) Early service cost per demand node Late service cost per demand node Hard time window of demand node i Soft time window of demand node i Vehicle capacity Demand of node j Maximum available time for each vehicle Optional large number The node indicating the disposal site and the number of total nodes in the network with the first node being the depot Unit of loading time for vehicles at demand nodes Unit of discharging time for vehicles at the disposal site Time for traversing edge (i , j) Converter coefficient of distance to cost (Iranian rial/km)
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