INTRODUCTION
Managing waste is a mammoth task as it needs to be collected, transported and finally disposed of. Beltrami and Bodin (1974) were firstly introduced Vehicle Routing Problem (VRP) in municipal waste collection in New York City where 25,000 tons of waste needed to be collected. In general, Capacitated Arc Routing Problem (CARP) is another kind of routing problem specifically designed to formulate vehicle routing operation in solid waste collection or snow plow. This routing model was introduced by Golden and Wong (1981) and considered as a special domain of VRP but on the other hand, CARP has been comparatively neglected. Since then, CARP progressed in theory and applications and had shown important roles in waste collection industry. Some of the latest developments and applications of CARP could be seen in Letchford and Oukil (2009); Christiansen et al. (2009); Santos et al. (2010); and Gouveia et al. (2010).
However, very few researches considered external factors (such like weather and temperature) in modeling CARP. To our knowledge, Amponsah and Salhi (2004) has considered element of hot weather in modeling CARP and developed a constructive heuristic based on look ahead strategy which takes into account the environmental aspect as well as the cost to solve the routing of garbage collection. Another work is done by Hsu et al. (2007) where the time-varying temperatures and human interaction during cargo opening have affected onto VRP model. However, their work was done onto food transportation and in contrary was applied to VRP which in practice its vehicle's operation is difference to CARP. By this means, this study tries to investigate the influence of rainy weather onto vehicle's operation in waste collection. Objectively, this study aims to determine the total cost for a vehicle and constructing the routes that minimizes the total trips needed to complete the services for both weather-type operations.
CARP and VRP are coexist with the same purpose but originated from different problem background. In CARP, customers' demands are located along the arcs and the vehicle is giving its service when it moves from one arc to another. While VRP, which is also known as node based routing; the vehicle is giving its service when it arrives at a certain node or point. In other words, in waste collection from CARP point of view, the customers are located along the arcs, not at the nodes. Both are NP-hard problems, rich in research and no method could be claimed as the best so far. A method usually fit for one specific problem and only suit for a certain routing model. Met heuristic methods such as tabu search or genetic algorithms however are the popular solutions used by mathematician in order to find the optimal routing path of the vehicles and to seek the lowest cost.
The mathematical structure of CARP is a network graph where each junction is jointed by a point (node) and lines are drawn connecting two nodes, called arcs or edges. The operation of the vehicle starts and ends at the depot, O and services each arc only once. The customers' demands (or quantity of garbage), [q.sub.ij] Greater than 0 and service cost, [c.sub.ij] Greater than 0 are associated to every arcs. The total demand, Q must not exceed the capacity of the vehicle, W, that is Q[less than or equal to]W. In CARP, each arc in the graph can be traveled in both direction and each vertex corresponds to a road junction (node). Some variants extensions on CARP also can be seen Lacomme et al. (2005); Chu et al. (2006) where periodic CARP (PCARP) was applied; Bautista et al. (2008) and Christiansen et al. (2009) solved mixed CARP (MCARP) and CARPSD respectively.
This study also describes a new model of CARP, by introducing a mesh network which approximately represents the layout of resident houses area in Malaysia. Basically, the houses are located side by side along the road and each road is connected by a main road as the backbone (Fig. 1).
[FIGURE 1 OMITTED]
MATERIALS AND METHODS
Data source: The primary data is a real-life observation on solid waste collection in Johor Bahru, the capital city of Johor, Malaysia for 32 operational days. We collected the raw data onto one identical truck operation in waste collection sub-contractor in South Johor. We delivered our study on one residential area in Johor Bahru that 1266 houses involved in this research. The Table 1 below displays primary or raw data for one identical truck in 32 operational days.
Author: Zuhaimy Ismail, Mohammad Fadzli Ramli
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