Modelling tank truck routing for city park watering problems in Surabaya

Surabaya City Government tries to have 20% public and 10% private green open space to obey regulation of Indonesian Law No. 26/2007, so that the City Government is actively increasing the number of public green space by creating city parks. With the ever-increasing amount of green open space, maintenance activities are needed, one of which is to do routine watering every day. The problem often faced by the City Government is determining the truck routes to optimize traveling time. Many variables can affect this traveling time, among others, demand, number of vehicles, vehicle capacity, time windows, operating hours and vehicle routes. In practice, a large number of watering locations, irregular routes, and uneven service area assignments often result in overtime which impacts the next shift working hours. The water truck routing problem can be categorized as NP Hard so that the process of scheduling and determining routes use Ant Colony. The objective of this study is to develop a model that can minimize the total routing time and the number of vehicles in the process of filling and watering from the depot to the park. The scenarios developed provides savings in terms of time minimization and distribution of assignments.


Introduction
According to Indonesian Law No. 26/2007, the city area should have minimum 30% of green open space, consisting 20% of public and 10% of private. To carry out this regulation, the Surabaya City Government is actively focusing on the addition number of parks, while keeping maintaining the existing parks by watering them every day. One of the problems faced by the city government in watering activities is determining the number of vehicles used to fulfill the needs of watering plants at each point, where each park has a different demand. In addition to demand at several points, there are still other variables which effects this activity such as vehicle capacity, shift time limits, operational working hours and vehicle routes. The variation and irregular values of these variables often results in employee overtimes or vehicles returning late to the rayon office. These overtime and lateness result in disruption of the next work shift (afternoon shift) because the allocation of available vehicles is only 1 vehicle per district.
The watering truck routing problem is the extention of Vehicle Routing Problem (VRP). While the VRP is a problem of which the vehilce visiting each point only once, the problem needs to be split the service so that the division of tasks between vehicles is evenly distributed. So, it needs additional constraints, especially the time windows constraints. Therefore, the problems in this study can be classified as a models of Vehicle Routing Problem with Time Windows (VRPTW) by adding split service.
The approach used to solve the problem is an Ant Colony Optimization (ACO), a meta-heuristic method, by considering a number of parks that must be visited by vehicles before they are returning to the depot within a time limit shift. The use of ACO algorithm is expected to help find the best value with faster computing time than the one of exact algorithm. As seen in Figure 1, the truck departs from the depot with empty tank and fills the water in the nearest river (pickup node). Then, the vehicle goes to the nearest park for watering. For park that have demand less than or equal to truck capacity, trucks only need once to do watering (unloading). However, when the demand for a park is more than the truck capacity, the park can be visited several times until all demands are met, either with the same or different trucks. For example, as seen in Figure 1, vehicle 1 initially fills with water in river 2 and unload it in park 1. Because the demand for park 1 exceeds the capacity of truck 1, then truck 1 returns to refill water in the nearest river, in this case at river 3. After all, 1 park demand is fulfilled, then truck 1 continues the journey to the next watering location. This means that in this case, park 1 is served twice by truck 1.

Ant Colony Optimization for Watering Routes for City Parks
There are two main stages for developing ACO model to solve this problem, namely the construction of Traveling Salesman Problem (TSP) routes and improvement routes by dividing into several subroutes.

Construction of a TSP route using the Ant Colony Optimization approach
The process of TSP construction routes with the Ant Colony Optimization algorithm is carried out in several stages as seen in Figure 2.  o Parameter: a) Early pheromones ( 1 ) The pheromone value will always be updated in every algorithm iteration, starting from the first iteration until the maximum iteration is determined or has reached optimal results. b) Visibility Index (h) The visibility value between nodes is the inverse of the distance ( The evaporation ratio is the rate of pheromone evaporation which has value 0 <ρ <1.

d) Number of ant groups (N)
The ACO algorithm is a population-based metaheuristic, so the search for solutions directly based on certain groups. The specified number of ant groups will be run in one iteration. There is no definite provision regarding the number of ant groups to produce an optimal value. So, it takes several trials to get the best results. e) Pheromone level index (α) and visibility index (β) The α value is the pheromone weight τ and β is the weight that controls the visibility of the pheromone level. To simplify the calculation, the values of the two indices are equalized to 1.

f) Number of candidates
To facilitate the selection of the next node for each vehicle, selected candidate nodes are created. For candidate nodes that have been selected by one vehicle, they will not be selected by another vehicle. g) Maximum iteration The maximum number of iterations is fixed as long as the algorithm runs. For the optimal value of a maximum iteration, several trials need to be done to get the best results.
b. Probability and selection of the next node Calculation of the probability to select a segment using the = ×ℎ ∑ ×ℎ . For each segment, a cumulative probability range is related to the segment selection. Then certain values are chosen based on random numbers in the range (0.1). Specific segments will be selected based on random numbers generated. After each ant occupies each of the specified points, the ant will start to travel from the first point of each as a point of origin and head for one of the other points as a destination. Then from the second point of each, the ant will continue its journey by selecting one of the points that have not been visited as the next destination point. Points that have been served will be stored in a taboo list so that they are not visited again. The ant journey continues until all points are visited one by one.

c. Calculation of travel time
The total travel time is calculated after an ant has completed the entire route and returned to the depot, starting from the depot to the river, river to park, park to park, and park to depot. The total travel time value is stored in memory as optimal local (lk). e. Iterate For each iteration that is done, the taboo list is first emptied to be refilled in the order of new points in the next iteration. Then iterates for stages (b) to (d) until it reaches a maximum iteration or has reached convergence. From the overall iteration will be obtained the optimal global value of the minimum total travel time.

Dividing VRP Sub-Routes
The following is an algorithm carried out in finding route recommendations for watering city parks in Surabaya. The results of the Ant Colony Optimization TSP will be used as a basis for making VRP sub-routes that have been adapted to existing constraints. f. Selection of water uptake A visit to the water collection point is a soft constraint, so this visit is carried out if the truck capacity = 0. There is no specific process in selecting the water filling point because it only considers the smallest travel time from the last truck location and the next watering point.

Result and Discussion
The algorithm is tested using Intel® core ™ i5-2450m CPU @ 2.50GHZ 4 GB RAM. The parameters used in this testing as follow: the evaporation value ρ=(0.3; 0.6; 0.9), the number of ants=(5; 10) and the maximum iteration of (10; 100; 500). Running models are carried out by 10 replications and the best objective function value is selected from these ten replications. Table 1 shows that the minimum, average, and standard deviation values of ten replications for these various parameters. Based on the results on Table 1 From above trials and considerations, a new experiment is conducted which uses the evaporation coefficient parameter ρ = 0.6, the number of ant groups m = 5 and the number iteration i = 50 with ten replications. The result of this experiment can be seen in Table 2. The assignment of the test results using the ACO model does not violate existing constraints in terms of capacity or time window with all demands in each park can be served all. The total number of vehicles available at the city is currently 9 units, while the recommendation of this study only requires eight units of vehicles. So, the demands of each park will be able to be served all of them. The city also still have a spare tank truck that will stay at the depot as a backup vehicle in the event of an increase in the number of demands or when there is a vehicle which has break down condition. The back up vehicle is very important due to every day the park must always be watered. Otherwise, the survival of plants as a green space in the city of Surabaya will be disrupted. This optimization result with the 3558.6 minutes total traveling time is better than the one of existing condition, with the 3866 minutes.

Conclusion
The development of ACO model for been applied for finding the truck routing in watering parks in the city of Surabaya. The model tries to determine the routes of the vehicles and the number of vehicles needed. The parameters used in the ACO model test for watering parks in the city of Surabaya were obtained from a trial of several parameters with 10 replications in each combination. The results of the selected parameters are parameters that have a small standard deviation can provide the minimum objective function value. The recommended route generated by the ACO algorithm model with the parameter evaporation value 0.6, the number of ants 5 and a maximum number iteration of 50 for watering parks in the city of Surabaya produces a goal function value of 3558.6 minutes by using 8 units of vehicles. This assignment does not violate existing contraints in terms of vehicle's capacity or time window with all demands in each park can be served all.