The 6th Regional Symposium on Infrastructure Development
RSID6-TRP22
Optimization of Scheduling and Dispatching RMC Truck using Genetic Algorithms for One plant –Multi sites Autthapon Sirisuwan Master Student, Department of Civil Engineering, Faculty of Engineering, Khon Kaen University, 40002, Thailand, E-mail:
[email protected] Ladda Tanwanichkul Lecturer, Department of Civil Engineering, Faculty of Engineering, Khon Kaen University, 40002, Thailand, E-mail:
[email protected] ABSTRACT Ready mixed concrete (RMC) has become widely used for building and construction industry in Thailand. In general, one or two staffs usually are employed for manually managing order scheduling especially in a single RMC plant. Experienced staffs are therefore required in this type of plant. Discontinue However, over- or underestimation order flow can be often occurred leading to be unsatisfied customers and even possibly losing later orders. This study therefore aims to develop a model using as a support tool for optimizing the RMC delivery schedules in a type of one plant-multi sites. The Genetic Algorithm (GA) is a heuristic approach, which tries to mimic the natural behavior in searching processes associated with rules of reproducing populations. It relies on an intelligent search of a large but finite solution space using statistical methods. Thus GA has been extensively used in variety of research problems including scheduling. Scheduling and Dispatching RMC trucks (SDRMC) associated with GA model will be used to provide optimal scheduling for a set of customers in one day orders. By using the existing one-day orders in a single plant, schedule from the SDRMC model outperforms results from the exact method by total waiting time. Therefore based on GA-RMC scheduling, plant orders could be expanded because of reducing excess waiting time. Keyword: Dispatching, RMC Scheduling, Ready Mixed Concrete, Genetic Algorithm, Topic: Transportation Engineering and Planning
1. Introduction Ready Mixed Concrete (RMC) has been widely employed in Thailand for many years. In order to reduce cost of setup plant at the construction site, an RMC truck was therefore invented to deliver RMC to the construction site. Due to time limitation, a plant manager usually has to consider both timeliness and flexibility for matching up the working processes of different construction sites [1*]. From the business point of view, the manager generally desires to dispatch RMC trucks for maximum number of construction sites in order to maximize the production and profits. Moreover, discontinuous jobs are also avoided by using a large number of RMC trucks causing a long queue at the construction site. This becomes drawbacks from dispatching manually by human i.e. the plant manager because he often dispatches RMC trucks based on his own experiences which could be inefficient and may increase costs for their business.[1] reported that dispatching efficiency depends on sequence of RMC trucks delivering to customer with right quantity and on time of customer requirement. This kind of problem is similar to one of classic operation research problem i.e. ‘Traveling salesman problem, TSP’ but the trip can be more than one trip per one customer. In the Scheduling and Dispatching RMC problem so called ‘SDRMC’, the more complex problem is, a larger number of possible answers are. Due to limitation of human efficiency, the size of SDRMC problem in the real situation, large order of concrete to a large number of sites may generate huge answer which over capacity of human to schedule and dispatch RMC trucks for the highest efficiency within a limit working
Atthaphon Sirisuwan, Ladda Tunwanichkul
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time. This research therefore works on developing the optimization model for scheduling and dispatching RMC truck problem with one plant – multi sites. This problem can be categorized as NP-Hard problem [12] therefore heuristics techniques have been introduced using to solve SDRMC problem. Genetic Algorithm, one of popular heuristics techniques used to solve NPHard problem, will be employed in developing modeling [1*]. 2. The dispatching model In the ideal RMC delivery to construction site, it is assumed that a RMC truck for casting concrete arrives at the same time of the previous RMC truck which just finishes casting concrete. This research therefore, aim to develop an efficient and effective schedule of dispatching RMC trucks in order to minimize the total waiting duration of RMC trucks at construction sites without breaking off the operations of casting concrete Input parameter 1. Start casting duration 2. Traveling Duration (go-back) 3. Casting Duration 4. Concrete Mixing Duration 5. Number of own truck 6. Max capacity of truck 7. Required amount of RMC 8. Buffer Duration
Model
Genetic algorithms
Input
Dispatch Sequence
The optimal Output
Dispatching Schedule
Simulation
Figure 1: Model of dispatching [1].
3. Genetic algorithms for optimizing the schedule of dispatching RMC trucks The efficiency of RMC truck schedule relies on the order of truck delivery to customers with the right type and quantity of concrete and on time based on requirement of customer. Therefore the higher number of customers may exponentially cause the more complexity of SDRMC problem. The total number of answer for SDRMC problem can be calculated from the equation (1). m k j ! j 1 TS m
(1)
k ! j
j 1
Where: TS is the total solution space. kj is the required number of RMC deliveries. m is the number of construction sites that request RMC deliveries. j is the index of construction site j. Genetic Algorithm (GA) is a search algorithm initiated in 1975 by Holland, which are base on the mechanics of natural selection and genetics to search through decision space for optimal solution [9], [10]. There are six components in GA including Chromosome Structure, Initial Population, Fitness Function, Selection, Genetic Operators, and Termination Condition (for further details please see [11]). Fig. 2 represents structure and process of SDRMC model using to determine an optimal solution based on genetic algorithm.
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Define population size, crossover rate, mutation rate. Generate random initial population. Calculate fitness function values. Rank population by fitness. Select parents. Crossover. Mutation. Calculate fitness of child. Add child to population.
Convergence condition satisfied?
No
Yes Output best solution.
Figure 2: Structure of Genetic Algorithms for optimizing the schedule of dispatching RMC trucks
Components of SDRMC model are described in following sections. This is reviewed and modified based on [1], [4], and [11] with adaptation of specific SDRMC problem. 3.1. Chromosome Structure: The first step in designing a genetic algorithm is to set up a representation scheme or encoding scheme. The encoding is said to map solutions of the problem to be solved onto a ‘set of finite strings over a finite (usually small) alphabet’. In SDRMC model, the permutation coding of “Site ID” as a real number is used as shown in Fig. 3.
Figure 3: Chromosome Structure
3.2 Initial Population: An initial population is a start set of chromosomes used for reproducing new generations until the best solution is achieved. 50 chromosomes are generally generated to be the first set of population using for selection in the later step. 3.3 Fitness Value: A chromosome measures the quality of a solution to show the fitness of the solution by comparison with the problem environment. A fitness function of a problem commonly generates an output from a set of input parameters i.e. a chromosome composition. Therefore, in simulation process, the fitness value of a dispatching schedule is determined by minimizing the total duration (Min(wc)) that the RMC trucks wait at construction sites and construction sites wait for arrival the RMC trucks. 3.4 Selection: The selection process is a process to direct the GA search toward promising regions in a search space therefore the selection is an important mechanism in a GA procedure. In SDRMC model, composition of proportional selection and roulette wheel method is used based on mathematical formula shown in Eq.2-3 F Pi N i , for i 1,2,....N pop (2) Fi j 1 Fi = Min (wc) (3) Where, wc is the total duration that the RMC trucks wait at construction sites and construction pop
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sites wait for arrival the RMC trucks, Pi is the proportional of selection, Fi is the fitness value of chromosome i, Npop is the size of population. 3.5 Genetic Operators: A mating procedure is an evolving process in a GA for generating a new chromosome from one or two existing chromosome. One or two existing chromosomes are called a ‘parent’ while an offspring is called ‘new chromosome’. Two GA operators are employed in this research i.e. Crossover and Mutation. Crossover: One-point crossover is used as shown in Fig. 4. Parents
Childs
Figure 4: One-point crossover
1 2
Mutation: Self-mutation is employed in SDRMC as shown in Fig. 5. 1
2
3
4
5
6
9
7
8
Point of mutation
Figure 5: Self mutation
3.6 Termination condition: Three possible stopping criteria may be used in heuristics methods [11]: An optimal solution is found. A maximum number of iterations are reached which is the method that used in this research. The maximum number of iterations is 50 generations for a small problem and 100 generations for a large problem. The number of successive iterations when changes of fitness function are less than a specified value. 4. The computer program A user-friendly computer is developed by using Visual Basic 6 programming which can be used to help the batch plant manager quickly to generate an efficient dispatching schedule. Fig. 6 and 7 present the interface of program.
Figure 6: Dispatching RMC program page one.
Atthaphon Sirisuwan, Ladda Tunwanichkul
Figure 7: Dispatching RMC program page two.
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4.1 Input Two areas are required users to add input data in the first page (see Fig. 6). The first area is the section of “The Batch Plant”, which includes the data related to the batch plant operation. The data include Number of sites, Maximum Capacity of Trucks, Number of own Truck, and Concrete Mixing Duration. The second area is the section of “Operation data of sites”. This contains data related to different construction sites that request RMC deliveries including Start casting duration, Casting duration, Traveling Duration (go and back), Buffer Duration, and Required amount of RCM. In the second page is the section of “GA Parameters”, which includes “Population size”, “Crossover rate”, “Mutation rate” and “Generation” shown in Fig. 7, after the data need for two pages are entered, the program will be ready to optimize the dispatch schedule. 4.2 Output There are two windows for reporting results from the SDRMC model. The first page shows the simulation result of dispatching schedule, which indicates a dispatch sequence, simulation departure and arrival time of each truck, casting duration, ending time of casting and the arrival time of each truck to the plant as shown in Fig.6. The second page present the population status indicates the performance of GA operation and graphic results (see Fig.7). 5. Results and discussion
Figure 8: Dispatching RMC Schedule Optimizer for 7 sites using the SDRMC model
A number of real problem data [1] were used to test accuracy, stability, and efficiency of the SDRMC model. The tests were performed in the laptop computer with the platform of AMD 1.6 GHz with 1450 MB RAM. In this paper, two problems i.e. small and large problem will be presented for comparison of between exact method and SDRMC model. A small problem includes three construction sites whereas 7 construction sites are in a large problem. 560 and 7.8 x 1016 different dispatching schedules can be calculated from the small and large problem respectively. Population size of 50, crossover rate of 0.8, and mutation rate of 0.2 recommended by [11] were used for both problems. It was found that the SDRMC model generate an optimal solution within only 59 seconds with the optimal solution of total waiting duration 119 minutes
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and optimal solution which is found in 1st generation, which is the same solution found by the exact technique but 270 seconds were used in the exact method for the small problem. In the large problem of 7 construction sites, it is impossible to solve by exact method due to large spacing but it took only 366 seconds to generate an optimal solution by using the SDRMC model with 233 minutes of total waiting duration for not interrupt casting operation. The graph of the best solution in each generation of the large problem is presented in Fig. 8. The SDRMC model therefore presents a good performance because trend of the best solution is converged to an optimal solution, which is found in 47th generation. Details of the small and large problem are shown in Table 1 and 2 respectively. Table 3 presents comparison between exact method and the SDRMD, GA based model in computation time, potential answers, total waiting time (optimal solution), and generation number when optimal solution found in the SDRMC model. Table1: Information of the dispatching operation for 3 sites. Start casting
Site
time
Casting Duration
Travel duration go
Travel duration back
Buffer duration
No. of RMC Deliveries
Site 1
08: 00
20 min
30 min
25 min
30 min
2
Site 2
08: 00
30 min
25 min
20 min
20 min
3
Site 3
08: 30
25 min
40 min
30 min
15 min
3
No. of own truck Mixing duration Max. capacity of truck
5
trucks
3
min
6
M3
Table2: Information of the dispatching operation for 7 sites. Start casting
Casting
Travel duration
Travel duration
Buffer
No. of RMC
time
Duration
go
back
duration
Deliveries
Site 1
08: 00
20 min
30 min
25 min
5 min
3
Site 2
08: 00
30 min
25 min
20 min
5 min
4
Site 3
08: 30
25 min
40 min
30 min
15 min
4
Site 4
08 :00
10 min
15 min
15 min
5 min
5
Site 5
08: 00
35 min
35 min
30 min
5 min
2
Site 6
08: 30
15 min
45 min
35 min
10 min
2
Site 7
08: 00
20 min
20 min
20 min
10 min
5
Site
Number of own truck Mixing duration Max. capacity of truck
15
trucks
3
min
6
M3
Table3: Comparison of results of RMC Schedule from Exact method and the SDRMC, GA based model. No. of site
No. of RMC deliveries
1.
3
8
2.
7
25
Example Problem
Possible dispatching schedules
Computation time
Total Waiting Time
Optimal Generation No. (GA)
Exact
GA
Exact
GA
560
270 seconds
59 seconds
106 min
119 min
1
7.8 x 1016
NA
366 seconds
NA
233 min
47
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6. Conclusion and future works The optimization of scheduling of dispatching RMC trucks was carried out in this study using the SDRMC model. The comparisons between the SDRMC model based on GA and the exact method proved the capability and efficiency of GA in scheduling and dispatching RMC trucks. However, some inputs and outputs for the SDRMC are required to fine-tune to be closed to the real situation such as traveling time and casting time. Such data directly affect the schedule and dispatch of RMC trucks in the SDRMC. Moreover, the more accuracy of input data will provide better solution from the SDRMC. 7. Acknowledgments This study was funded by Thai Research Funding for Master Research Grant (TRFMAG: WindowII). The authors would like to thank Khon Concrete Co., Ltd. for supporting the data used in this project. References [1] Chung-Wei Feng, Tao-Ming Cheng and Hsien-Tang Wu. 2003. Optimizing the schedule of dispatching RMC trucks through genetic algorithms. [2] Chung-Wei Feng and Hsien-Tang Wu. 2006. Integrating fmGA and CYCLONE to optimize the schedule of dispatching RMC trucks. Automation in Construction 15 (2006) 186 – 199 [3] Ming Lu and Hoi-Ching Lam, Optimized concrete delivery scheduling using combined simulation and genetic algorithms, Proceeding of 2005 Winter Simulation Conference, 2005 [4] Tao-ming Cheng, Chung-wei Feng and Ming- yuan Hsu, An integrated modeling mechanism for optimizing the simulation model of the construction operation, Automation in Construction 15 (2006) 327 – 340 [5] Ming Lu, Michael Anson2, S. L. Tang, and Y. C. Ying4, HKCONSIM: A Practical Simulation Solution to Planning Concrete Plant Operations in Hong Kong Journal of Construction Engineering and management, Vol.129, No. 5, October 1, 2003. [6] Daoxiong Gong and Xiaogang Ruan, A Hybird Approach of GA and ACO for TSP, Proceedings of the 5TH World Congress on Intelligent Control and Automation, June 15-19, 2004, Hangzhou, P.R. China [7] Tommelin, I. and Li, A.E.Y. 1999. Just-in-time concrete delivery: mapping alternatives for vertical supply chain integration. Seventh Conference of the International Group for Lean Construction, Berkeley, CA, 97-108. [8] D. Naso, M. Surico and B. Turchiano, Just-In-Time Production and Delivery in Supply Chains: a Hybrid Evolutionary Approach, IEEE International Conference on Systems, Man and Cybernetics, 2004 [9] Holland, H. (1975), “Adaptation in Natural and Artificial System”, Ann Arbor: the University of Michigan Press, Michigan [10] Goldberg, D.E. (1989), “Genetic Algorithm in Search, Optimization, and Machine Learning”, Addison-Wesley Publishing [11] Ladda Pitaksringkarn (2006), “Logistics Modelling: Agricultural Facility Location analysis”, Ph.D. Thesis, University of South Australia [12] Nagorn Inpayung (2548) “Discrete Optimization in Transport and Logistics”: SE-EDUCATION , 2003.
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