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Optimized Allocation of Equipment for Earthwork Projects According to Cost and Time Criteria

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Optimized Allocation of Equipment for Earthwork Projects According to Cost and Time Criteria OPTIMIZED ALLOCATION OF EQUIPMENT FOR EARTHWORK PROJECTS ACCORDING TO COST AND TIME CRITERIA Abbas Rashidi 1, Hossein Rajaie 2, Ayoub Hazrati 3 1 Lecturer, Civil Engineering Department, Islamic Azad University, Semnan Branch, Iran E-mail: [email protected] 2Assistant Professor, Civil Engineering Department, AmirKabir University of Technology, Tehran, Iran 3 Graduate Student, Civil Engineering Department, AmirKabir University of Technology, Tehran, Iran Abstract. In earthwork projects, especially in developing countries, major amounts of costs are spent on equipment. Therefore in such projects, the procedures in which proper equipment are allocated are of great importance to contractors. Furthermore, using mathematical methods in optimum allocation of equipment can cause cost decrease. At the same time the mathematical methods can play the role of a communal basis for contractors and owners. In this paper using a relatively large scale earthwork project as a case study, considering the project time schedule, equipment allocation will be done. The Queue theory will be used as the controlling tool for checking the accuracy of number of allocated equipment. Finally, the effect of any changes in number of equipment on the project duration will be assessed and the project sensitivity to any type of equipment will be studied. Comparison between calculation results and field observations and actual records shows a good compatibility between calculations and actual project conditions. Key Words: Transportation, Working cycle, Equipment, Queue Theory, Optimized Allocation 1 INTRODUCTION The history of Queue theory goes back to 1909. In this year A. K.Erlang, a Danish engineer, issued a paper on the Queue systems and waiting time in telecommunication systems, for the first time. In 1953 David G. Kendall formulated the Queue theory to the form known today and showed the empirical applications of this theory for different problems. The first book discussing the basis and applications of Queue theory issued in 1958 by Philip M. Morse. After that, the Queue theory has been used extensively in solving different problems related to giving better service to telecommunication customers, transportation network users and hospital clients and production procedure in factories and technological complexes. The main components of Queue system are interiors (customers) and service suppliers. When a customer refers to a system for receiving service, two different cases may happen. If one of the service suppliers is free, then giving the service to the customer begins immediately. On the other hand if all service suppliers are busy, then the customers should wait and thus the queue will be made. Figure 1 shows the main components of Queue system 1. The objective of solving the Queue system problem is twofold: finding the time percentage that the total system is free due to the absence of customers and waiting time of any customer in the queue and simultaneously optimizing these times. In most of the Queue systems, the Abbas Rashidi , Hossein Rajaie and Ayoub Hazrati mentioned times are accidental in nature. For this reason the probability theory is used extensively in solving Queue problems. Service Canals Queue Customer's Entry Customers Exit Figure 1: Components of Queue system Depending on the choice of statistical process for the mode of customer entering into the system and customer exit rate, several models has been proposed for simulating the Queue problem. The most common of which is Classic or model. In this model it is assumed that the time interval between entering of two subsequent customers and the time of providing service for them is following exponential functions. Service providers' number for each separate system is equal to 1, the number of customers is potential and the queue capacity is limitless. The entering process of customers is similar to Poison's model. The entering rate of customers is assumed to be independent of the number of customers in the system 2. In the truck filling and refilling problem, the trucks are assumed as the customers of Queue system. Loaders are known as service providers in this system. One loader along with specified number of trucks is known as a Queue system. The objective of solving this problem is to determine the number of loaders and trucks in a manner to increase the probability of truck existence for one loader as much as possible. In other words, by allocating appropriate number of trucks the loader will be always busy. Since the duration required for each loading & traveling operation is independent and is not related to the previous or next loading & traveling operations, the Poisons statistical distribution is used and the probability of existence of at least one truck for each loader, using Queue theory can be determined with following equations 3: −1 n n! i (1) P0 = ∑ (r) i=0 (n − i)! Pt = 1− P0 (2) t r = 1 (3) Tt n : Number of trucks for each loader P:0 The probability of non-existence of at least one truck for one loader in a specified time interval Pt : The probability of existence of at least one truck for one loader in a specified time interval r : Loading duration to travel duration t1 : required Time for truck loading by loader, Tt : Travel duration Abbas Rashidi , Hossein Rajaie and Ayoub Hazrati 2 PROJECT DESCRIPTION The under study project includes excavation, compaction and grading of a relatively large site, located in the Southern Pars Especial Economical Zone in the south of Iran. Figure 2 shows the site plan and the coordinates of some corner points (The north direction is not exact). The site area is about 23500 m2. On the western side of the site (left side of 6-1 axis) and eastern side of the site (right side of 3-2 axis) neighbor sites are located. The suggested way for transferring soil is using 5-4-3 axis which has good accessibility to the main road and lower elevation than the northern axis (1-2 axis). D-8 bulldozers have the role of earth excavation and soil transformation to the southern side of the site, where the loaders fill the trucks. If the high number of machineries in the southern side decreases the efficiency and cause wasting of time, the northern side can alternatively be used for soil loading and transformation. According to topographical maps and soil specification of site (20% composed of rock and 80% of hard compacted soil) the excavation volume is equal to 205500 m3 loose soils. The area considered for soil depot is located in 4 to 5 kilometers distance from the main site. Considering the site broadness, after finishing the excavation, the final surface should be graded by graders and compacted by rollers. Considering the project time schedule, total time considered for the excavation and grading is 60 working days. Daily working hours are 12 hours which has 10 efficient working hours. Figure 2: Site plan and corner point coordinates 3 GRADER AND ROLLER SELECTION Usually in earthwork projects the following operations are done: - Soil excavation by different type of bulldozers with various engine powers related to soil type - Soil loading with different type of loaders - Transformation of loaded soil and unloading in depot by truck - Grading of final surface by grader, Watering and compaction by different type of rollers 4. As the duration of grading and compaction operations' are related to the surface of the site and as the time of this operations have no relationship with the volume of excavation, firstly, time and machinery required for these operations will be determined. Abbas Rashidi , Hossein Rajaie and Ayoub Hazrati If a G-14 model grader with 1200 m2 per hour efficiency or a similar model is used, the total area of the site will be graded in two working days (20 efficient working hours). Two different methods have been used in calculation of work performance of different equipment: - Work performance calculation based on machinery catalogs while considering project conditions 5. - Data collection from 5 different earth moving contractors which execute projects in the same area and calculating the average work performance of equipment. If a significant difference exists between two mentioned methods' calculations, the lower value will be used in calculations. Considering the allocation of two 12-14 tons static rollers with the average efficiency of 420 m2 per hour, the total area of site will be compacted in 3 working days. To provide sufficient humidity for the compaction operations a water tank is used during the operation period . Considering the above calculations, 5 days of the total project duration is allocated for grading and compaction operations and 55 days will remain for excavation operation. 4 NUMBER OF BULLDOZERS CALCULATION Considering that 55 days are allocated for excavation and the amount of loose soil is equal to 205500 m3 and at the same time considering the average work performance of 130 m3 loose soil for D-8 type bulldozer, the number of required bulldozer for the mentioned project can be determined as follows [5]: 205500 Number of required bulldozer: = 2.87 55×10 ×130 Therefore 3 bulldozers are needed. 5 COMPLETE WORKING CYCLE A complete working cycle includes following parts 6: - Time required for loading a truck by loader (t1) - Time required for truck traveling to depot (t2) - Time required for truck unloading (t3) - Time required for returning of truck (t4) - Time required for truck to get to appropriate direction to be loaded by loader (t5) If the travel duration is shown by Tt and complete working cycle duration is shown by TC then: Tt = t2 + t3 + t4 + t5 (4) Tc = t1 + t2 + t3 + t4 + t5 (5) Among the above mentioned times, duration of traveling to and retuning from depot (t2 and t4) are related to truck speed and traveling distance and are unequal for different projects.
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