New Developments in Structural Engineering and Construction Yazdani, S. and Sing, A. (eds.) ISEC-7, Honolulu, June 18-23, 2013 OPTIMAL FLEET SELECTION FOR EARTHMOVING OPERATIONS JIALI FU 1, ERIK JENELIUS 1, and HARIS N. KOUTSOPOULOS 1 1 Division of Traffic and Logistics, KTH Roal Institute of Tecnolog, Stockolm, Sweden Eartmoving operations often involve a large number of speciall designed equipment wit significant purcasing/leasing prices, ig operating and maintenance costs. Hence, coosing te rigt fleet is a major concern from te construction planners point of view. Tis paper presents a metodolog tat combines discrete-event simulation and optimization to solve te optimal fleet selection problem for eartmoving operations. Two optimization objectives are formulated and solved using te proposed framework and a genetic algoritm: minimization of Total Cost of Ownersip (TCO) and imization of productivit. Furter, a two-stage rating sceme is introduced to arrange te fleet configurations so tat te optimization algoritm converges to a fleet wit better second-stage performance wile te first-stage performance remains at te same level. Te case stud sows tat te proposed mecanism can effectivel allocate an optimal equipment combination for eartmoving operations and ence serve as an efficient tool for construction management. Kewords: eartmoving operations, equipment selection, simulation optimization, discrete-event simulation, genetic algoritm. 1 Introduction Eartmoving operations are a fundamental part of construction engineering and are regularl impacted wit uncertaint. Accurate productivit estimation and cost analsis are necessar before and during a construction project to ensure tat te project is completed witin te targeted timetable and budget. Equipment selection is one of te most important decisions to guarantee te success of a construction project. Normall, tis is done using rules of tumb and engineering experience. In recent ears, simulation and optimization metods ave been used to enance te stud of construction engineering. AbouRizk and Si (1994) developed an optimization metod wic utilizes te dela statistics of resources and reasonable matcing among resources to guide te simulation sstem to searc for te most appropriate resource allocation. Minimizing unit cost, imizing production rate and 1 optimizing resource utilization were te objectives studied. Marzouk and Moseli (2000) presented an automated sstem tat integrates a simulation module and a genetic algoritm for optimizing eartmoving operations. Total project cost, overall project duration and idle time for specific piece of equipment are estimated using simulation and fed into te genetic optimization algoritm to select an optimal fleet. Zang (2008) formulated a multi-objective problem and incorporated simulation witin a particle swarm optimization algoritm to look for potential equipment configurations. Te performance of different fleet combinations was evaluated wit respect to a multiple attribute objective function and statistical metods for variance reduction were introduced to andle stocasticit in te performance. Ceng and Yan (2009) created a mecanism tat incorporates a so-called mess genetic algoritm and a simulation engine to optimize resource utilization wit
Instructions for Preparing Manuscripts Autor 1, Autor 2, and Autor 3 respect to te production rate or unit cost. Tis mecanism could generate various working scemes of te eartmoving operations and build te necessar components for conducting simulation in eac sceme. However, te above studies solve te optimal fleet selection problem from a predetermined equipment configuration, i.e. te optimize te decision variables given tat te loading unit of a specific model is consistent wit a auling unit model. Decision variables refer to te number of equipment units wile variables capturing te properties of equipment, suc as model and capacit, are important as well. It is time-consuming to precalculate te good matc between equipment tpes as te numbers of variables increase. In tis paper, we formulate an optimal fleet selection problem were te performance of eartmoving operations is measured using te Total Cost of Ownersip concept (TCO) or productivit. Te eartmoving operations are modeled and simulated using a developed simulation platform (Fu 2012a). In earlier work (Fu 2012b) we designed and used a genetic algoritm (GA) to interact wit te simulation platform to searc for an optimal fleet configuration in terms of TCO, considering a set of qualitative and quantitative variables. In tis stud, we extend te GA wit a two-stage ranking procedure wic could furter improve its performance. Numerical examples of TCO minimization and productivit imization are given to demonstrate te effectiveness of te proposed optimization algoritm. Te remainder of tis paper is organized as follows. Section 2 formulates te optimal fleet selection problem wile considering two different objectives. Section 3 describes te essential features of te proposed simulationbased optimization approac to solve te problem of interest. Numerical examples of te optimization problems are sown in Section 4. Section 5 concludes te paper. 2 Optimization Problem Formulation Two optimization problems are formulated and studied in tis paper: TCO minimization productivit imization Tese two conflicting objectives are te most commonl used in te construction business. TCO is originall a management accounting term designed to estimate te direct and indirect costs of an investment. A TCO analsis takes into account te acquisition cost, te operating cost and te productivit, and provides a clear picture of profitabilit. TCO is defined as te cost per production unit, and is calculated as te quotient of te total cost per operating our and te production per operating our. TCO consists of te capital cost (purcasing cost, residual value, depreciation, interest, insurance, and taxes) and te operating cost (operator cost, fuel consumption, wear parts, preventive maintenance and repair cost). Te operating cost is subjected to te uncertainties of te operating environment. Productivit is defined as te output per unit time from te entire fleet, and is normall measured in ton per operating our. 2.1 TCO minimization Eq. (1) formulates te TCO minimization problem: min subject to TCO P P min L B l xlb, N l1 b1 H 1 x lb, N 0,1,2,..., N 0,1,2,..., N (1) were P is te production rate (ton/), P min te minimum production rate defined b te user, N and N te imum number of 2
New Developments in Structural Engineering and Construction Yazdani, S. and Sing, A. (eds.) ISEC-7, Honolulu, June 18-23, 2013 loading and auling units respectivel, x lb, te integer variable representing te loading unit of model l wit bucket size b, te integer variable referring to te number of auling units of model. Te first tree constraints in Eq. (1) ensure tat te production rate is not lower tan te required minimum value and te numbers of loading and auling units are witin te given imum quantities. Te last two constraints define te integer ranges of te variables x lb, and. 2.2 Productivit imization Te productivit imization problem is given in Eq. (2). subject to P P Cap cruser L B l xlb, N l1 b1 H 1 x lb, N 0,1,2,..., N 0,1,2,..., N (2) Te first constraint in Eq. (2) ensures tat te productivit is not above te capacit of te cruser, Cap cruser. Te cruser capacit is an important factor tat affects te entire fleet s productivit. As sown in Fu (2012b), overcapacit of equipment can lead to te productivit exceeding te cruser capacit b crusing material during breaks in a work sift. However, tis situation is not alwas allowed b labor regulation since some operators will be forced to work overtime wile oters are on lunc break. Tus, fleet combinations wit overcapacit will be eliminated from te searc space in te optimization process using tis constraint. 3 Simulation-based Optimization using Genetic Algoritm Simulation is a widel used tool in operations researc due to its abilit to model complex sstems at te desired level of detail. In recent ears, simulation tecniques ave been used to model te processes in construction engineering. A discrete-event simulation platform (Fu 2012a) is utilized in tis stud to model eartmoving operations. Tis platform was developed based on te well-known CYCLONE modeling metod (Halpin and Riggs 1992) and captures te interactions between resources at a ver detailed level. Te duration of eartmoving activities can be modeled as deterministic or stocastic. Troug te simulation, TCO, productivit, queue statistics etc. can be observed in order to evaluate te performance of alternative fleet configuration. A genetic algoritm is designed in tis stud to searc for potential optimal fleet configurations witout exaustivel testing all combinations. Genetic algoritms belong to te class of evolutionar computation algoritms wic imitate te process of natural selection (Gen and Ceng 2000). Figure 1 demonstrates te cromosome structure designed in te GA implementation. Te genes in te first part of te cromosome are te integer variables x lb, representing te number of loader tpe l wit bucket size b. Te second part of genes wit das-dot line refers to te quantit of auling unit. Tis GA mecanism ten carries on te standard procedure until te fitness value of te optimal solution does not improve for a certain number of iterations or te GA reaces its imum number of iterations. Te basic steps are outlined below: (i) Simulate eartmoving operations and calculate te fitness values of te current population. 3
Instructions for Preparing Manuscripts Autor 1, Autor 2, and Autor 3 Decision variables for loading unit Crossover point Decision variables for auling unit xl,b x1,1 x1,2 x1,3 x1,4 x2,1 x2,2 x2,3 x9,1 x9,2 x10,1 x10,2 x10,3 x10,4 1 2 3 4 5 6 Decision variable for loading unit tpe 1 wit bucket tpe 1 Decision variable for auling unit tpe 1 Figure 1 Te cromosome structure in genetic algoritm (ii) Rank te population according to te fitness (te value of te objective function) of cromosomes and select a pair of parent cromosomes for reproduction from te current generation. (iii) Perform crossover wit probabilit pc of selected parent cromosomes at te predetermined point to form offspring. In tis GA metod, te crossover point is cosen between variables for loading and auling units, as sown in Figure 1. (iv) Mutate te cromosomes wit mutation rate p m for preservation of diversit. (v) Go to step (ii). Te required user inputs for implementing GA are population size N, crossover probabilit p and mutation rate p. c 3.1 A two-stage ranking process in GA m A two-stage ranking sceme in step (ii) of te GA procedure is introduced in tis stud so tat fleet combinations tat ave te same objective value are rated again using anoter secondar objective. Taking te TCO minimization problem as an example, a fleet wit te same unit cost and iger productivit is preferred over one wit lower productivit. Hence, te productivit is considered as te second aspect in te ranking process. Te fitness of cromosomes is first arranged according to te objective value (TCO), and ten ranked again b teir productivit. In tis wa, for fleet combinations wit te same TCO values, te one wit iger production rate will ave iger rank and ence iger probabilit to be selected to produce offspring. For te 4 productivit imization problem, te TCO value is cosen as te criterion in te second ranking procedure. Intuitivel, lower TCO for te same production rate indicates lower production cost. In contrast to using a multi-objective formulation of te problem, tis two-stage ranking procedure allows te user to define te objectives of a project on two levels of priorit. First of all, te users do not need to test different weigt parameters of eac objective before obtaining a satisfactor result. Secondl, tis metod can find fleets wit better overall performance compared to single objective optimization. Tis two-stage metod is tus more straigtforward and less computationall demanding for construction management applications. 4 Case Stud A real-world numerical example of quarr site operations is given ere to demonstrate te proposed GA. Te quarr site is situated in te nort of Stockolm, Sweden and produces gravel, aggregate, and sand all ear round. Te uncrused material is eiter obtained on site or purcased from oter construction sites. In tis example, te uncrused material is first loaded b te loading equipment into te auling units, wic travel to te dumping station to empt te load into te cruser. Te auling units ten return to te loading station to begin anoter load-aul ccle, and te material is crused in several processing units until it reaces te desire size. Details of te operation can be found in Fu (2012b). Te average densit of te uncrused rock is 1.60 ton/m 3 and te cruser as a capacit of 500
Productivit (ton/) TCO (SEK/ton) New Developments in Structural Engineering and Construction Yazdani, S. and Sing, A. (eds.) ISEC-7, Honolulu, June 18-23, 2013 m 3 / wit a opper of 50 m 3 connected on top. Te tpe and capacit of available equipment emploed in tis operation are given in Table 1. Te duration and fuel consumption of eartmoving activities of te macines are provided b te equipment manufacturer, Volvo Construction Equipment. Te activit durations are considered to be deterministic in tis case stud. Table 1 Available equipment tpes and capacities Equipment Tpe Capacit (m 3 ) Loader Hauler Volvo L60G 2.1, 2.3 Volvo L70G 2.3, 2.4 Volvo L90G 2.5, 2.8 Volvo L110G 3.0, 3.4 Volvo L120G 3.3, 3.6 Volvo L150G 4.0, 4.4, 4.5 Volvo L180G 4.4, 4.6, 4.8 Volvo L220G 4.9, 5.2, 5.6 Volvo L250G 5.7, 6.4 Volvo L350G 6.6, 6.8, 6.9, 7.7 Volvo A25F 15.0 Volvo A30F 17.5 Volvo A35F 20.5 Volvo A35FS 20.5 Volvo A40F 24.0 Volvo A40FS 24.0 generations, crossover rate, and mutation rate are set to 40, 100, 0.5 and 0.3, respectivel after a few trials wit te algoritm. Furter, te GA terminates te simulation-optimization process if te optimal fleet does not cange in 20 generations. 4.1 TCO minimization Using te proposed simulation optimization algoritm, te result for TCO minimization (Eq. (1)) is sown in Figure 2. Te upper plot displas te TCO value of te optimal fleet in GA iteration, and te lower plot depicts te production rate for te corresponding fleet. Te GA successfull finds an optimal solution alread at iteration 4 and computes 440 /11525 1.4% of total possible solutions. In tis case, tere are no configurations wit te same TCO value and te second stage of our two-stage ranking tecnique does not come into action. 6.8 6.7 6.6 6.5 6.4 492 490 488 GA convergence Due to te spatial limitations of te site, onl one loading unit and at most five auling units can be emploed in te eartmoving process. Te total number of equipment combinations for tis operation is tus 5 6k 1 25 11525 k 1 k (3) were 25 is te number of combinations for te loading unit wit different bucket capacities given in Table 1, and 6 is te number of auling unit models. In te application of te GA, te population size, imum number of 5 486 Number of iterations Figure 2. TCO minimization - GA convergence 4.2 Productivit imization Figure 3 sows te GA convergence of te productivit imization problem (Eq. (2)). We observe tat te objective function (production rate) alread converges to its optimum in te first iteration sown in te upper plot, but te TCO value in te lower plot continues to decline until iteration 40 since tere are several alternatives wit te same production rate. Wit deeper examination of te optimal fleet in eac
TCO (SEK/ton) Productivit (ton/) Instructions for Preparing Manuscripts Autor 1, Autor 2, and Autor 3 iteration, we observe tat te cruser capacit restrains te productivit and te GA selects te ceaper and slower equipment so tat te auling units wait less at te dumping station. Hence, we can conclude tat te twostage ranking process can guide te GA furter to better solutions wen tere are multiple combinations wit te same firststage objective value. In tis problem, te two-stage GA searces troug 740/11525 2.4% of all possible solutions before finding te optimum at iteration 7. 496 495.5 495 494.5 494 493.5 7.4 7.2 7 Figure 3. Productivit imization - GA convergence Te optimal fleet configurations for te two optimization problems formulated in tis eartmoving operation are summarized in Table 2. Table 2 Optimal fleet configurations TCO minimization Optimal fleet L60G 2.3m 3 2 aulers of A25F TCO (SEK/ton) 6.41 6.85 Productivit (ton/) 5 Conclusion GA convergence 6.8 Number of iterations Productivit imization L150G 4.4m 3 2 aulers of A35F 489.60 495.62 In tis paper, we present a framework wic integrates a discrete-event simulation platform wit a genetic algoritm to solve te optimal fleet configuration problem for eartmoving 6 operations. Two different objectives, TCO minimization and productivit imization are formulated and demonstrated wit a case stud. Te case stud sows tat te proposed metod can efficientl find an optimal combination of construction maciner wile eac stage of te two-stage ranking metod as its own objective function. Hence, it is an efficient, effective tecnique tat can assist te project management in fleet selection. Here we onl stud te deterministic duration of eartmoving activities. It will be interesting in future work to compare te performance of te proposed simulation optimization sstem wile taking te stocasticit into account, and to analze te impact of activit duration variabilit on te optimal fleet configuration. References AbouRizk, S., Si, J., Automated construction simulation optimization. Journal of Construction Engineering and Management, ASCE 120 (2), 374-385, 1994. Ceng, T. M., Yan, R. Z. Integrating Mess Genetic Algoritms and Simulation to Optimize Resource Utilization. Computer-aided Civil and Infrastructure Engineering 24 (6), 401-415, 2009. Fu, J., A Microscopic Simulation Model for Eartmoving Operationn, in te International Conference on Sustainable Design and Construction, 218-223, Zuric, Switzerland, 2012a. Fu, J., Simulation-based Optimization of Eartmoving Operations using Genetic Algoritm, te 17 t International Conference of Hong Kong Societ for Transportation Studies (accepted), HongKong, 2012b. Gen, M., Ceng, R., Genetic Algoritms & Engineering Optimization, Jon Wile & Sons, 2000. Halpin, D. W., Riggs, L. S., Planning and Analsis of Construction Operations, Jon Wile & Sons, 1992. Marzouk, M., Moseli, O., Optimizing eartmoving operations using object-oriented simulation, in te Winter Simulation Conference, 1926 1932, Orlando, USA, 2000. Zang, H., Multi-objective simulation-optimization for eartmoving operations, Automation in Construction 18 (1), 79 86, 2008.