Simulation for Selecting Road Works Equipment

Efficiency of road works is conditioned by selection of machines and synchronizing their operations. Modelling these works using queuing theory allows the planner to conduct an in-depth analysis of the system’s operation to find the best machine types and their optimal number. For simple cases, analytic formulas are used to calculate such parameters as a probability of a server’s standing idle, average length of a queue, or average waiting time. However, complex real-life systems are to be analyzed more efficiently by means of simulations. The paper presents simulation model of a road repaving project. Using it, the authors evaluated the economic effect and output of the system served by different machine sets. Applying a number of additional optimization criteria (cost, productivity, machine utilization rates, etc.) the authors were able to find most suitable machine sets.


Introduction
Solving practical problems of business operations and selecting best options is a complex task -even if the decision environment is treated as deterministic. The methods of supporting the decision making process are numerous, they develop continuously and find many applications (Keršulienė, Turskis 2011;Stanujkic et al. 2012).
From the point of decision making, construction may be considered an especially challenging branch of industry as, regardless of country, technology level or economic conditions, it is prone to considerable operational risk (Ghoddousi, Hosseini 2012). Thus, the assumption of deterministic character of construction projects may lead to wrong decisions, and many researchers propose tools or methodologies aimed to improve construction planning. For instance, Paslawski (2011) puts forward that flexibility is needed to manage construction risks successfully and prompts adjusting to dynamically changing environment by preparation of alternative solutions. Jaskowski and Sobotka (2012) argue that, in the scheduling process, it is possible to form new performance variants by changing activity precedence logic in a way that leads to minimizing the project duration without exceeding the allowed budget. Jaskowski and Biruk (2011) propose a different method of improving the construction planning reliability: the method bases on the idea of schedule buffer allocation; proper buffer sizing is claimed to reduce negative effects of random conditions occurring as the project progresses, and improve efficiency of project activities. Some of the researchers model uncertainty using fuzzy logic (Han, Liu 2011;Keršulienė, Turskis 2011) or interval grey numbers (Stanujkic 2012;Zolfani et al. 2012).
However, for optimization of complex management processes the stochastic simulation is recommended and used by many researches, especially in combination with optimization algorithms (Biruk, Jaskowski 2008;Jaskowski, Biruk 2011;Napalkova, Merkuryeva 2012).
Many construction processes are of cyclic nature, with operations repeated in the same sequence that results from method of their execution. Duration of such repeated operations is usually a little different in each cycle. This is due to a variety of factors affecting productivity of the resources and changing conditions of work. Thus, cyclic construction processes are stochastic, possible to be modeled as queuing systems, and examined by means of simulations or tools of statistical analysis. The results of such analyzes are the basis for planning the works with respect to composition of machine sets or worker crews, estimating process time, and harmonizing the work. Simple queuing systems have been described by analytical formulas that concern mean utilization rates of servers, mean waiting time, mean service time, probability of a certain number of arrivals to the system, etc. However, real-life systems are complex (a number of servers processing customers in sequence, in parallel, in a mixed manner; a number of queue with different serving disciplines; a number of customer types) and take form of queuing networks. If the systems actually operate, information on their performance is possible to be collected on site and analyzed by means of statistical methods. In the case of systems at the planning stage, computer simulations provide input for the analysis.

Computer simulations of queuing networks
Simulation is a technique used to imitate operation of a real-life system by means of a dynamic model. In the case of computer simulation, the real-life system is modeled by means of a computer program. Depending on the character of the model's state variables, simulation methods are continuous (if the state transition is of continuous character), discrete (discrete event simulations), or hybrid. Continuous simulations are rarely used for the analysis of queuing networks (Roy, Mohopatra 1993). The literature on the subject recommends discrete simulation to analyzing complex systems (Özgün, Barlas 2009).
Before simulation tests are conducted, a model of the real-life system has to be built. There are three basic modeling strategies for defining the concept of model analysis and the way of its creation (Abduh et al. 2010). These are: − process interaction (PI) strategy that focuses on transaction flows inside the systems, − activity scanning (AS) strategy that identifies processes and conditions required for their complection, and − event scheduled strategy (ES) based on model ling events that are likely to occur or whose occurrence has been planned. In practice, these strategies are used in combinations. In the case of construction processes, a combination of AS and ES strategies is recommended, and referred to as the three-phase activity scanning method.
It was the basis for the Halpin's CYCLONE method of modelling cyclic construction operations (Halpin 1977).
Here, the graphic model of a system uses only 5 elements (Table 1). Resources (units) are moved between network elements along the arcs according to the system's logic. Unit flows are held in a queue (to be served or to start work) and in the "normal activity" or "COMBI activity" elements (for the time of conducting processes), and then they are forwarded to the next elements (by being duplicated). The "counter" block enables the user to count the number of cycles and units of output. The "function" block allows for consolidation of resources (turning them into products). It is possible to connect normal activities, COMBI activities, and "function" blocks by probabilistic arcs -this facilitates modeling of optional processes of certain probability of occurrence.
CYCLONE has found application in a number of computer simulators designed for analysis of construction processes. Some of them are MicroCYCLONE, DISCO, PROSIDIC, INSIGHT, RESQUE, STROBOSCOPE, SIMP-HONY, WebCYCLONE, COOPS, UM-CYCLONE, COM-Sim. The CYCLONE modeling approach was also implemented in the COST (Construction Operations Simulation Tool) by Cheng et al. (2000), that allows the user to model activity times as fuzzy numbers. Cheng and Feng (2003) integrated CYCLONE simulation with a genetic algorithm to facilitate finding optimal resource combinations. Abduh et al. (2010) argue that the main practical problems of using simulations for analyzing construction processes are related with limited access to input (lack of statistical data on construction activities' times with respect to distribution types and parameters), lack of modeling expertise (the existing software requires from the user much more than basic computer skills, sometimes the user has to translate a graphic model into a computer program, the simulation reports have to be interpreted), and software accessibility (costly licenses). Construction practitioners prefer widely available software and universal systems facilitating calculations (like spreadsheets) to single-purpose specialized systems, regardless of their commercial or in-house origin.
The authors used WebCYCLONE (Halpin et al. 2003) as a simulation toll was used. The tool is available free of  (Martinez 2001).

Example
The object of analysis is a road resurfacing project in Netherlands. Its location, and location of asphalt plants providing the material, is presented in Fig. 1. The resurfacing process comprised the following operations: milling the old wearing course, transporting the reclaimed material to a stacking area, transporting asphalt mix to the construction site, and placing new wearing course. Milling the old wearing course was planned to be done by means of three milling machines. Reclaimed material was loaded into trucks and transported to a stacking area at the Brabantse Asfalt Centrale in Helmond (BAC) asphalt plant that was also the basic supplier of asphalt mix for the project. Considering the limited number of scales available at the plant, only 2 trucks were possible to be unloaded at a time.
Two suppliers of asphalt mix were available: − the main was BAC, with a mean capacity of 240 Mg of mix/h; − an auxiliary plant, Asfalt Centrale Limburg in Stein (ACL), with a mean capacity of 130 Mg/h. Placing new wearing course was planned to be conducted by 2 pavers that covered half of the lane width at one run. Both the asphalt mix and reclaimed material were to be transported by 4-axle trucks. To avoid traffic problems, the rate of placing the new wearing course was to be close to the rate of milling. This was an underlying assumption with regard to the selection of milling machines and pavers type (capacity) and number. Fig. 2 presents a CYCLONE model of this resurfacing process -usual in the practice of such projects. Table 2 lists the input data -durations of activities, including  distribution type and parameters of probabilistic values. Input for the analysis was collected during observation of works performed in the past and executed in similar conditions. Some durations were assumed to be deterministic, and they are expressed by one value, in minutes. The value characterizing an activity of exponential distribution is the mean reduced by the shift of the waiting time distribution, and is also given in minutes. In the case of beta distribution, the values are maximum duration, minimum duration, and shape parameters, in minutes. The truck ride times include time for maneuvers at the destination points and organization-related activities, such as answering to calls and document handling. The rides are modeled by two blocks because this was necessary to allow for their being of shifted exponential distribution. The unit cost of machines (wet with driver), based on information from the market, were assumed as follows: for trucks 30 EUR/h, for pavers -50 EUR/h, for milling machines -90EUR/h. The repaving process was simulated to run for ten 8-hour working shifts. The aim of simulation was to find the number of trucks to serve the process, and frequencies (probabilities) of the trucks' selecting optional routes: − after dumping the mix into loaders (decision node 21: p1 is the frequency of trucks' heading for collection of reclaimed material, and p2 is the frequency of the tricks' going to BAC asphalt plant to fetch asphalt mix, p2 = 1 -p1); − after arriving at BAC plant (node 25: q1 is the frequency of the truck's going to ACL plant, and q2waiting at BAC to be loaded, q2 = 1 -q1). During simulation, the milling machines' and pavers' utilization rates were checked: they are required to be similar, with minimum idle time, to assure uniform rate of work and low cost. Similarly, the number of trucks loaded at asphalt plants was checked to assure that the plant's capacity was not exceeded: it was assumed that the average load of a truck was 26.5 Mg, so the BAC plant would not be able to load more than 724 trucks, and the ACL plant -392 trucks during 10 days of work.
The 1 st stage of simulations consisted of analyzing the effect of probabilities p1 and q1 on the milling machines' and pavers' capacity utilization level, in this case measured by the mean waiting time (so the mean time of pavers' or milling machines' waiting before being served by a truck). Table 3 lists simulation results for the assumed number of trucks in the system (10 trucks). Changing the number of trucks is not expected to affect the proportion between the milling machines' and pavers' capacity utilization levels. The results indicate that milling machines had long idle times. The lowest mean idle time for milling machines was obtained for p1 = 1, so in the case that deliveries come only from the main asphalt plant (BAC), and the trucks move to serve the milling process immediately after unloading asphalt mix.  The next stage of analysis was devoted to finding ways of reducing idle time of milling machines and pavers -and checking if there are grounds for increasing the number of trucks in the system, which inevitably increases cost of transport. Table 4 lists the results of simulations for different numbers of trucks. The lowest cost of machine set per truck loaded with milled material (so the unit production cost in the leading process) was obtained for 12 trucks in the set, but in this case the milling machines had quite a lot of idle time. This reduces the speed of repaving works. Therefore, the 3 rd stage of analysis considered the grounds for changes to the organization of works by excluding one asphalt plant (ACL) and allowing the trucks to move from the pavers directly to the milling machines. It was assumed that the travel time between stacking area at BAC and the milling area is a random variable of exponential distribution, mean value of 5.28 min and a shift of   Fig. 3. Table 5 lists simulation results for different values of probability r1 (r2 = 1 -r1) of selecting an option of going directly from the BAC's reclaimed material stacking area to the milling area, instead of taking the asphalt mix and going to the pavers. This simulation was conducted for 13 trucks (the number of trucks is not expected to affect the proportion between capacity utilization levels of milling machines and pavers). The results indicate that at the probability r1 = 0.57 corresponds to the lowest mean idle time of milling machines and pavers due to waiting for trucks. Table 6 presents the results for different numbers of available trucks. The lowest cost of the machine set per truck loaded with reclaimed material is obtained in the case of 18 trucks employed to serve the process; moreover, it is with a satisfactory level of milling machines' and pavers' capacity utilization. So in the analyzed case, a set of 18 trucks cooperating with 2 pavers, 3 milling machines and 1 asphalt plant provides lowest cost of repaving, as the speed of milling and paving is similar. The repaving cost is by 23% Table 6. Simulation results for different numbers of trucks in the system (simulation of ten 8-hour shifts, at r1 = 0.56)