Optimum Equipment Allocation Under Discrete Event Simulation for an Efficient Quarry Mining Process

Abstract

This study presents a discrete event simulation model to minimize operating costs in quarry mining processes by determining the optimal allocation of backhoes and dump trucks, which are the primary mining equipment. The modeling focuses on four principal vehicle types (24-ton dump truck, 2.0 m³ backhoe, 41-ton dump truck, 4.64 m³ backhoe) commonly deployed in quarry mining. The simulation replicates the sequential mining stages involving soil removal, rock ripping (weathered rock or weathered soil), and blasting operations. This methodology is applied to a case study of mining process planning under resource constraints, incorporating real-world quarry conditions in South Korea. Results demonstrate that optimizing the number of equipment units reduces construction costs and shortens the construction period by decreasing dump truck waiting times. When the number of backhoes is limited to 10 during operations, findings indicate an increase in costs and a gradual decline in net profit. Additionally, the interaction between the 24-ton and 41-ton dump trucks is shown to influence the optimal allocation strategy. The simulation-based optimization executes iterative experiments for each scenario, yielding statistically robust results within a 95% confidence interval, thereby supporting informed decision-making for managers.

1. Introduction

In recent decades, there has been a persistent demand for aggregates such as sand, gravel, and crushed stones in construction applications [1]. For instance, the U.S. produced about 2.7 billion tonnes of aggregates (valued at USD 13.7 billion) in 2000 [2], and annual production remained at approximately 2.54 billion tonnes in 2021 [3]. In 2020, South Korea produced 25.68 million tonnes of aggregate resources. When comparing the land area of South Korea (100,210 m²) to that of the U.S. (9,830,000 m²), both countries display a similar production of aggregates per unit area (258.39 tonnes/m² for the U.S. and 256.26 tonnes/m² for South Korea). As reported in [4], the aggregates market size in China is projected to rise to USD602.9 billion by 2027, up from USD429.0 billion in 2020, primarily due to increased construction activities.

In South Korea, for example, among aggregate resources, crushed stones from mountains accounted for 70.52% of total production in 2020 [5]. This indicates that USD 91.90 million out of a USD 130.30 million market relies on the production of crushed stones. In 2019, the U.S. produced 1.53 billion tonnes of crushed stone through 1430 companies across 50 states [6]. Although the production of crushed stones imposes adverse environmental impacts (i.e., deforestation), it remains essential for economic development and the survival of individuals who reside in buildings and use various infrastructures. In South Korea, there were 369 companies in the aggregate industry in 2016, and 233 of them (63.14%) producing crushed stones belonged to the forest aggregate sector [7].

Operational efficiency in surface mining that produces crushed stones and soil depends on several factors, including drill and blast efficiency, crusher plant performance, resource allocation, and production sequencing [8]. Sobko et al. [9] asserted that improved drill and blast efficiency can lower mining process costs by directly increasing productivity. Conversely, the other three factors mainly concern the scheduling and management of existing resources, as adopting new technologies or equipment involves substantial expense. Paricheh et al. [10] demonstrated that the proper timing and placement (OT-OL) of the crusher plant help maintain both reliability and cost-effectiveness in the mining operation. Additionally, planning an effective blast schedule can increase existing production by 29% [11]. According to [12], around 60% of total operational costs in surface mining are influenced by material transportation by rail, truck, belt conveyor, or hydraulic transport, indicating that optimal transportation management can substantially lower mining process costs. For example, in the Pasir open-pit mine in Indonesia, the total operating cost of USD 19.48/ton included drilling at USD 0.61/ton (3%), blasting at USD 0.84/ton (4%), loading at USD 4.51/ton (23%), transportation at USD 10.27/ton (53%), and maintenance at USD 3.24/ton (17%) [13], highlighting the dominant role of transportation costs in overall expenditures. Dabbagh and Bagherpour [14] further revealed that truck allocation alone can increase stone productivity in an open pit mine by 4.1%. Therefore, effective scheduling and management of existing resources are key challenges in mining operations.

To maximize profits, it is essential to conduct mining operations while keeping operating costs to a minimum [15], which requires efficient planning and management of processes such as mining, drilling, transportation, and blasting. Capacity planning plays a critical role in developing an effective mine production system and, in this context, refers to establishing a plan that identifies the amount of mining equipment necessary to optimize mining efficiency in a given scenario [16]. Particularly, since transportation costs account for more than 50% of total operating expenses, proper allocation of mining and transport equipment is a key factor in maximizing mine profitability [17]. In summary, exceeding the optimal capacity of mining and transport equipment within the confined space of a mine can increase operational expenditures and reduce profits margins due to inefficiencies, making it crucial to assign the correct quantity of such equipment to achieve profit maximization.

The objective of this study is to reduce the operating costs associated with quarry mining and determine the optimal allocation of backhoes and dump trucks, which serve as the primary mining equipment, by employing discrete event simulation (DES). A discrete event simulation model is constructed using AnyLogic Professional 8.7.7 software, which, as opposed to traditional mathematical methods like linear programming, can accommodate the nonlinear and complex interdependencies among elements of the quarry mining process [18]. The modeling encompasses four principal types of vehicles used in quarry operations (24-ton dump truck, 2.0 m³ backhoe, 41-ton dump truck, 4.64 m³ backhoe), and the simulation captures the sequential processes of soil excavation, rock lipping (weathered rock or weathered soil), and rock blasting. This simulation model is designed to determine the optimal deployment plan for mining equipment at a quarry in Changwon-si, Gyeongsangnam-do, a representative mining site in Korea. Consequently, the proposed methodology effectively reduces the operational costs of quarry mining by leveraging simulation techniques under realistic operating scenarios.

The contributions of this study are as follows. First, whereas prior research focused only on two types—single ore (mineral) and ore by-product (waste) from mines—this study incorporates both the open-pit mining process and the underground tunnel transport process. Furthermore, it accounts for variations in equipment efficiency depending on the rock type being mined within the quarry. Second, unlike earlier works that dealt with mines extracting a specific mineral, this study targets a quarry. Therefore, it distinctly addresses transport efficiency variations based on three different rock types: soil, ripping rock, and blasting rock. Third, this study diverges from previous research that primarily employed mathematical optimization methodologies by utilizing discrete event simulation, which enables simultaneous consideration of open-pit mining and tunnel transport processes. By incorporating complex, practical conditions, this study provides a framework for industry practitioners and researchers to develop more realistic and representative scenarios when analyzing or evaluating the mining process in future studies.

The remainder of this paper is structured as follows. Section 2 describes the quarry mining process, as well as simulation modeling and optimization approaches. The simulation-based equipment allocation framework is provided in Section 2.3. In Section 3, the experimental results for the proposed methodology are presented using the collected data set from an actual quarry in Changwon-si, Gyeongsangnam-do, South Korea, while Section 4 analyzes the experimental findings. Section 5 concludes this paper and suggests directions for future research.

2. Materials and Methods

2.1. Quarry Mining Process

Depending on the mining process, quarry mining is generally categorized into two types: surface mining (or open-pit mining) and underground mining (or tunnel mining) [19]. Surface mining begins when mining and transportation equipment ascend the haul road, which is constructed as a flat, stepped path leading from the top of the mountain targeted for mining. The first step involves mining equipment removing overburden materials such as trees and soil, after which the exposed rock is extracted, loaded by dump trucks, and transported via the haul road [20].

On the other hand, underground mining, unlike surface mining, carries out mining and transportation by excavating underground tunnels. Multiple tunnel mining methods are available, and the selection of resource extraction techniques depends significantly on the mine’s purpose, operational conditions, and surrounding environment [21]. Nevertheless, in most cases, ores and waste materials extracted from underground tunnels are transported using one or a combination of systems such as dump trucks, conveyor belts, shafts, and rails [22]. In recent years, shafts that allow vertical access deep into the mountain have become a common approach, and this study also applies a transport system utilizing vertical tunnels in underground mining.

The primary objective of surface mining is typically to extract commercially valuable materials from the mine [23]. In the case of the quarry examined in this study, however, the output largely consists of crushed stone excluding soil, and this stone is distributed and sold to various development projects. The civil engineering aim here focuses on securing a broad and level land area. Thus, while surface mining methods are employed throughout, the operation does not target specific minerals, but rather involves the extraction, transportation, and supply of general stones constituting the quarry. The quarry mining workflow addressed in this study is outlined in Figure 1.

As shown in Figure 1, the quarry mining operation includes five main processes. (1) Excavation: soil or stone is excavated directly from the mountain’s surface using backhoe equipment, or underground stone is extracted with drills and explosives. (2) Loading: backhoe equipment transfers the previously mined materials to dump trucks. (3) Transport: once fully loaded, dump trucks carry the materials to the designated supply location. (4) Unloading: upon arrival, dump trucks unload and deliver the soil or stone. (5) Crushing: stone is further processed or sorted using backhoe equipment or crushers. These five processes are repeated throughout the lifecycle of the quarry. The machinery managing these cycles, primarily mining and transport equipment, is classified as a major system that demands considerable capital expenditure, with investments reaching several billion dollars over a period that ranges from a few years to several decades [24].

Quarry mining employs backhoes, loaders, and dump trucks as its primary equipment. Backhoes, fitted with fork-shaped shovels, excavate soil and rocks covering the quarry and are also utilized for loading the extracted materials onto transport equipment such as dump trucks. Loaders facilitate the movement of large quantities of mined materials over short distances within the site or assist with loading these materials onto dump trucks. Dump trucks transport substantial quantities of soil and rock to either an internal or external destination relative to the tunnel.

The classification of rock types extracted from quarries is closely linked to the operational characteristics of mining equipment. Soil is characterized as a mixture composed of sand, gravel, cobblestone, and other components. Material that has undergone sufficient weathering to allow excavation using a hydraulic ripper is categorized as ripping rock. Crushed stone refers to layers suitable for blasting [25]. Each rock type demonstrates varying levels of mining and loading efficiency, which results in differences in transport volume when loaded onto dump trucks. In this study, backhoes and dump trucks are employed for the quarry mining process, excluding loaders, and work efficiency is evaluated for three material types: soil, ripping rock (rip rap), and crushed stone. Additionally, this analysis incorporates the procedure of utilizing vertical tunnels and conveyors for transporting mined stone through tunnels.

2.2. Simulation Modeling and Optimization in Quarry Mining

Studies on the optimization of mining operations are typically classified into surface (or open-pit) mining and underground (or tunnel) mining, depending on the location of the resource. Mathematical optimization approaches, such as linear programming (LP) and mixed-integer linear programming (MILP), have been extensively adopted to reduce operating expenses. Ercelebi et al. [26] identified profitability as the primary metric and highlighted that reducing costs can be achieved by optimizing combinations of surface mining equipment. A closed queuing network-based model was used to determine the optimal number of trucks per backhoe, while a truck dispatching model, formulated as an LP model, assigned trucks to backhoes to achieve minimum loading and transportation costs comparable to results from the network theory-based approach. Ozdemir and Kumral [27] maintained that optimizing individual phases—such as drilling, blasting, loading, hauling, and coal preparation—in an open-pit coal mining process does not ensure system-wide optimization. They introduced a cost model that incorporates the entire mining cycle, proposing a holistic approach to minimize aggregate mining costs. Campeau et al. [28] introduced a branch-and-cut-based optimization model to determine the optimal short-term production plan necessary for a Canadian underground gold mine. The development of a short-term production plan for underground mines is complex due to the presence of numerous interdependent decisions. Ben-Awuah et al. [29] applied a mixed-integer linear programming (MILP) optimization framework to achieve simultaneous minimization of mining costs across open pit and underground mines. Nonetheless, the limitations of the MILP mathematical approach precluded the inclusion of detailed process-level mining operations.

However, production plans developed through mathematical optimization techniques are limited in their ability to generate detailed plans that incorporate the complex interdependencies among factors such as work cycles, backhoe movements, and truck allocation. To address these limitations, advanced modeling methodologies like simulations should be utilized [30]. In research related to surface mining, Upadhyay et al. [31] developed a short-term mining plan using the MOOT (Mining Operation Optimization Tool), which integrates discrete event simulation and an optimization module for open-pit mines. The objective of their study was to generate a production schedule that maximizes the operational efficiency of mining equipment within the constraints of stringent mining operation strategies while ensuring compliance with required quality and target production volumes. Afrapoli et al. [32] identified that the optimal decision-making framework for dynamically allocating trucks to backhoes in the current FMS (Fleet Management System) of iron ore open-pit mining focused solely on a single objective function. To address this, they utilized discrete event simulation to model the operation of backhoes and trucks, and subsequently developed an optimal truck dispatching model formulated as a multi-objective function (Multi-Objective Optimization) based on operational data from the simulation model, thus mitigating the limitations of the existing FMS. Abolghasemian et al. [33] approached the mining operation optimization problem by employing a two-step methodology for a real-world open-pit mine. Initially, they built a detailed representation of the open-pit mining process using discrete event simulation and conducted simulation optimization experiments incorporating heuristic and metaheuristic methods such as scatter search, tabu search, and neural network algorithms. Nevertheless, due to the prolonged computational time, which represents a significant drawback of simulation optimization, they introduced a meta-model, or surrogate model, to estimate the total production quantity accurately and determined the optimal capacity plan using experimental design techniques. Additionally, in the context of underground mining studies, Greberg et al. [22] implemented a discrete event simulation framework to assess a range of alternatives for complex underground mining operations. Using this model, they identified the optimal quantity of large dump trucks to deploy as a replacement for the traditional ore passing system, based on specific production targets. Runciman [34] highlighted the essential requirement of comprehensive testing and system improvements prior to the deployment of new mining equipment, advocating for simulation-based techniques as both an effective assessment tool and a valuable instrument for preliminary system design. The study conducted a simulation that demonstrated more efficient use of the remote mining system, revealing that monthly production could increase by as much as 45% compared to the current mining production process.

As current methods employing mathematical optimization techniques (e.g., LP and MILP) face challenges in adequately representing the interdependencies among various elements in the mining stage, alternative research is being undertaken utilizing simulation modeling. In this study, we will apply DES to comprehensively address both the open-pit mining process and the underground tunnel transportation process, enabling resource allocation that aims to minimize transportation costs.

2.3. Simulation-Based Equipment Allocation in Quarry Mining

To achieve cost minimization in quarry mining operations through effective equipment allocation, this study adopts a simulation-based optimization framework utilizing DES, as illustrated in Figure 2. It consists of two parts: one is simulation modeling, and the other is optimization, which uses the developed simulation model to predict performance and perform optimization for various alternatives (values of decision variables). Under the given study objective, DES modeling begins with the collection of operating parameters, geospatial information of quarries, and details of mining equipment, followed by an evaluation of the simulation model to identify potential functional errors (verification) and to ensure it appropriately captures the key features of the actual quarry mining process (validation). If the simulation model contains errors or fails to accurately represent the intended system, further data sampling is conducted for the modeling process, securing a robust and dependable simulation model [35]. Once the DES model is validated, it serves as a predictive tool for assessing performance under various alternatives. In simulation-based optimization, the DES model is used for forecasting key metrics (e.g., production volume) across various equipment allocation scenarios, and decision variables for each scenario are evaluated iteratively until the optimal solution is identified. The proposed framework addresses the mining equipment allocation problem with the objective of reducing mining costs (see Equation (1)).

In this study, to obtain geographic input data required by the simulation model under the specified framework, data is sourced from the Building Information Model (BIM) [36] that is created following the geological analysis of the quarry (see Figure 3b for a sample). The examined quarry mine shown in Figure 3a has a height of 130 m and is segmented into 13 stages at intervals of 10 m. The highest stage is designated as the first stage, with the 13th stage as the lowest. The volume of rock within each stage is subsequently categorized according to rock type, and these data are measured and recorded.

2.3.1. Optimization Model

As depicted in Figure 2, simulation-based optimization is implemented by considering the allocation of four principal equipment types (24-ton dump, 2.0 m³ backhoe, 41-ton dump, 4.64 m³ backhoe) in the quarry mine. Equations (1)–(4) define the optimization relationships.

$$\mathrm{M}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{z}\mathrm{e} Z=\mathrm{E}\left[{\sum }_{i\in \mathrm{I}}{f}_c\left(X_i\right)\right]$$

(1)

subject to

$$f_c\left(X_i\right)={\sum }_{j\in \mathrm{J}}{\alpha }_{ij}{\beta }_{ij}{X}_{ij} \mathrm{for} \forall i\in \mathrm{I}$$

(2)

$$X_i={\sum }_{j\in \mathrm{J}}{X}_{ij} \mathrm{for} \forall i\in \mathrm{I}$$

(3)

$$0 \le { X}_{ij} \le {\gamma }_{ij}$$

(4)

Equation (1) aims to minimize the operational equipment cost needed to process a specified production volume, with the decision variable taking integer values for the quantity of each of the four equipment types ($X_1$: dump truck 24 t; $X_2$: backhoe 2.0 m³; $X_3$: dump truck 41 t; and $X_4$: backhoe 4.64 m³) deployed in operation. Equation (2) defines the cost function, where $X_{ij}$ denotes the number of equipment i operable in quarry category j, ${\alpha }_{ij}$ indicates the operating time, and ${\beta }_{ij}$ refers to the unit operating cost per hour. Notice that the information on the four categories is described in

Table 1. Category information of the subject quarry mine.

Category	Stage	Depth (m)	Equipment
1	1~3 (Open-pit mining)	0~30	Dump truck 24 t and backhoe 2.0 m3
2	4~6 (Open-pit and tunnel mining)	30~60	Dump truck 24 t, dump truck 41 t, backhoe 2.0 m3, and backhoe 4.64 m3
3	7~9 (Open-pit and tunnel mining)	60~90	Dump truck 24 t, dump truck 41 t, backhoe 2.0 m3, and backhoe 4.64 m3
4	10~13 (Open-pit and tunnel mining)	90~130	Dump truck 24 t, dump truck 41 t, backhoe 2.0 m3, and backhoe 4.64 m3

. Equation (3) provides a constraint stipulating that the total number of pieces of equipment i deployed across all quarry categories matches the number of pieces of equipment i allocated within the subject quarry. Equation (4) restricts the number of pieces of equipment i assigned to quarry category j, ensuring it does not exceed the operational limits (${\gamma }_{ij}$) for each category. Table 1 details the definitions of four categories, each employing different equipment. It should be noted that Categories 2, 3, and 4, with Category 1 excepted, incorporate both open-pit mining and underground tunnel transportation (see Section 2.3.2 for further operational details in the four categories).

2.3.2. Simulation Model

DES is a simulation methodology driven by discrete event occurrences in system states, rather than continuous time flow (t), which reduces simulation model computation and facilitates rapid performance evaluation [37]. Figure 4 shows the discrete event simulation model for the 1–3-stage open-pit mining process. In this study, AnyLogic, a commercial simulation platform supporting DES, was used to model the open-pit mining process using discrete event simulation.

In Figure 4, 24-ton dump trucks (20 units) and 2.0 m³ backhoes (10 units) are utilized as mining equipment during stages 1 to 3 of the quarry (see Figure 4). The total rock volume for these stages is 8357 m³, and the process involves sequential mining and transport of soil, ripping rock (weathered rock or weathered soil), and blasting rock. The mined soil and ripping rock are immediately taken to the supply site without requiring crushing, while large blasting rock is sent to the crusher. After crushing, the processed rocks are transported by a separate set of 24-ton dump trucks (10 units) stationed at the crusher.

On the other hand, the remaining 4~13 stages involve a combination of open-pit mining and tunnel mining methods. Here, soil and ripping rock are handled using the open-pit mining process, while only blasted rock is transported through underground tunnels (see Figure 5). In stages 4 to 13, the equipment utilized includes 24-ton (10 units) and 41-ton (10 units) dump trucks, as well as 2.0 m³ (10 units) and 4.64 m³ (10 units) backhoes. The cumulative rock volume extracted from stages 4 to 13 is approximately 200,000 m³, with blasted rock constituting 95% of this total; the majority of this blasted rock is excavated using dynamite. Consequently, most equipment is designated solely for the loading and transportation of rocks fragmented by dynamite blasting. The 24-ton dump truck is paired with the 2.0 m³ backhoe for loading and transporting earth and ripping rock, excluding blasted rock, while larger equipment such as the 41-ton dump truck and 4.64 m³ backhoe are utilized for the loading and transportation of blasted rock. It should be noted that the 41-ton truck, as a larger transport vehicle compared to the 24-ton truck, demonstrates lower safety and transport efficiency during long-distance repeated hauling, and its primary function is to drop rocks into the vertical mine shaft. Rocks deposited in the vertical mine shaft are subsequently transported via conveyor installed within the underground shaft and are separated by size using sorting equipment. Among these, smaller rocks are reloaded onto the 24-ton truck and delivered directly to the supply site without passing through the crusher, whereas larger rocks are conveyed to the supply site via a long conveyor system.

3. Results

3.1. Scenario

As stated in Section 2.3, the proposed simulation model is applied to a quarry mine in Changwon-si, Gyeongsangnam-do, South Korea, and simulation experiments are conducted using the parameters provided in

Table 2. Simulation parameters of the proposed framework.

Parameters	Value	Description
${\mathrm{a}}_{1j}\left(s_1\right)$	Triangular (2.87, 3.53, 5.03) min	Time required for loading soil into a dump truck (24 t) across all categories
${\mathrm{a}}_{1j}\left(s_2\right)$	Triangular (4.7, 6.0, 8.52) min	Time required for loading ripped rock into a dump truck (24 t) across all categories
${\mathrm{a}}_{1j}\left(s_3\right)$	Triangular (10.10, 12.06, 13.24) min	Loading time for blasting rock using a 24 t dump truck across all categories
${\mathrm{a}}_{3j}\left(s_3\right)$	Triangular (9.5, 10.84, 12.24) min	Loading time for blasting rock using a 41 t dump truck across all categories
${\mathrm{m}\mathrm{c}}_{1j}\left(s_1\right)$	15.67 m3	Soil loading capacity of a 24 t dump truck across all categories
${\mathrm{m}\mathrm{c}}_{1j}\left(s_2\right)$	15.16 m3	Ripping rock loading capacity of a 24 t dump truck across all categories
${\mathrm{m}\mathrm{c}}_{1j}\left(s_3\right)$	15.16 m3	Blasting rock loading capacity of a 24 t dump truck across all categories
${\mathrm{m}\mathrm{c}}_{3j}\left(s_3\right)$	24.47 m3	Blasting rock loading capacity of a 41 t dump truck across all categories
${\mathrm{a}}_{1j}\left(A\right)$	Uniform (11.7, 13.5) min	Transport time for a 24 t dump truck on route A across all categories
${\mathrm{a}}_{1j}\left(B\right)$	Uniform (5.3, 7.5) min	Transport time for a 24 t dump truck on route B across all categories
${\mathrm{a}}_{1j}\left(C\right)$	Uniform (3, 5.05) min	Travel time for a dump truck (24 t) on route C across all categories
${\mathrm{a}}_{3j}\left(D\right)$	Uniform (3.88, 4.33) min	Vertical shaft travel time for a dump truck (41 t) across all categories
${\mathrm{c}}_{ij}\left(·\right)$	Triangular (3.9, 4.1, 4.3) min	Unload duration for a dump truck (24 t, 41 t) across all categories
${\beta }_{1j}$	USD 48.88/h	Operational cost of a dump truck (24 t) across all categories
${\beta }_{2j}$	USD 266.80/h	Operational cost of backhoes (2.0 m3) across all categories
${\beta }_{3j}$	USD 111.19/h	Operational cost of a dump truck (41 t) across all categories
${\beta }_{4j}$	USD 255.74/h	Operational cost of backhoes (4.64 m3) across all categories
${\mathrm{w}\mathrm{t}}_{ij}\left(·\right)$	-	Queue time for a dump truck (24 t, 41 t) across all categories

. It is important to note that these parameters are derived from actual operating data collected between 1 July 2022 and 31 August 2022 from the target quarry mine.

Using the developed simulation model and the parameters listed in Table 2, a simulation experiment is conducted according to the scenario outlined in

Table 3. Experiment scenario.

Category	Equipment
1 (1~3 stages)	Backhoes (2.0 m3)	10 units	Dump trucks (24 t)	30~90 units
2 (4~6 stages)	Backhoes (2.0 m3)	10 units	Dump trucks (24 t)	20~60 units
	Backhoes (4.64 m3)	10 units	Dump trucks (41 t)	10~30 units
3 (7~9 stages)	Backhoes (2.0 m3)	10 units	Dump trucks (24 t)	20~60 units
	Backhoes (4.64 m3)	10 units	Dump trucks (41 t)	10~30 units
4 (10~13 stages)	Backhoes (2.0 m3)	10 units	Dump trucks (24 t)	20~60 units
	Backhoes (4.64 m3)	10 units	Dump trucks (41 t)	10~30 units

. As described in Section 2.3.2, there are four categories involving different equipment and operational procedures (i.e., open-pit mining at stages 1~3 and a combination of open-pit and tunnel mining processes at stages 4~13).

Under the experimental conditions specified in Table 3, the simulation-based optimization framework illustrated in Figure 2 is implemented to determine the optimal values of the decision variables detailed in

Table 4. Variables of the proposed framework.

Variables	Default Value	Description
$X_{2j}$	10	Number of backhoes (2.0 m3) across all categories
$X_{42}$	10	Number of backhoes (4.64 m3) assigned to category 2
$X_{43}$	10	Number of backhoes (4.64 m3) assigned to category 3
$X_{44}$	10	Number of backhoes (4.64 m3) assigned to category 4
$X_{1j}$	10	Number of dump trucks (24 t) across all categories
$X_{32}$	10	Number of dump trucks (41 t) assigned to category 2
$X_{33}$	10	Number of dump trucks (41 t) assigned to category 3
$X_{34}$	10	Number of dump trucks (41 t) assigned to category 4

. Unlike backhoes, which must operate at designated locations in mining operations, dump trucks are flexible in both deployment and quantity, making their number the sole decision variable in this study.

3.2. Result

The simulation experiment was repeated 30 times for each scenario, following the optimization objective function outlined in Section 2.3.1.

Table 5. Optimization result.

Category	Equipment
1 (1~3 stages)	Backhoes (2.0 m3)	10 units	Dump trucks (24 t)	63 units
2 (4~6 stages)	Backhoes (2.0 m3)	10 units	Dump trucks (24 t)	44 units
	Backhoes (4.64 m3)	10 units	Dump trucks (41 t)	21 units
3 (7~9 stages)	Backhoes (2.0 m3)	10 units	Dump trucks (24 t)	46 units
	Backhoes (4.64 m3)	10 units	Dump trucks (41 t)	15 units
4 (10~13 stages)	Backhoes (2.0 m3)	10 units	Dump trucks (24 t)	46 units
	Backhoes (4.64 m3)	10 units	Dump trucks (41 t)	15 units

summarizes the optimization outcomes for the four categories. The proposed simulation-based optimization model identified the optimal solution using the OptQuest^® 9.1.2 software embedded in AnyLogic Professional 8.7.7 simulation software.

Figure 6 presents results for Category 1, indicating that deploying 10 backhoes (2.0 m³ capacity) with a total of 63 dump trucks (24 t) yields the lowest total operating cost at USD 48,071. This demonstrates that an allocation of 6.3 dump trucks (24 t) per backhoe (2.0 m³) is the most cost-effective arrangement for mining operations. The convex nature of the cost curve results from the increased driving distance as the number of dump trucks decreases, leading to higher total operating costs; therefore, the configuration providing optimal efficiency for the specified mining volume achieves the lowest total operating expense.

In Category 2, the configuration of 10 backhoes (2.0 m³), 44 dump trucks (24 t), 10 backhoes (4.64 m³), and 21 dump trucks (41 t) produced the lowest operating cost at USD 104,952. Figure 7 displays a three-dimensional analysis of construction costs as a function of the number of dump trucks (24 t and 41 t). The trend observed in Figure 7 illustrates that increasing the number of 24-ton dump trucks while reducing the quantity of 41-ton dump trucks results in a decrease in total operating costs. However, minimizing the number of dump trucks may initially reduce vehicle-related operating expenses, but it may ultimately increase the total operating cost due to prolonged investment in the mining process.

Figure 8 presents the total operating cost for each scenario in Category 3. The total operating cost exhibits a convex relationship, initially declining and then rising as the quantity of 41-ton dump trucks decreases and similarly declining and then rising as the number of 24-ton dump trucks increases. From Figure 8, it is clear that the minimum total operating cost, amounting to USD 345,010, is achieved when 10 backhoes (2.0 m³), 46 dump trucks (24 t), 10 backhoes (4.64 m³), and 15 dump trucks (41 t) are deployed, representing the optimal configuration. The reduction in the required number of 41 t dump trucks in Category 3 compared to Category 2 is attributable to the lower quarry height in Category 3. This results in a shortened supply route for 24 t dump trucks and enhances the operational efficiency of the 41 t dump trucks.

Figure 9 displays the experimental outcomes for Category 4. Under the deployment of 10 backhoes (2.0 m³), 46 dump trucks (24 t), 10 backhoes (4.64 m³), and 15 dump trucks (41 t), the total operating cost reached its minimum at USD 658,893. For Categories 3 and 4, the sole distinguishing factor is the quarry’s working height, as the equipment allocation and route configurations are consistent. However, the total operating cost in Category 4 is notably higher than in Category 3, which is due to the increased volume of rock processed as quarry operations advance. With the rock amount continuously increasing, maintaining a fixed number of 10 backhoes (2.0 m³) and 10 backhoes (4.64 m³) during this experiment may extend the mining period in Category 4, potentially raising mining costs and reducing profitability. This highlights the importance of evaluating scenarios that incorporate additional backhoes in subsequent operations.

4. Discussion

Utilizing the proposed simulation model, this study investigates the impact of varying the number of operating 24-ton and 41-ton dump trucks on total operating costs across four categories. Compared to backhoes, which are costly and operate at designated locations during mining, this study focuses on determining the optimal operational strategy for dump trucks, which are comparatively more cost-effective and simpler to manage.

In Category 1, the total operating cost curve exhibited a convex profile, demonstrating that adjusting the number of dump trucks in operation can alter the total operating cost in a nonlinear manner by affecting the driving distance per dump truck. The analysis indicated that the minimum total operating cost was USD 48,071 when 10 backhoes (2.0 m³) and 63 dump trucks (24 tons) were utilized. In Category 2, the total operating cost curve also displayed nonlinear characteristics similar to Category 1; however, the curve was more intricate due to the simultaneous operation of both 24-ton and 41-ton dump trucks. Notably, when both 24-ton and 41-ton dump trucks were distributed to meet the workload, optimal efficiency was achieved as costs decreased in a valley-shaped pattern. Specifically, for this case, deploying 10 backhoes (2.0 m³), 44 dump trucks (24 t), 10 backhoes (4.64 m³), and 21 dump trucks (41 t) resulted in the minimum operating cost of USD 104,952. Similarly, Category 3 achieved the lowest total operating cost of USD 345,010 with the deployment of 10 backhoes (2.0 m³), 46 dump trucks (24 tons), 10 backhoes (4.64 m³), and 15 dump trucks (41 tons), while Category 4 reached the minimum total operating cost of USD 658,893 under the same equipment allocation. However, because these experimental results were based on the condition of 10 backhoes per category, the optimal plan could change if this assumption is altered. Nonetheless, since the proposed framework allows adjustment of backhoe quantities, establishing a new optimal production plan that accounts for diverse equipment operation scenarios could lead to substantial reductions in quarry mining operating costs.

5. Conclusions

In this study, the DES modeling technique was applied to determine the optimal equipment allocation for the quarry mining process. The DES accounted for the interactions among heterogeneous equipment, whose operational efficiency varies depending on the different rock types encountered in the quarry, and captured the complexity of both open-pit mining and underground tunnel transport operations. Utilizing this realistic simulation model, simulation-based optimization was conducted, demonstrating that cost-effective quarry mining operations can be achieved by allocating the optimal number of equipment units. The results indicate that the total operating cost increases if the number of dump trucks is either insufficient or excessive. More specifically, the proposed simulation-based optimization framework identifies optimal alternatives to minimize total costs across four quarry mining scenarios for 24-ton and 41-ton dump trucks, as well as 2.0 m³ and 4.64 m³ backhoes. For quarry category 1, the maximum total operating cost decreased by 19.93% from USD 60,043 to USD 48,071; for quarry category 2, the maximum total operating cost decreased by 77.28% from USD 461,989 to USD 104,952; for quarry category 3, the maximum total operating cost decreased by 63.89% from USD 955,550 to USD 345,010; and for quarry category 4, the maximum total operating cost decreased by 71.69% from USD 2,327,306 to USD 658,893. Therefore, the proposed framework employing DES supports managers and engineers in mitigating financial risks by enabling prediction of operating costs through a high-fidelity simulation model prior to commencing actual quarry mining operations, which inherently involve substantial costs.

While the proposed framework provides an efficient solution for quarry mining operations, it assumes that the efficiency of dynamite resources and input manpower is unlimited. This assumption arises because the model presumes that blasting with dynamite is carried out daily by workers prior to the deployment of backhoes or dump trucks for mining and loading. Although these material and human resources lie outside the primary focus of this study, their impact on mining efficiency is still significant, whether directly or indirectly. Future work should enhance the modeling of the quarry mining process by incorporating a broader range of resource characteristics and enabling decision-making involving a more extensive set of variables.