System Dynamics and Sustainable Solution: The Case in a Large-Scale Pallet Manufacturing Company

Abstract

The proposal in the present research study is the result of a more than two-year process developed in a pallet manufacturing company for anchor enterprises in Southern Sonora, Mexico dedicated to beer production and export to the United States of America. Considering the high pallet demand for this supplier, a strategic plan was created in 2021, establishing an important project for developing technological solutions to improve decision making supported by graphical user interface and focused on sustainability. This study shows the application of system dynamics in all the wood and pallet manufacturing processes with a strategic sourcing supply chain. The method used for its development had the following stages: (1) developing the mapping process; (2) creating the causal loop diagram; (3) developing a flow and stock model with the representing mathematical equations; (4) simulating and validating current scenarios; (5) evaluating normal, optimistic, and pessimistic scenarios with multicriteria decision making using Technique to Order Preferences by Similarity and the Ideal Solution (TOPSIS) and Faire Un Choix Adéquat (FUCA); (6) building the graphical interface. The most relevant results for the company were having quantitative information regarding the pallet demand required by the main client for wood availability, which was the main restriction in the supply chain. The solution was based on four validation tests that allowed decision makers to support the production proposals considering the assistance of the dynamic models. The main conclusion demonstrated that using well-defined operation rules and policies—considering the installed capacity and pallet demand through the model solution—allows anticipating decisions on pallet quantity and reducing the risk of out-of-time deliveries.

1. Introduction

Developing suppliers is an important aspect for enterprises that depend on response time and product quality. Suppliers have turned out to be critical elements for organizations since they are the persons responsible for providing on-time materials and services [1]. They are part of the supply chain that provides the production link and allows evaluating decisions between the interactions generated in this first client–supplier internal relationship [2]. In this sense, when evaluating and selecting suppliers, the objectives of the organization should be coordinated and an eye kept on quality standards, costs, and delivery time, among other variables. Thus, robust methodologies capable of managing such complexities are needed. For this purpose, the system dynamics methodology enabled simulating complex systems from different operational rules and policies [3,4,5,6]. Therefore, causal models were constructed based on the systematic thought theory.

Literature Review

The causal diagrams analyzed the cause–effect relationships between the variables that conformed the model with behaviors denominated as reinforcement (R) and balance (B). These models helped to know the different connected loops that create, on the one hand, mental models and, on the other hand, simulation models to understand the systematic thought complexity and to obtain the conclusions from data and decision making [7].

Likewise, the simulation model was developed in Stella^® Architect—a simulator that uses solution algorithms of differential equations—based on Chapra and Canale [8], using Euler’s and Runge–Kutta methods. Subsequently, the model validation was performed, considering the proposals of Kleinjen [9] and Barlas and Carpenter [10]. With these proposals, the sensitivity analysis generated the different scenarios in situations evaluated by time and analyzed from the perspective of pessimistic and optimistic behaviors from the current scenario given by the response of the model initially implemented [11].

The scenarios required the selection of the most critical variables to apply a multicriteria decision-making (MCDM) analysis considering two techniques: (1) Technique to Order Preferences by Similarity and the Ideal Solution (TOPSIS) and (2) Faire Un Choix Adéquat (FUCA) developed by Fernando et al. [12] and Wang and Rangaiah [13]. The results of both techniques were 15 scenarios, classified in 5 current, 5 pessimistic, and 5 optimistic scenarios for decision making based on data.

Saha et al. [14] used mathematical models and algorithms to determine the optimal rate of investment in technology of green preservation and dynamic investment strategy for waste reduction. The present research study shows a production proposal of pallets distributed to a beer company. The dynamics system models included multicriteria techniques as part of their procedure for selecting the best scenario from the optimization criteria in the following variables: wood storage, wood with fungus, clean wood, pallet warehouse inventory, sawdust inventory total pallets for clients, and cash inflows.

Given the complexity of the existing mathematical models, as well as the nomenclature used in the development of the solutions, the graphical user interface generated a more adequate understanding and interactions between the user and the computer [15,16].

The present study was developed in a pallet manufacturing company with an average volume of 38,000 pallets/month to supply a beer company from Southern Sonora, Mexico, which produces and distributes to the United States of America in great volumes. In 2021, a strategic planning exercise was developed, integrating three pallet manufacturing companies into the project. The 2021–2026 strategic planning exercise developed by Lagarda Leyva and Zavala [17] generated a strategic map, where the objective in the process perspective was defined as technological solutions for improving decision making in complex environments.

As a result of this effort, and to give a response to the strategic objective, the project of developing a technological solution was performed in 2021 based on a graphical user interface and the system dynamics methodology proposed by Forrester and Sterman [18,19]. The decision makers’ interest was to have a model that allowed balancing planning and managing the responsible acquisition of raw matter and minimizing the risks [20]. Thus, the current production capacity and future needs of investment were measured to meet the daily pallet demand and the requirements of the mega Southern Sonora beer producer for export to the USA.

Diverse investigations have used the Data Science (DS) approach to analyze the behavior of the inventories facing disruptive events and their propagation in the network. Different empirical studies have been developed with simulations to evaluate the pallet supply chain behavior. Among those that stand out are Gnoni et al. [21], who developed a simulation model to compare scenarios in terms of time of the provider service and internal and global operation costs. The results confirmed that better coordination of the reverse chain agents increased the yield of all the systems.

On the other hand, Valerio and Gnoni [22] studied the behavior of the feedback loops generated in the pallet supply chain. Their objective was to describe the critical factor in a pallet logistic network or exchange system, using a causal diagram and developing a tool based on simulation to help the logistic agents and to design efficient organizational scenarios for these systems.

Newman et al. [23] developed a simulation model in experimental conditions that included variability levels of demand, quantity of pallets available for the system, incremental load time, and rejection rate when pallets of general usage were made. In the majority of cases, their results indicated a significant system yield increase with pallets of general usage, except for the incremental load time and waste rates associated with pallet assemblage, which were higher.

Dynamics systems evaluate the effect of inventory delays that happen in the supply chain where the dependence from one link to the other is given. For example, starting from the materials, transformation processes and deliveries to clients should comply with delivery time to maintain the expected inventories. Nabil [24] set out this dependence through system dynamics for different operational conditions with a manufacturing simulation model that comprised a quality control unit, which was also a system bottleneck. Therefore, the size of the optimum lot was demonstrated, giving place to a minimum delivery time and whose level of optimum inventory agreed with the one expected.

The main contributions set up previously for each of the authors may be expressed, as shown in

Table 1. Main contributions from each of the authors.

Author (s)	Novelty	Study Effectiveness
[3]	Founder of the dynamics system methodology	Applied methodology of different business environments; the methodology is the basis of the proposed construction for the industrial sector.
[4,6]	Use of the systemic thought as support for the causal diagram construction	Variable and parameter complexity analysis from the systemic approach; bases for the selection of variables and their relationship presented in different R and B loops.
[7]	Guide for using Stella Architect software version 3.3	Contributions on the use of Stella Architect Software for simulation, sensitivity analysis, design, and development of the graphical user interface.
[8]	Set up the logics in which the methods of Euler, Runge Kuta of order 2 and 4 function	Use of the iterative numerical resolution of differential equations (Euler and compared with Runge–Kutta).
[9,10,19,25]	Validation methods	Offer different validation methods of system dynamics models.
[11]	Study of qualitative scenarios	Theoretical basis to understand the exogenous and endogenous variable behavior in qualitative environments.
[12,13]	Use of the multicriteria method for the selection of the best scenarios	Selection of the most critical variables to apply a multicriteria decision making TOPSIS and FUCA.
[14,26,27,28]	Mathematical models and metaheuristic algorithms	Using mathematical and metaheuristic models applied in the supply chain and manufacturing under a sustainable approach.
[15]	Causal diagram development for the health sector analysis	Proposal of the causal R and B models to represent the complexity of the hospital system of the Province of Quebec, Canada.
[16]	Graphical user interface	Design of graphical user interface with combinatorial optimization problems.
[5,18,19,29]	Initial contributions of system dynamics methodologyMethodologies with different applications in businesses using validation technique models.	Basis of theoretical and practical application in different environments, such as the supply chain analysis projects.
[21,22,23]	Empirical support studies to develop causal loops, simulating optimistic/pessimistic scenarios from current ones and their validation in the pallet manufacturing business	Developed a simulation model to compare scenarios in terms of time of the provider service and internal and global operation costs. Designing closed causal loops and use of simulation as supported tools developed to help logistics decisions in organizations under different scenarios.

.

2. Materials and Methods

The materials used in this study were (1) Vensim PLE^® (Versión 8.2.1, Ventana System Inc., Harvard, MA, USA, 2019) to draw loops B and R; (2) Stella^® Architect, 2023 (Version 3.3, Isee Systems Inc., Lebanon, NH, USA, 2023) to build the flow and stock diagrams, simulations; GUI. These software were selected because they included the module to design the graphical user interface with the pallet producers. (3) Excel^® (Microsoft, Redmond, WA, USA, 2018) was used for processing data and information (TOPSIS and FUCA).

2.1. System Dynamics Stage

The method used to develop the technological solution considered the five stages described as follows [3,4,5,29]:

Mapping the pallet factory supply chain. The system approach was used to analyze each one of the pallet manufacturing process links in general. The result generated was a diagram observing the client–provider relationships in the supply chain and considering wood provision (stock), pallet production, and delivery to clients, as well as aspects related to waste reassessment (reverse logistics).

Developing the causal loops diagrams. Taking mapping the pallet supply chain as a reference, an analysis of the cause–effect relationships was carried out, classified as reinforcer (R) and balance (B) loops to understand the complexity of all the manufacturing processes and deliveries from the system dynamics perspective.

Developing the flow and level diagram with the mathematical equations that represent them. For the diagram construction, Stella^® Architect software, version 3.3 was used considering all the model parameters from the relationships between them. The mathematical equations that totally represented the system behavior were constructed.

Simulating and validating the current scenario. Likewise, the simulation was made from the current pallet manufacturing conditions. The average error validation techniques were used from the production reality versus the solution offered by the model.

Building a graphical interface. This was the last step where the technological solution in an environment was concentrated, where the decision maker can incorporate input data to the model and execute it for decision making in the pallet supply chain.

2.2. Multicriteria Decision Making

After creating the dynamics model, three scenario categories were considered: current, optimistic, and pessimistic. Each scenario, when executed, considered the following parameters as variation methods: (a) delivery time of wooden pallets; (b) delivery time of pallets to the final customer; (c) price per pallet according to demands. All these values were modified according to the scenarios executed. In the case of the current scenario, the selected values were those that the company provided at the moment of developing the solution; in the pessimistic scenario, these parameters of the same three indicators were considered as the ones that would put the organization at risk, that is, in terms of the same three parameters rising considerably. Finally, in the optimistic scenario, the three same parameters were considered improved to put the organization in the ideal situation to cover the commitments with the main client.

Each one of these scenarios considered 5 alternatives; thus, 15 alternatives were taken into account and evaluated by the following criteria, the same that were validated by the organization from the following 8 variables that were considered in the process analysis of the scenarios in the FUCA and TOPSIS methods, with the optimization criteria and weighting value assigned by the company:

• WS—wood storage (units); refers to the quantity of wood available in the organization coming mainly from Mexico cut into pieces in the measurements required for the pallets.
• WF—wood with fungus (units); considered as a high risk if assembled as pallets due to the effect of the humidity captured during transportation, since the pallet may reach its destination with fungi due to its sensitivity. Upon arrival, wood is treated with an established cleaning process by the company.
• WC—wood clean (units). Clean wood refers to the total quantity of wood ready to be assembled to make the pallets.
• AP—the pallets assembled from the wooden pieces required for their production.
• IPW—inventory in the pallet warehouse (units); refers to the inventory of the pallets generated and stored in the warehouse for its distribution.
• SI—sawdust inventory (tons); refers to the quantity of sawdust generated as part of the planning process of the wooden pieces, which represents a loss but that is used and sold as a secondary product.
• TPC—total pallets per client (units); refers to the total quantity of pallets assigned to the clients of the organization.
• CI—cash inflow (MXN); refers to the daily money income in the organization, of which the production cost has been deducted (data not available because of confidentiality); thus, the sale price generates the organization utility.

The next step was necessary to define pesos/weighting to calculate each of the criteria (i.e., its degree of importance) and to define the objective to be reached (maximize or minimize). Then, the variables were listed, with weighting in parenthesis: minimize WS (10%); minimize WF (10%); maximize WC (15%); maximize AP (15%); minimize IPW (10%); minimize SI (5%); maximize TPC (15%); maximize CI (20%)

Once the previous information was defined, a decision matrix was created, such as the one shown in

Table 2. Main contributions for each of the authors.

Criteria	WS	WF	…	CI
Objective	Max/Min	Max/Min	…	Max/Min
Weight	Whole Value 0 and 1	Value between 0 and 1	…	Whole Value 0 and 1
Alternative 1
Alternative 2
…
Alternative 15

Source: own production (2023).

.

Finally, MCDM techniques were used to rank the alternative. The techniques selected were TOPSIS and FUCA because they were easy to use and have demonstrated good performance in solving matrixes with considerable criteria [30]; furthermore, both methods are widely used in diverse research environments [31,32,33,34]. It is important to highlight that the description of the methods is beyond the reach of this research study.

3. Results

The results are presented below, considering the six steps of the proposed procedure.

3.1. Mapping the Supply Chain of Pallet Manufacturing

In general, Figure 1 shows the pallet supply chain where each stage is explained separately.

The links in Figure 1 are explained as follows:

Supply. The supply starts with wood provision for the sawmills (in the states of Durango, Chihuahua, Sonora, and Sinaloa), mainly from the massive pine tree forests. The wood is transported in different forms toward the warehouses of the different pallet manufacturers. All the sawmills should have the commitment of reforesting in conjunction with official entities (1, 2, 3, 4, 11).

Production. Each manufacturer independently runs its internal processes according to personnel, physical infrastructure, and available equipment, as well as the human resources assigned according to expertise and performance in the tasks assigned (4, 5, 6, 7, 9, 11). All the manufacturers—as previously mentioned—should be committed to reforest jointly with the official entities.

Finished product distribution. The pallets are set up in the different transportation modes used by each of the manufacturers and placed in the final client warehouse (6, 7, 8).

Final client. The main customer that has been analyzed is the brewery company, based on the scheduled demands of pallets; according to the orders, the production process is established, generating income for the organization from the entries (8, 9, 11). The clients must promote the behavior of reforesting in conjunction with official entities and their providers.

Reverse logistics. This stage takes place in each pallet factory when wood cannot be exploited to make pallets, such as waste generated (sawdust and profile wood, among others). In the same manner, pallets are recycled and placed as second-hand products for a certain type of client (10, 11) (achieved by the main wood used as raw matter for pallet manufacturing).

3.2. Creating the Causal Diagram from the Dynamics Hypotheses

A dynamics hypothesis allows generating the idea that the causal diagram structure could communicate in terms of its dynamic behavior associated with the variables of the analysis from the existing relationships, among them Sterman [19]. Considering the previous mapping of the supply chain, the causal diagram was developed, as shown in Figure 2, where the type B and R loops can be observed from the three dynamics hypotheses as follows:

• Hd1: the wood for pallet construction depends on availability and permits to cut pine trees in the cities that offer this product;
• Hd2: the amount of pellet production depends on the final client from the operation rules of 30% assigned only for the local supplier;
• The wooden quantity in the inventory depends on the pallet demand to ship beer to the final client.

The diagram shows three reinforcing (R1, R2, R3) and three balance (B1, B2, B3) loops.

The reinforcing R1 (1→2→3→1) loops’ dynamics can be explained as follows: the more sawmills that exist, the more that uncontrolled tree felling reduces wood availability per available tree, which implies trees replanting per each eliminated tree so that sawmills continue producing wood.

The B1 (4→5→6→4) loops expose in their dynamics that the more wood there is available the greater pallet production is allowed. According to a dynamics inventory, the difference is reduced because the warehouse is full with the required amount, reducing the input of the available wood to the production process.

The reinforcing R2 (5→7→5) loops establish that greater pallet production depends on demand and sales grow in the time required to maintain high pallet production levels.

The reinforcer B2 (8→9→8) loop is represented by the pallet inventory growth dynamic variables delivered to the final client by the effect of the high beer consumption demand in the USA, which in time reduces the pallet inventories.

The reinforcing B3 (10→11→10) loops are composed of dynamic wood reduction (sawdust) variables due to the effect of high pallet production, which in time increases sawdust inventories.

3.3. Creating Flow and Level Diagrams with the Model Equations

The flow and level diagram was created from the logics of the supply chain operation for the wood input process, pallet manufacturing, and delivery to clients and also considering the reductions (sawdust) produced, as shown in Figure 3.

The data for the model development were provided by the company to simulate the changes in the most sensitive parameters and were validated for the construction of the different scenarios.

The flow and stock diagram was arranged in sectors by the raw material input sent to the production process, considering the wood was free from fungi; otherwise, it should be prepared for entry as clean wood. For this purpose, the wood passes through a brushing and chlorinating procedure before starting the process.

The other sector was composed of the waste generated from the work made on the wood in the process of transforming into pallets, which accumulated sawdust in tons per week. The pallet sale sector for the mega beer company was considered, based on the demand by the United States of America.

The simulation model required feeding the flow and level diagram with dynamic equations, which were composed of the flow and levels according to their type. Part of the equations that composed the model are shown to illustrate their use as follows:

Stocks:

Pallet_assembly(t) = Pallet_assembly (t-dt) + (“Entry-pallet assembly_pallet flow”-toward_sealing −
Waste) × dt

(1)

Inventory_in_pallet_warehouse (t) = Inventory_in_pallet_warehouse(t-dt) +
(Warehousing_Finished_product − Final_brushing) × dt

(2)

Sawdust _Inventory(t) = Sawdust _Inventory(t-dt) + (steelrin) × dt

(3)

Conveyor

Conveyor_to_pallet distrubution_pallets(t) = Conveyor_to_pallet distrubution_(t- dt) +
(Final_brushing − loading_pallets_on_trucks) × dt

(4)

Oven:

inventory_in_transit(t) = inventory_in_transit (t-dt) + (pallets_in_trucks − final_client) × dt

(5)

Queue:

Loading_trucks(t) = Loading_trucks(t-dt) + (loading_pallets_on_trucks − pallets_in_trucks) × dt

(6)

Flows:

“Entry-assembly_pallet flow” = Wood_Clean/ft_of_wood_per_pallet

(7)

Final_brushing = Inventory_in_pallet_warehouse/rate_of_wood_brushed

(8)

Auxiliary

Cash_inflows = Sales × Sales_price_per_pallet

(9)

Difference = Storage_capacity - Wood_storage

(10)

The rest of the equations and parameters used, as well as the units, can be consulted in Appendix A.

3.4. Simulation and Validation of the Current Scenario

The model simulation was based on Euler’s method developed by Chapra and Canale [8], with the support of Stella^® Architect software 3.3. The results of the model are shown in Figure 4, to observe the number of pallets generated at the end of the month.

As observed, the simulation showed that, at the end of the month, 39,493 pallets were made to be delivered to the main client. The relative error validation applied was the first test, as proposed by Barlas [25]; it established that a model was valid if the error rate was lower than 5%; thus, the following Equation (11) was performed:

$$\% \mathrm{relative} \mathrm{error}=\left|\frac{\mathrm{Simulated} \mathrm{data}-\mathrm{Real} \mathrm{data}}{\mathrm{Real} \mathrm{data}}\right|\times 100$$

(11)

The validation test was performed considering the real data provided by the manufacturing company of the average production, which was 38,130 pallets/month.

$$\% \mathrm{relative} \mathrm{error}=\left|\frac{\mathrm{39,493}-\mathrm{38,130}}{\mathrm{39,493}}\right|\times 100=3.4512\%$$

Therefore, 3.4512 < 5% concluded that the model was valid.

From this result, it could be established that the model came very close to reality; thus, it was valid and reliable given that the relative error was lower than 5%. Therefore, the relative error rate of 3.4512% < 5% was allowed. To confirm the result of the relative error validation test, the following were also applied.

The second test was the extreme conditions proposed by Sterman [19]. This model assigned zero value in the output rate parameter; from there, the production input and output flows were not performed. Additionally, the rest of the structures (stocks, ovens, and conveyors in some cases) were maintained with the initial values; in others they had zero values. See Appendix D.

The third test was the expert validation. This test was presented to the businessmen of the organization, who executed the model and agreed that the results were approximate to reality (also confirmed by the relative error test applied in the first case).

The fourth test was consistent in the units used in the model, where 100% of them were coherent on the left and right sides of each of the developed equations or, in its case, the value of the assigned parameter.

3.5. Building the Graphical Interface with the User

Building the graphical interface with the user represented the technological solution that integrated the previous stages. Starting from the flow and level model and its equations, the graphical interface user was built from the logical behavior of the pallet supply chain dynamics model using Stella^® Architect software elements for its design.

Figure 5 shows one of the screens that composed the graphical interface where different variables were evaluated by using parameters according to the organization policies.

This screen shows six variables that were simulated for decision making based on data. As can be observed, the total pallets to be delivered to the final clients (mostly to the mega beer producer company) showed a daily behavior. The delivery programmed in this simulation at the end of the month was 39,700 pallets compared with 38,200 in real pallet manufacturing company. In this case and according to this situation, the users had the option to consider two policies: (1) pallet time delivery that was between one and two days and (2) sale price for each pallet.

With these data, the graphical behavior can be observed in sales, total pallets for the clients, as well as pallets in the warehouse inventories, the amount of work in assembling, and wood that arrives with fungi. One of the highly relevant datum was the income for the organization at the end of the month.

3.6. Evaluating Scenarios: Normal, Optimistic, and Pessimistic Using Multicriteria Decision Making

The current value of the pallet supply chain allowed generating five scenarios that were stimulated using the software Stella^® Architect (2023 Version 3.3, Isee Systems Inc., Lebanon, NH, USA), as shown in Table 2. Each of the scenarios had eight variables for model analysis. In addition,

Table 3. The MCDM TOPSIS for the analysis of the current five scenarios.

Multicriteria Method: TOPSIS			WS	WF	WC	AP	IPW	SI	TPC	CI
		Max/ Min	Min	Min	Max	Max	Min	Min	Max	Max
Ranking	R		0.1	0.1	0.15	0.15	0.1	0.05	0.15	0.2
5	0.4592	C-1	13,055	3463	184,505	10,625	14,209	20	38,071	8,185,775
4	0.4926	C-2	40,274	1424	235,469	15,777	15,223	33	39,176	9,428,340
3	0.5407	C-3	7611	3795	255,872	17,139	22,816	40	39,719	9,993,869
2	0.5109	C-4	40,274	1175	257,681	17,701	16,619	43	40,488	8,268,623
1	0.7651	C-5	13,055	986	269,594	17,738	20,396	47	39,493	9,557,924

Notes: WS—wood storage (units); WF—wood with fungus (units); WC—wood clean (units); AP—assembly pallets (units); IPW—inventory in pallet warehouse (units); SI—sawdust inventory (tons); TPC—total pallets for clients (units); CI—cash inflows (MXN); R—relative proximate value; MCDM—multicriteria decision making. Source: own production (2023).

shows the optimization elements used associated with a percentage weighting that was decided by the MCMC methods (based on the overall values) which of the scenarios were the best among the 15 evaluated. Appendix B and Appendix C show the macros represented in the matrixes that allowed obtaining the ranks of the scenarios analyzed by the FUCA and TOPSIS methods.

Considering the TOPSIS and FUCA analyses, the best scenario was number 5, which offered 0.7651, and the worst scenario was number 1.

The MCDM FUCA method is presented in

Table 4. FUCA for the analyses of current five scenarios.

Multicriteria Method: FUCA			WS	WF	WC	AP	IPW	SI	TPC	CI
		Max/ Min	Min	Min	Max	Max	Min	Min	Max	Max
Ranking	Weight Sum		0.1	0.1	0.15	0.15	0.1	0.05	0.15	0.2
5	4.20	C-1	13,055	3463	184,505	10,625	14,209	20	38,071	8,185,775
4	3.50	C-2	40,274	1424	235,469	15,777	15,223	33	39,176	9,428,340
3	2.65	C-3	7611	3795	255,872	17,139	22,816	40	39,719	9,993,869
2	2.55	C-4	40,274	1175	257,681	17,701	16,619	43	40,488	8,268,623
1	1.90	C-5	13,055	986	269,594	17,738	20,396	47	39,493	9,557,924

Notes: WS—wood storage (units); WF—wood with fungus (units); WC—wood clean (units); AP—assembly pallets (units); IPW—inventory in pallet warehouse (units); SI—sawdust inventory (tons); TPC—total pallets for clients (units); CI—cash inflows (MXN); R—relative proximate value. Source: own production (2023).

, showing the lowest value associated with the scenarios to consider as the best positioned.

The best-positioned current scenario was number 5 and the worst was number 1, considering that the values were 1.90 and 4.20, respectively.

The simulation of the 15 scenarios (5 current, 5 pessimistic, and 5 optimistic) was analyzed and compared with TOPSIS and FUCA (see

Table 5. Analysis of scenarios with the MCDM TOPSIS method.

Multicriteria Method: TOPSIS			WS	WF	WC	AP	IPW	SI	TPC	CI
		Max/ Min	Min	Min	Max	Max	Min	Min	Max	Max
Ranking	R		0.1	0.1	0.15	0.15	0.1	0.05	0.15	0.2
11	0.5282	C-1	13,055	3463	184,505	10,625	14,209	20	38,071	8,185,775
3	0.5978	C-2	40,274	1424	235,469	15,777	15,223	33	39,176	9,428,340
4	0.5964	C-3	7611	3795	255,872	17,139	22,816	40	39,719	9,993,869
5	0.5942	C-4	40,274	1175	257,681	17,701	16,619	43	40,488	8,268,623
1	0.6793	C- 5	13,055	986	269,594	17,738	20,396	47	39,493	9,557,924
14	0.4640	P-1	13,055	3642	315,978	20,826	25,041	52	17,321	4,640,803
8	0.5400	P-2	13,055	1545	289,314	18,122	20,105	40	19,490	5,669,753
12	0.5178	P-3	7611	956	141,879	9676	5869	11	17,840	5,678,938
15	0.4223	P-4	7611	3798	119,253	8342	3733	6	15,400	4,530,354
13	0.5008	P-5	40,274	970	147,734	9781	10,598	13	28,813	7,931,546
10	0.5334	O-1	40,274	1630	128,049	8732	10,434	10	39,144	10,200,449
7	0.5596	O-2	40,274	2015	209,242	13,909	12,923	23	39,733	8,655,700
9	0.5375	O-3	13,055	6250	225,344	14,497	15,727	26	44,684	10,870,243
6	0.5796	O-4	7611	4779	237,114	15,709	15,378	29	42,713	8,953,504
2	0.6069	O-5	40,274	2057	240,789	16,438	19,298	32	46,733	10,906,535

Note 1: WS—wood storage (units); WF—wood with fungus (units); WC—wood clean (units); AP—assembly pallets (units); IPW—inventory in pallet warehouse (units); SI—sawdust inventory (tons); TPC—total pallets for clients (units); CI—cash inflows (MXN). Note 2: R—relative proximate value; C—current; P—pessimistic; O—optimistic; MCDM—multicriteria decision making. Source: own production (2023).

).

Table 5 shows the comparison of each of the 15 scenarios analyzed, from which the best results were obtained. From the scenario type, the following were determined:

• Optimistic scenario. The overall value obtained with TOPSIS was 0.6069, given in optimistic scenario 5 and classified in range 2.
• Pessimistic scenario. The value generated with TOPSIS was 0.5400 for pessimistic scenario 2, classified in rank 8.
• Current scenario. The value generated with TOPSIS was 0.6793 for current scenario 5, ranked 1.

On the other hand,

Table 6. Analysis of scenarios with the MCDM FUCA method.

MCDM Method: FUCA			WS	WF	WC	AP	IPW	SI	TPC	CI
		Max Min	Min	Min	Max	Max	Min	Min	Max	Max
Ranking	General Value		0.1	0.1	0.15	0.15	0.1	0.05	0.15	0.2
13	9.45	C-1	13,055	3463	184,505	10,625	14,209	20	38,071	8,185,775
7	7.15	C-2	40,274	1424	235,469	15,777	15,223	33	39,176	9,428,340
3	6.10	C-3	7611	3795	255,872	17,139	22,816	40	39,719	9,993,869
4	6.15	C-4	40,274	1175	257,681	17,701	16,619	43	40,488	8,268,623
1	5.15	C-5	13,055	986	269,594	17,738	20,396	47	39,493	9,557,924
10	8.35	P-1	13,055	3642	315,978	20,826	25,041	52	17,321	4,640,803
8	7.50	P-2	13,055	1545	289,314	18,122	20,105	40	19,490	5,669,753
12	9.30	P-3	7611	956	141,879	9676	5869	11	17,840	5,678,938
15	12.00	P-4	7611	3798	119,253	8342	3733	6	15,400	4,530,354
14	9.65	P-5	40,274	970	147,734	9781	10,598	13	28,813	7,931,546
11	8.85	O-1	40,274	1630	128,049	8732	10,434	10	39,144	10,200,449
9	8.15	O-2	40,274	2015	209,242	13,909	12,923	23	39,733	8,655,700
5	6.75	O-3	13,055	6250	225,344	14,497	15,727	26	44,684	10,870,243
6	6.80	O-4	7611	4779	237,114	15,709	15,378	29	42,713	8,953,504
2	5.50	O-5	40,274	2057	240,789	16,438	19,298	32	46,733	10,906,535

Note 1: WS—wood storage (units); WF—wood with fungus (units); WC—wood clean (units); AP—assembly pallets (units); IPW—inventory in pallet warehouse (units); SI—sawdust inventory (tons); TPC—total pallets for clients (units); CI—cash inflows (MXN). Note 2: C—current; P—pessimistic; O—optimistic; MCDM—multicriteria decision making. Source: own production (2023).

shows the MCDM FUCA method for analyzing the 15 scenarios.

Table 6 shows the three best results obtained from the 15 scenarios and their comparisons, taking into account the following:

• Optimistic scenario: the overall value with FUCA was 5.5, given in optimistic scenario 5 and classified in rank 2.
• Pessimistic scenario: the value generated with FUCA was 7.50 for pessimistic scenario 2, ranked 8.
• Current scenario: the value generated with the FUCA was 5.65 for the current scenario 5, classified in rank 1.

It is important to note that the best scenario in both methods was the current scenario 5 classified in rank 1, with the overall value of 0.6793 for TOPSIS and a value of 5.15 for FUCA.

Table 7. Comparative MCDM FUCA and TOPSIS method for analyses in optimistic scenarios.

Optimistic Scenarios	MCDM1 = TOPSIS		MCDM2 = FUCA
	Position	Value	Position	Value
O-1	10	0.5335	11	8.85
O-2	7	0.5596	9	8.15
O-3	9	0.5375	5	6.75
O-4	6	0.5796	6	6.80
O-5	2	0.6069	2	5.50

Notes: MCDM—multicriteria decision making. Source: own production, 2023.

shows the similarity of the FUCA and TOPSIS results in the five optimistic scenarios of the pallet supply chain analyzed.

The scenario with the greatest agreement in both methods was the optimistic 5, where TOPSIS offered 0.6069 as the general value, with ranking in second place. Likewise, FUCA offered 5.5 as the general value and was also classified in second place. Thus, optimistic 5 was the best scenario according to both MCDM methods, taking into account the variable and parameter analyses selected in the dynamic model.

4. Discussion

Developing DS models using scenario simulation and analyses evaluated complex systems in a determined time horizon. The decisions for the interested parties should be highly relevant, considering sustainability as the focus of decisions. In this sense, developing these proposals for the pallet manufacturing company generated quantitative information (social, economic, and environmental data) that has been processed in different scenarios and placed in a graphical interface to facilitate parameter input and modification. Thus, the policies under which the organization would be operating within a determined time were considered.

Discussions of results stem from other empirical studies where most of the DS methodology stages have been implemented.

The merit of the DS model consisted of forming efficient complex feedback mechanisms integrating parameter changes from small to large that were by chance (fortuitous) or continuous. The variation produced when the control variables did not depend linearly on others emerged in the feedback mechanism due to the presence of non-linear relationships [35]. In the same manner, Franco [36] mentioned that no official markers, methods, or tools were available to support and measure enterprise transition from a linear to another circular system.

Using the tools employed in a development project proposal where process flow diagrams were used, Navarro et al. [37] set up models to develop an operational concept of an Internet of Things (IoT) in the palletized distribution supply chain and generated two contributions: (1) the first concept of operations that described how the proposed IoT system was useful and boosted efficiency improvements in the process of designing packing; (2) the second one was the definition of the requirements, using semantics for expanded sequence diagrams and the signal elements of the System Modeling Language (SysML) in the True Model-Based Requirements (TMBR) approach.

Likewise, Ren et al. [38] used simulators for decision making, as the one used in this project, with Stella^® Architect, version 3.3, Isee Systems Inc., Lebanon, NH, USA. In their proposal, the authors showed that their work dealt mainly with how to help pallet managers select a specific type of pallet from the cost perspective of the supply chain. AnyLogic version 8.3, The Anylogic Company, Oakbrook Terrace, IL, USA was used to simulate the functioning of the pallet management systems.

On the other hand, Balakirsky [39] utilized USARSim^®, version UT3VB1.5, SourceForge Company, San Diego, CA, USA, to explore the role of the simulation to compare to what point the automation metrics could calibrate the quality of a pallet; the simulator allowed studying the interconnection between hidden internal boxes and parameters that could not be determined by mere statistics. Likewise, Guan et al. [40] used simulation to evaluate the shipment of assembly line components in a digital factory based on the process analysis of the pallet dynamic demands.

In the pallet company simulation model, Stella^® Architect was used to simulate the scenarios and, from there, selection was made with the multicriteria analysis. The simulators found in [41] concerned the economic analysis of the promising wood products in the forest sector of Letonia. The objective was to analyze three products: bio-oil, lyocell, and xylene. Currently, none of the products are made in Letonia. The system dynamics model was used with the Powersim Studio 8 software to determine which of the products had greater added value and which was more feasible for use.

The use of the model validation techniques to measure the reliability of the proposed model was based on the works of Barlas and Carpenter [10]. These authors established that, since the model was assumed from a real system, it could be false or true. When the adequate algorithms were used and compared with the empirical study, its validity was automatically revealed as false or true. Thus, the result depended on the formal precision of the assumed model. Similarly, Barlas [25] mentioned that, for the model behavior validity, the general validation of the simulation was an important part. The challenge consisted of designing novel quantitative tests appropriate for evaluating the behavior of system dynamics given by the behavior of the composition patterns instead of the individual data points. One of the proposals to validate the model was the test of the relative error.

In this sense, for the pallet project, the relative error test allowed including the results from the real data and assuming the proposed model. The results obtained allowed assuming that the model was close to reality starting from the compliance of the criterium established, considering the result of the simulation data.

The use of the methods that considered the analysis of the most relevant ones were important in developing the model scenarios. For this purpose, FUCA and TOPSIS multicriteria analyses were used, as in the works of Duc [42], who demonstrated that the FUCA method could be used in mechanical processing for multicriteria decision making that did not require data standardization. To select the best scenarios from the simulation and sensitivity analysis, eight decision variables were considered, which competed based on the maximum and minimum optimization criteria according to Bachar et al. [26]. These authors used a traditional technique to examine the global optimization of the profit and decision function variables in an energy consumption project of an intelligent manufacturing company, where the demand was considered flexible. In the same manner, in another study in demand analysis, Raj et al. [27] developed a sustainable ecological production model taking into account the variable demand. These authors found that controlling the fluctuating demand and rebuilding imperfect products made the model production profitable. Soumya et al. [28] demonstrated the application of the proposed solution through numerical and graphical sensitivity analyses.

In the same manner, Baydaş and Pamucar [43] applied seven multicriteria methods to evaluate the performance of companies in the financial sector, demonstrating that FUCA was the most simple methodology compared with the others they used (PROMETHEE, FUCA, TOPSIS, SAW, CODAS, COPRAS, and MOORA). On the other hand, Narendra et al. [44] developed a model applying system dynamics to describe the wood biomass production potential starting from rehabilitating degraded lands. The result showed that all scenarios achieved reducing the degraded land area by 16%. The energetic wood plantations could reduce the numbers of unemployment by one half of the simulated amount while applying a moderate, optimistic, or very optimist scenario; the number of unemployment would only remain one quarter by 2040. The optimistic scenario was considered applied in the degraded land rehabilitation.

Finally, the graphical user interface (GUI)-supported software was usually large and complex and difficult to implement, debug, and modify, as established by Myers [45]. This software generated the communication between decision makers and the technological solution (GUI), allowing the use of graphical elements, as well as a table of data that allowed having the information in the time line established according to the policies and rules of the organization. It is important to highlight that, for the organization under study, GUI was supported by mathematical models that generated each of the variable behaviors starting from the defined parameters according to the interest of the organization.

This solution considered elements of sustainability, where SD was used as an analysis tool [46,47,48] and scenario analysis was used for data-driven decision making [49,50,51]. The benefits for the company and decision makers had theoretical and methodological contributions as a basis. From the theoretical perspective, different authors’ contributions were used, using the system dynamics approach based on optimization with diverse mathematical algorithms to manage inventories from products made and delivered [52].

5. Conclusions

The use of DS in the projects related with the supply chain projects allowed evaluating the methodology potential in the organization environment dedicated to the pallet production conditioned to the important demands for mega companies of the Southern Sonora region. This analysis allowed the pallet manufacturing company to have and include critical elements in providing wood inputs, pallet production, and the distribution process in compliance with the quality and time demanded.

The most relevant conclusions in the present research study were having the support of a system dynamics model for decision making concentrated in the graphical user interface, which made it more accessible to the persons working, without necessarily having knowledge of the system. The model considered 31 variables and 8 parameters that were included in the different equations.

On the other hand, developing the scenarios helped the company to observe a time line of the production and inventory behavior. In this manner, they could satisfy the demands of the main client and make the necessary preparations to comply with each one of the (max/mini) criteria of the eight variables of major relevance associated with the model.

Likewise, the support of the proposed procedure was based on the real and theoretical empirical studies that provided assurance to future decisions, such as the scenario with the greatest agreement in both methods, e.g., the optimistic 5 where TOPSIS offered 0.6069 as the general value, with ranking in second place And, in the same manner, where FUCA offered 5.5. as the general value, with ranking in second place.

The previous data were provided by the company for model construction. Thus, by applying the test of the relative error percentage and comparing it with reality, the result had 3.4% of relative error against the 5% allowed, which supposed that the model adhered to reality.

On the other hand, the academic environment allowed promoting real cases for students and academics to include as part of the curriculum courses in teaching system dynamics methodology.

Future work to be performed should include variables that allow evaluating alternatives of a more robust circular economy in the dynamic model to take advantage of the rejected pallet and wood waste, which in time generates huge inventories that may be revalued to generate income for the organization.