Integrating Multi-Dimensional Value Stream Mapping and Multi-Objective Optimization for Dynamic WIP Control in Discrete Manufacturing

Abstract

Discrete manufacturing environments face increasing challenges in managing work-in-process (WIP) inventory due to growing product customization and demand volatility. While Value Stream Mapping (VSM) has been widely used for process improvement, traditional approaches lack the ability to dynamically control WIP levels while optimizing multiple performance dimensions simultaneously. This research addresses this gap by developing an integrated framework that synergizes Multi-Dimensional Value Stream Mapping (MD-VSM) with multi-objective optimization, functioning as a specialized digital twin for dynamic WIP control. The framework employs a four-layer architecture that connects real-time data collection, multi-dimensional modeling, dynamic WIP monitoring, and execution control through closed-loop feedback mechanisms. A mixed-integer optimization model is used to balance time, cost, and quality objectives. Validation using a high-fidelity simulation, parameterized with real-world industrial data, demonstrates that the proposed approach yielded up to a 31% reduction in inventory costs while maintaining production throughput and showed a 42% faster recovery from equipment failures compared to traditional methods. Furthermore, a comprehensive sensitivity analysis confirms the framework’s robustness. The system demonstrated stable performance even when key operational parameters, such as WIP upper limits and buffer capacity coefficients, were varied by up to ±30%, underscoring its reliability for real-world deployment. These findings provide manufacturers with a validated methodology for enhancing operational efficiency and production flexibility, advancing the integration of lean principles with data-driven, digital twin-based control systems.

1. Introduction

Discrete manufacturing workshops constitute a critical component of modern industrial systems, with their internal logistics efficiency directly impacting overall operational performance. Manufacturing enterprises today face increasingly personalized and diverse customer demands, requiring them to ensure product quality and control production costs while continuously enhancing production flexibility and market responsiveness. In this context, the management of work-in-process (WIP) inventory significantly influences production line rhythm and resource utilization efficiency, ultimately affecting order delivery times and overall operational costs. The inherent characteristics of discrete manufacturing environments—small batch sizes, multiple product varieties, and complex processes—create constantly changing internal logistics systems that pose significant challenges to traditional workshop management methods.

The management of WIP, a key element in manufacturing operations, faces notable deficiencies in current practice. WIP level fluctuations significantly impact production efficiency, resource utilization, and quality control. Excessive WIP levels not only increase material accumulation and capital occupation but also elevate storage and handling costs while potentially increasing the risk of batch quality issues. Conversely, insufficient WIP levels may lead to production line stagnation and capacity waste, affecting order delivery schedules. For discrete manufacturing environments characterized by multi-variety, small-batch production, achieving dynamic WIP control supported by multi-dimensional data from Value Stream Mapping (VSM) would help internal logistics reach optimal balance across key indicators including time, cost, and quality.

Value Stream Mapping has emerged as a widely recognized lean tool for identifying waste and analyzing process bottlenecks. Rother and Shook (2003) [1] pioneered the use of VSM into lean production practices, establishing the theoretical foundation for value stream optimization. Since then, both academia and industry have conducted extensive research on further leveraging VSM in lean and sustainable production. Researchers have increasingly focused on incorporating environmental and social performance elements into traditional VSM analysis, while many practitioners have dedicated efforts to expanding VSM for more intuitive identification and assessment of environmental and social impacts in production processes, thereby obtaining more comprehensive improvement plans [2,3].

Recent developments have significantly expanded VSM’s application scope. Faulkner and Badurdeen (2014) [4] introduced the “Sustainable Value Stream Mapping (Sus-VSM)” concept, incorporating energy consumption, waste management, and social metrics into VSM to address environmental performance and social responsibility alongside lean principles. Vinodh et al. (2016) [5] integrated Life Cycle Assessment (LCA) with VSM to form an “LCA-integrated VSM” framework for evaluating carbon emissions, resource depletion, and other environmental impacts in manufacturing processes. Jamil et al. (2020) [3] systematized the implementation path of sustainable VSM based on the DMAIC cycle, emphasizing energy conservation, emission reduction, and environmental friendliness at each stage to form a continuously improving closed loop. Batwara et al. (2023) [6] summarized the potential of Value Stream Mapping coupled with Industry 4.0 technologies in sustainable manufacturing systems from a triple bottom line perspective, suggesting that in digitalized and intelligent contexts, VSM can not only present material, information, and value flows but also provide a basis for real-time monitoring and optimization of in-plant carbon footprints and resource utilization efficiency. This trend is confirmed by recent research, which includes systematic literature reviews that have produced conceptual frameworks for VSM in the Industry 4.0 era [7] and the development of “Intelligent VSM” models that utilize IoT for real-time monitoring and lead time reduction [8]. Further studies have explored how Industry 4.0 trends can accelerate traditional lean processes within global value chains by leveraging digital structures, and have highlighted the role of integrating specific cyber-physical systems and computer vision tools to optimize manufacturing performance and enhance economic output [9,10].

In the domain of WIP control, academia and industry have conducted in-depth discussions on effectively limiting and managing workshop WIP levels. Traditional pull control systems such as Kanban and CONWIP (constant work-in-process) are commonly used to constrain WIP levels in production systems, thereby shortening production cycles and improving overall efficiency [11]. However, with increasingly diverse manufacturing environments and fluctuating order demands, researchers have focused more attention on the performance of Kanban and CONWIP systems in complex scenarios involving multiple products, multiple processes, and random processing times [12,13]. For discrete manufacturing workshops with multi-product assembly or unbalanced production rhythms, researchers have proposed hybrid or improved production control systems such as Base-Stock Kanban-CONWIP (BK-CONWIP), Base-Stock-CONWIP (B-CONWIP), and multi-loop CONWIP to balance throughput, WIP, and delivery dates [11,14].

Multi-objective optimization research has made significant progress in discrete manufacturing and semiconductor manufacturing environments. This approach has been widely applied to balance throughput, WIP, delivery dates, costs, and sustainability factors such as energy consumption and carbon emissions [15,16]. To solve such multi-objective problems, researchers typically employ heuristic algorithms, metaheuristic algorithms, or hybrid methods combining simulation with metaheuristic algorithms to find pareto-optimal solutions among concurrent and conflicting objectives [17,18]). In production scheduling contexts, genetic algorithms (GAs) are commonly combined with other intelligent algorithms (such as Long Short-Term Memory networks, and ant colony algorithms) to simultaneously reduce workpiece flow time while controlling WIP levels or energy consumption [15,19]. In factory layout or logistics sectors, multi-objective evolutionary algorithms are used to comprehensively consider material handling costs, system throughput, WIP, resource utilization, and transportation conflict rates [20,21].

Despite these advances, a critical gap remains at the intersection of these fields. First, traditional VSM approaches are inherently static and lack the mechanisms for dynamic, real-time feedback required for modern production control. Second, existing WIP control strategies often rely on idealized assumptions and fail to holistically address the competing, multi-dimensional objectives of a complex manufacturing system (e.g., time, cost, and quality). Consequently, there is a clear need for an integrated, multi-objective decision-making framework capable of supporting dynamic WIP control in real-world, high-variability environments.

To address these challenges, this study proposes an integrated framework for dynamic WIP control that synergizes Multi-Dimensional Value Stream Mapping (MD-VSM)—an approach that extends traditional VSM to simultaneously map and analyze time, cost, and quality performance dimensions—with multi-objective optimization, functioning as a specialized digital twin, where a high-fidelity virtual model of the manufacturing system is created using discrete-event simulation techniques. By integrating real-time data streams from the factory floor, this digital twin enables a dynamic, closed-loop feedback system. It leverages machine learning algorithms for predictive analytics, allowing for proactive and adaptive decision-making that simultaneously balances the competing objectives of time, cost, and quality. The effectiveness and robustness of this framework are rigorously validated through extensive simulation experiments—including a comprehensive sensitivity analysis—which demonstrate its ability to significantly improve performance and resilience in complex manufacturing environments, with implications extending to other high-stakes sectors like healthcare manufacturing.

The remaining sections of this paper are structured as follows: Section 2 introduces the methodology, Section 3 describes the experimental design, Section 4 presents results and discussion, Section 5 outlines managerial implications, and Section 6 concludes the study.

2. Materials and Methods

2.1. Digital Twin Framework for Dynamic WIP Control

The underlying conceptual framework is a specialized digital twin (DT) designed for dynamic WIP control in discrete manufacturing [22]. A digital twin is a virtual representation of a physical object or process, used to analyze and simulate the behavior of its real-world counterpart to understand, predict, and optimize performance. To realize this concept, the framework’s virtual model is constructed as a high-fidelity, discrete-event simulation, accurately mirroring the complex interactions and stochastic nature of the workshop. Furthermore, the integration of artificial intelligence, particularly machine learning for predictive analytics, is central to the twin’s intelligence, enabling proactive control based on anticipated WIP fluctuations [23]. While the DT concept is established in areas like supply chain management, its application for integrating multi-dimensional performance metrics (time, cost, quality) with AI-driven, real-time WIP control at the workshop level remains an area for focused development. Recent studies have demonstrated the value of such integrated, data-driven frameworks in adjacent domains like supply chain management, where they connect with ERP systems to manage risks and enhance operational resilience [24], underscoring the practical relevance of the approach presented herein.

To operationalize this, the proposed MD-VSM framework is structured as a hierarchical digital twin architecture, as illustrated in Figure 1. This architecture consists of four interconnected layers that create a closed-loop system connecting the physical workshop with its virtual model: (1) Real-time Data Acquisition and Preprocessing, (2) Multi-dimensional Mapping, (3) Dynamic Monitoring and Control, and (4) Production Execution and Feedback. This structure embodies the core components of a modern digital twin—the physical entity, the simulation-based virtual model, and the data connection, as well as an AI-driven decision-making engine—to facilitate intelligent, closed-loop control.

The data acquisition layer acts as the link to the physical twin, collecting information from sensors, Manufacturing Execution Systems (MESs), and Enterprise Resource Planning (ERP) systems, which is then preprocessed for standardization. The multi-dimensional mapping layer constitutes the virtual model, creating a network of process nodes with metrics spanning time, cost, quality, and WIP dimensions. The dynamic monitoring and control layer embodies the twin’s analytical engine, employing threshold-based detection and predictive algorithms for real-time state assessment and optimization. Finally, the production execution layer provides the feedback loop, translating the twin’s decisions into operational instructions for the physical workshop.

Data collection integrates structural mapping of process nodes, temporal measurements of processing times and delays, and cost parameters across operations. The performance metrics framework evaluates manufacturing through indicators in four dimensions (Equation (1)):

$$P_{\mathrm{system}} = f\left(T, C, Q, W\right)$$

(1)

where T represents time-dimension metrics (cycle time, lead time), C denotes cost metrics (inventory holding, equipment utilization), Q captures quality metrics (yield rate, rework percentage), and W indicates WIP-related metrics (level, distribution, turnover). These metrics enable real-time assessment of control strategies and system performance optimization.

2.2. Mathematical Modeling of WIP Dynamics

The dynamic behavior of WIP in discrete manufacturing systems requires rigorous mathematical formulation to capture its temporal evolution and interdependencies with other performance dimensions. The foundation of our approach is a discrete-time WIP balance equation that tracks inventory fluctuations at each process node. For any workstation i ∈ M at time period t, the WIP balance is governed by

$$W_i(t+1)=W_i(t)+{\mathrm{In}}_i(t)-{\mathrm{out}}_i(t)$$

(2)

where W_i(t) represents the WIP level at workstation i during period t, while ${\mathrm{In}}_i(t)$ and ${\mathrm{out}}_i(t)$ denote material inflow and outflow rates, respectively. This balance equation accounts for various stochastic factors including upstream supply variability, transportation delays, processing time fluctuations, and quality-induced rework.

The multi-dimensional coupling mechanism establishes quantitative relationships between WIP dynamics and other key performance metrics. In the temporal dimension, system throughput rate λ is expressed as a function of WIP distribution and processing capabilities:

$$\lambda =f(\{W_i\},\{c_i\})$$

(3)

where W_i represents the collective WIP levels across all workstations and c_i captures workstation capacities. This function typically exhibits non-linear characteristics, with diminishing returns as WIP exceeds certain thresholds due to congestion effects. The cost dimension integrates multiple expenditure components affected by WIP fluctuations:

$$C_{\mathrm{WIP}}(t)=C_h{\displaystyle {\sum }_i{W}_i(t)}+C_t{\displaystyle {\sum }_i{\mathrm{In}}_i(t)}+C_s{\displaystyle {\sum }_i\max \{0,W_{\min ,i}-W_i(t)\}}$$

(4)

where C_h denotes unit inventory holding cost, C_t represents unit material transportation cost, and C_s signifies the stockout penalty coefficient. The quality dimension displays non-linear relationships with WIP levels, captured by the defect rate function:

$${\beta }_i(W_i(t))={\beta }_{0,i}+k_{1,i}\max \{0,W_i(t)-W_{\max ,i}\}+k_{2,i}\max \{0,W_{\min ,i}-W_i(t)\}$$

(5)

Here, β_0,i represents the baseline defect rate, while k_1,i and k_2,i quantify the quality impact coefficients for excessive WIP (above W_max,i) and insufficient WIP (below W_min,i), respectively.

These mathematical models collectively form a comprehensive optimization framework with the objective function:

$$\mathrm{Minimize}Z={\alpha }_1{T}_{\mathrm{total}}+{\alpha }_2{\displaystyle {\sum }_t{\displaystyle {\sum }_i{W}_i(t)+{\alpha }_3{\displaystyle {\sum }_t{\displaystyle {\sum }_i{\gamma }_i{\beta }_i(W_i(t))}}}}$$

(6)

The weighted coefficients α₁, α₂, and α₃ enable customized prioritization among competing objectives based on specific manufacturing contexts and strategic priorities. The term γ_i represents the unit cost associated with a defect at workstation i.

2.3. Dynamic WIP Control Strategy

The dynamic WIP control strategy integrates real-time monitoring with predictive capabilities to manage inventory fluctuations in discrete manufacturing environments. Our approach combines threshold-based detection, prediction-based feedforward mechanisms, and multi-objective optimization to achieve optimal performance across time, cost, and quality dimensions. The threshold-based real-time monitoring component establishes workstation-specific safety corridors that define acceptable operating ranges. These thresholds are determined by analyzing upstream supply capabilities, downstream demand patterns, workstation processing capacities, and quality variation risks. The monitoring system triggers appropriate control responses when WIP levels approach or exceed these boundaries: reducing upstream material release rates when WIP exceeds the upper threshold, increasing resource allocation when WIP falls below the lower threshold, and maintaining current parameters when operating within the safety corridor.

The prediction-based feedforward control mechanism enhances the system’s proactive capabilities by forecasting potential WIP fluctuations before they manifest as disruptions. This approach employs a rolling time horizon prediction model that leverages historical WIP patterns, equipment status data, quality trends, and order deadline information to anticipate future system states. For relatively stable processes, traditional time-series models (e.g., ARIMA) provide sufficient accuracy, while more complex workstations with significant variability benefit from deep learning approaches (e.g., LSTM networks). The prediction module continuously evaluates potential WIP trajectory deviations and preemptively adjusts control parameters to maintain system stability, significantly reducing the impact of disturbances on manufacturing performance. This proactive adjustment mechanism represents a substantial improvement over reactive systems that respond only after deviations occur.

The multi-objective optimization model forms the decision-making core of the control strategy, balancing competing objectives through a comprehensive mathematical framework. The model incorporates a modified objective function that integrates equipment utilization, inventory efficiency, and quality performance:

$$\min Z={\displaystyle \sum _{i\in M}{\displaystyle \sum _{t\in T}\left[{\omega }_1{\left(1-\frac{{ \mathrm{Out} }_i(t)}{C_i}\right)}^2+{\omega }_2{\left(\frac{W_i(t)}{W_{\mathrm{target} ,i}}-1\right)}^2+{\omega }_3{\beta }_i\left(W_i(t)\right)\right]}}$$

(7)

Subject to equipment capacity constraints:

$$Ou{t}_i(t)\le \min \left\{C_i,W_i(t)\right\},\forall i,t$$

(8)

Process sequence constraints:

$$I{n}_{i+1}(t)=Ou{t}_i(t-\Delta ),\forall i,t$$

(9)

And WIP boundary constraints:

$$W_{\min ,i}\le W_i(t)\le W_{\max ,i},\forall i,t$$

(10)

where ω₁, ω₂, and ω₃ are dynamic weighting factors, and W_target,i represents the ideal WIP level for workstation i. This quadratic formulation penalizes both underutilization and overutilization of resources while maintaining WIP levels close to target values. The solution approach employs mixed-integer programming for small-scale systems and customized heuristic algorithms for larger manufacturing environments, with adaptation mechanisms that dynamically adjust weighting coefficients based on production priorities and real-time conditions.

Balancing the objectives in Equation (7) requires navigating complex trade-offs, particularly under stochastic conditions such as equipment failures. For instance, aggressively minimizing WIP to reduce cost (a high ω₂) might deplete safety buffers, making the system vulnerable to downstream starvation during an unexpected failure and thus compromising throughput (related to ω₁). Conversely, maximizing equipment utilization could lead to excessive WIP, increasing costs and potentially degrading quality (a high ω₃) due to prolonged storage. Traditional control systems like Kanban or CONWIP, which rely on static parameters, inherently struggle to manage these dynamic trade-offs. The superiority of the proposed framework lies in its adaptive nature. For large-scale implementations, this adaptability can be further enhanced by exploring quantum-inspired optimization algorithms [25], known for their potential to efficiently navigate vast and complex solution spaces. Furthermore, advanced AI heuristics, such as using neural networks for real-time tuning of the weighting coefficients (ω₁, ω₂, ω₃) [26], could offer even greater responsiveness, solidifying the model’s scalability and performance advantages in large, complex discrete manufacturing environments.

It is important to note the practical context for this solution approach. While the mixed-integer programming model can yield optimal solutions, its computation time grows with the scale of the problem (number of processes and length of the time horizon). Therefore, its direct application is best suited for small-to-medium scale systems or for offline strategic planning where longer computation times are acceptable. For large-scale environments requiring near-real-time decisions, the framework is designed to integrate heuristic or metaheuristic algorithms (e.g., GA or Simulated Annealing) that can generate high-quality solutions within shorter timeframes. The system’s robustness under high-variance conditions is achieved by implementing the optimization in a rolling-horizon framework. By repeatedly re-solving the model at short control cycles (e.g., every 5 min) using the latest system data, the strategy dynamically adapts to disturbances rather than relying on the convergence of a single, long-term plan.

3. Experimental Design

3.1. Simulation Platform Development

To validate the proposed WIP control strategy, a high-fidelity, discrete-event simulation platform was developed to create a dynamic digital replica of a realistic manufacturing environment. The platform was implemented using Python 3.8 (Python Software Foundation, Wilmington, DE, USA) with the SimPy library for dynamic modeling of production systems. The simulation architecture comprises five core functional modules: process modeling, material flow, dynamic events, multi-dimensional analysis, and control strategy. These modules interact through standardized interfaces, enabling flexible configuration and systematic evaluation of various control approaches.

The process modeling module implements a class inheritance structure to represent the 38 manufacturing processes from a 138 Ah power battery production line. Each process object encapsulates both generic attributes (equipment ID, process name) in the base class, while process-specific parameters (such as equipment capacity, maintenance schedules) and behaviors (such as quality fluctuation patterns) are implemented through derived classes. Each process object contains production capacity functions, maintenance time calculation functions, and quality fluctuation generation functions that accurately simulate the dynamic characteristics of actual processes.

The material flow module manages WIP transfers between processes based on discrete-event simulation principles, using event queues to manage material movement. To enhance simulation accuracy, this module integrates actual material handling delay data from the production line, with parameters for logistical times (e.g., loading/unloading) justified by statistical analysis of historical records. It also implements dynamic batch size adjustment capabilities. Through a customized routing algorithm, the module effectively handles complex material flow scenarios including parallel processes and cross-process transfers. The First-In-First-Out (FIFO) principle governs material transfers between processes, with buffer capacity for each process set to its 2 h production capacity.

The dynamic event module employs stochastic process theory to construct equipment failure and order variation models. Equipment failures follow a Weibull distribution (α = 150 h, β = 1.8), chosen for its proven effectiveness in reliability engineering for modeling the life cycle of industrial components. The distribution’s parameters were obtained through maximum likelihood estimation from one year of the production line’s historical failure data, ensuring the model’s fidelity. Emergency order insertions are generated according to a Poisson distribution (λ = 0.5 per shift), which is well suited for modeling random, independent events occurring over a constant average rate. Order sizes are simulated using Monte Carlo methods based on historical order patterns. The module also includes an event priority management mechanism to ensure timely response to critical events.

The multi-dimensional analysis module establishes a comprehensive performance evaluation system. Through a data subscription mechanism, it collects and calculates key indicators in real time, including time-dimension production cycles, cost dimension inventory occupation, and quality-dimension yield rates. To improve computational efficiency, the module employs an incremental update algorithm that recalculates only those metrics affected by changes. The module also provides data persistence interfaces to support storage and retrospective analysis of experimental data.

The control strategy module implements the MD-VSM-based dynamic WIP control algorithms. Using a layered design approach, the control logic is divided into decision, execution, and monitoring layers. The decision layer calculates optimal control parameters based on multi-dimensional data provided by MD-VSM; the execution layer transforms control commands into specific material release and equipment scheduling actions; and the monitoring layer tracks control effects in real time and triggers necessary strategy adjustments. Through loose coupling between modules, the platform offers excellent expandability and can easily integrate new control strategies for comparative validation.

The simulation system’s key parameters were configured based on high-fidelity operational data from a 138 Ah power battery manufacturer, our industrial partner, ensuring the model’s practical relevance. The data, sourced from the company’s Manufacturing Execution System (MES) and Enterprise Resource Planning (ERP) systems for the 2023 operational year, provides a robust foundation for the model.

Table 1. Key parameter configuration of the simulation system.

Parameter Category	Parameter Item	Value Range	Distribution Characteristics
Work-in-Process Cost	Electrode Preparation	42–58 CNY/unit-day	Uniform
	Cell Assembly	85–102 CNY/unit-day	Uniform
	Formation and Aging Stage	138–162 CNY/unit-day	Uniform
Equipment Cost	Coating Equipment	4200 CNY/h	Fixed
	Winding Equipment	3800 CNY/h	Fixed
	Formation and Aging	5600 CNY/h	Fixed
	Other Process	1200–2800 CNY/h	Classified by Equipment Value
Labor Cost	Skilled Operators	32 CNY/h	Fixed
	Maintenance Staff	58 CNY/h	Fixed
	Quality Inspection	45 CNY/h	Fixed
Energy Cost	Electrode Preparation	680 CNY/h	Fixed
	Cell Assembly	420 CNY/h	Fixed
	Formation and Aging	2400 CNY/h	Fixed
Logistics Parameters	AGV Running Speed	1.2 m/s	Fixed
	Process Distance	8–45 m	Layout-based
	Loading/Unloading Time	45–75 s/operation	Normal (μ = 60, σ = 5)
Quality Parameters	Coating Fluctuation	±2.5%	Normal (μ = 0, σ = 0.8%)
	Winding Fluctuation	±1.8%	Normal (μ = 0, σ = 0.6%)
	Welding Precision	±1.2%	Normal (μ = 0, σ = 0.4%)
	Capacity Consistency	±2.0%	Normal (μ = 0, σ = 0.7%)

Notes: (1) Equipment costs include depreciation, maintenance, and operations; (2) process distances are based on actual plant layout; (3) quality fluctuation parameters were derived from six months of statistical analysis.

presents the key parameter configurations across multiple categories, including WIP costs, equipment costs, labor costs, energy costs, logistics parameters, and quality parameters. The WIP costs vary by production stage (42–58 yuan/unit-day for electrode preparation, 85–102 yuan/unit-day for cell assembly, and 138–162 yuan/unit-day for formation stages), reflecting the increasing value addition through the production process. Equipment costs range from 1200 to 5600 yuan/h depending on equipment type, with formation equipment being the most expensive. Logistics parameters include AGV speed (1.2 m/s), inter-process distances (8–45 m), and material loading/unloading times following a normal distribution (μ = 60 s, σ = 5 s). Quality parameters model process-specific fluctuations, with coating and winding processes showing the highest variability (±2.5% and ±1.8%, respectively).

Table 2. Representative process parameters by production stage.

Stage	Process	Quality	Cost	Maintenance	Buffer	Distance
Electrode Preparation	Cathode Coating	0.993/0.007/0	4200/32/680	24 h/30 min	2982	28 m
	Anode Coating	0.995/0.006/0	4200/32/680	24 h/30 min	3784	25 m
	Cathode Slitting	0.989/0.007/0.85	2600/32/380	16 h/25 min	2416	15 m
Cell Assembly	Winding	0.950/0.012/0.94	3800/45/480	8 h/20 min	2346	32 m
	Ultrasonic Welding	0.985/0.008/0.75	2600/45/380	8 h/25 min	2174	12 m
	Tab Welding	0.985/0.008/0.72	2600/45/380	8 h/25 min	2174	12 m
Formation	Vacuum Baking	0.995/0.003/0	3400/32/2200	24 h/40 min	2468	45 m
	Formation	0.996/0.003/1.00	5600/52/2400	24 h/40 min	2248	38 m
	Aging	0.998/0.002/0	4200/32/2200	24 h/40 min	2044	40 m
Packaging	Capacity Testing	0.997/0.002/0	4800/45/580	24 h/40 min	2088	35 m
	DCR Testing	0.995/0.003/0	3200/45/420	16 h/30 min	2254	22 m
	Final Sorting	0.999/0.001/0	1600/45/180	16 h/20 min	-	-

Note: Quality parameters show (base yield rate/fluctuation standard deviation/rework rate); cost parameters show (equipment/labor/energy) in yuan/h; maintenance parameters show (interval time/duration); buffer capacity based on 2 h production capacity; distance shows material flow distance to next process in meters.

provides a condensed view of the process parameters for representative processes across the four main production segments. The complete configuration of all 38 processes is available in Supplementary Materials.

This simulation platform, with its detailed, data-driven process parameterization and modular architecture, thus provides a robust digital twin environment for rigorously testing and validating the proposed WIP control strategies under various operating conditions, allowing for systematic evaluation of performance across time, cost, and quality dimensions.

3.2. Scenario Design and Performance Metrics

Three typical scenarios were designed to validate the effectiveness of the proposed control strategy:

• Baseline scenario: Configured according to actual production line settings with initial WIP levels at 100% of theoretical optimal values.
• High-WIP scenario: Initial WIP levels at 150% of theoretical optimal values to test the strategy’s performance under inventory pressure.
• Low-WIP scenario: Initial WIP levels at 50% of theoretical optimal values to verify the strategy’s capability to handle material shortages.

Each simulation ran for 30 days, with the first 5 days designated as a warm-up period. The experimental parameters are shown in

Table 3. Experimental parameters.

Parameter Category	Parameter Item	Value	Description
Production	Daily planned output	21,780 units	Actual capacity level
	Batch size	120 units	Standard production batch
	Changeover time	90–120 min	Based on actual process data
Quality	First-pass yield target	82.85%	Actual production line level
	Rework rate limit	15%	Quality control requirement
	Quality inspection cycle	2 h	Standard inspection interval
Equipment	Failure interval	Weibull (α = 150, β = 1.8)	Fitted from historical data
	Repair time	LogNormal (μ = 4.2, σ = 0.8)	Unit: hours
	Planned maintenance	30–40 min/shift	Based on process requirements
Control	WIP upper limit coefficient	1.2	Relative to theoretical value
	WIP lower limit coefficient	0.8	Relative to theoretical value
	Control cycle	5 min	Feedback adjustment interval

.

A multi-dimensional performance evaluation system was constructed to analyze the proposed strategy from time, cost, and quality perspectives. To comprehensively assess the dynamic response characteristics of the control strategy, this study compared system performance across three typical scenarios (baseline, high-WIP, and low-WIP). The analysis focuses specifically on equipment failure events, which represent one of the most significant disruptions in discrete manufacturing environments.

The time dimension focuses on production system operational efficiency, including average production cycle time (h), process waiting time (min), and equipment utilization rate (%). The production cycle reflects the total time from raw material input to finished product output; process waiting time reveals material accumulation between processes; and equipment utilization rate reflects the production line’s capacity utilization level.

The cost dimension evaluates production operation economic performance, with core indicators including WIP inventory cost (yuan/unit), idle equipment cost (yuan/h), and labor overtime cost (yuan/shift). WIP inventory cost is calculated based on the actual occupation time of work-in-process and unit product value; idle equipment cost considers fixed expenses such as equipment depreciation and energy consumption; labor overtime cost reflects the human resource allocation costs caused by capacity fluctuations.

The quality dimension focuses on product manufacturing process reliability, including comprehensive first-pass yield (%), batch qualification rate (%), and rework ratio (%). Comprehensive first-pass yield reflects the product pass-through rate; batch qualification rate reflects the stability of batch production; and rework ratio reflects the ability to handle quality issues. These indicators are calculated based on real-time data from the production line’s MES system.

To ensure statistical validity of the experimental results, each scenario was replicated 30 times, and data was analyzed using a 95% confidence interval. This method effectively reduces the influence of random factors and improves the reliability of experimental conclusions. Additionally, data from the system warm-up period (first 5 days) was excluded from the calculations to obtain more accurate steady-state performance assessment results.

4. Results and Discussion

4.1. Baseline Performance Analysis

To conduct an in-depth analysis of the production system’s operational state under the baseline scenario, this study provides a systematic evaluation of the simulation results across multiple dimensions.

Figure 2 summarizes the system’s primary performance metrics across the dimensions of time, cost, and quality. In the time dimension, the average production cycle was 2.7 h, with process waiting times controlled at 10.2 min, indicating a relatively smooth production flow. From a cost perspective, WIP inventory cost (785,873 yuan) was the predominant expense, far exceeding equipment idle cost (74,466 yuan) and labor cost (5240 yuan). This cost structure, with a ratio of approximately 150:14:1, underscores the critical role of WIP management in cost control. In the quality dimension, the system demonstrated excellent stability, with a first-pass yield of 98.13%, a batch qualification rate of 94.67%, and a rework rate of 9.80%. The vast majority of processes achieved quality rates above 98%, with slightly lower performance in more complex operations like Winding (95.0%) and Wrapping (96.9%).

The distribution of WIP levels by process (Figure 3) reveals a significant imbalance. WIP levels in the electrode preparation stage were generally high, with particularly severe WIP accumulation in processes such as Gravure Stirring (372 units), Cathode Die Cutting and Slitting (358 units), and Anode Coating (378 units). Conversely, WIP levels in the Cell Assembly and Packaging and Inspection stages were relatively low, with most processes maintaining levels between 200 and 250 units. This distribution pattern indicates a significant accumulation of materials at the front end of the production line.

Process utilization rates (Figure 4) exhibit a distribution pattern that is highly correlated with the specific characteristics of the processes. Stirring processes (Gravure Stirring: 98.4%, Ceramic Stirring: 99.1%, Cathode Stirring: 98.4%, Anode Stirring: 98.5%), owing to their batch-processing nature and longer required processing times, maintained high equipment utilization rates. Likewise, critical long-duration processes such as Vacuum Baking (99.3%), High-Temp Soaking (96.8%), and High-Temp Aging (98.8%) also sustained high utilization, which reflects the rational allocation of capacity to these critical processes in the production plan. In contrast, inspection processes like X-ray (3.1%) and Matching (1.6%), along with certain assembly operations like Tab Welding (5.1%), exhibited relatively low utilization rates. This is primarily because these operations have short processing times and high efficiency, allowing them to complete their tasks quickly with the current capacity configuration. This utilization distribution model reflects a design philosophy where the distinct characteristics of each process were carefully considered. By incorporating appropriate capacity redundancy, the design ensures the stability and flexibility of the production flow, mitigating the risk of a full line stoppage caused by individual process failures. This differentiated utilization pattern is a manifestation of lean manufacturing principles: It ensures the efficient operation of critical processes while reserving the necessary elastic capacity in non-bottleneck processes. This elasticity is crucial for responding to various uncertainties in the production process.

4.2. Dynamic Event Response Analysis

To comprehensively evaluate the dynamic response characteristics of the proposed control strategy, this study compared system performance across three typical scenarios: baseline, high-WIP, and low-WIP. This section focuses on analyzing the system’s response to equipment failure events, providing valuable insights into the control strategy’s effectiveness in managing manufacturing disturbances. The comparative results are presented across several figures: Figure 5 displays the overall performance in terms of time, cost, and quality; Figure 6 details the WIP levels for each process; and Figure 7 illustrates the process-level utilization and quality rates.

The failure history records show that a total of 28 failure events occurred in the baseline scenario, including 1 critical failure, 12 general failures, and 15 temporary failures. The average duration for each failure category was 426 min, 94 min, and 23 min, respectively, closely matching the statistical characteristics of actual production line failures. During failure events, the system demonstrated effective dynamic adjustment capabilities.

When the coating machine (a critical process) experienced a major repair failure, the WIP control strategy responded promptly: First, it reduced the production pace of upstream mixing processes and decreased their equipment utilization from 0.97 to 0.52, which effectively prevented material accumulation. Simultaneously, the system appropriately increased the capacity utilization of downstream calendering processes (from 0.28 to 0.32) to accelerate consumption of existing work-in-process. Through this coordinated control mechanism, the system maintained batch qualification rates above 95% during the failure period, while keeping WIP levels within safe ranges across all processes. Notably, the production line returned to normal operating conditions within 30 min after failure recovery, demonstrating excellent self-healing capabilities.

For general and temporary failures, the strategy primarily employed localized adjustments. For example, during an 85 min die cutting equipment adjustment failure, the system only fine-tuned parameters for 2–3 adjacent processes without causing significant fluctuations across the entire production line. Analysis of failure response data across all scenarios revealed that the proposed dynamic WIP control strategy exhibited strong robustness under disturbances of different types and magnitudes. The strategy could promptly identify abnormalities and implement appropriate compensation measures, effectively maintaining production system stability. This multi-dimensional, data-driven dynamic control mechanism demonstrated superior adaptability and reliability compared to traditional fixed-parameter control methods.

4.3. Comparative Analysis of Control Strategies

The comparative analysis across the three scenarios (baseline, high-WIP, and low-WIP) provides valuable insights into the performance characteristics of the proposed control strategy under different operating conditions. Figure 5 illustrates key performance indicators across all scenarios, revealing several significant patterns. From a temporal perspective, production cycle times remain relatively stable across all scenarios (2.8 ± 0.1 h), demonstrating the control strategy’s ability to maintain consistent throughput despite varying initial WIP levels. However, process waiting times exhibit marked differences, with the high-WIP scenario showing 42% longer waiting times compared to the baseline, while the low-WIP scenario reduces waiting times by 26%. Equipment utilization rates remain consistent for bottleneck processes across all scenarios, indicating the strategy’s effectiveness in prioritizing critical resources.

The cost dimension reveals the strategy’s economic impact, with the high-WIP scenario incurring 38% higher inventory costs than the baseline, while the low-WIP scenario achieves a 31% cost reduction. Notably, the control strategy successfully reduces the high-WIP scenario’s inventory levels toward optimal values over time, demonstrating effective inventory correction capabilities. The inventory reduction rate averages 4.2% per day, suggesting that excess inventory can be normalized within approximately 12 days. In the low-WIP scenario, the strategy gradually rebuilds inventory at critical buffer points while maintaining lean operation elsewhere, optimizing the cost-service level trade-off.

Quality metrics demonstrate the strategy’s robustness, maintaining similar first-pass yield rates across all scenarios (82.5 ± 0.7%). This stability is particularly noteworthy in the low-WIP scenario, where reduced buffers might typically increase quality risks. The control strategy achieves this by dynamically adjusting process parameters based on real-time WIP conditions, revealing a sophisticated quality-awareness mechanism. Batch qualification rates show slight variations (87.3%, 86.1%, and 88.5% for baseline, high-WIP, and low-WIP, respectively), with the high-WIP scenario experiencing marginally lower rates due to increased handling and storage issues.

The strategy exhibits strong robustness against production disturbances across all scenarios. When facing equipment failures, the high-WIP scenario leverages its larger buffers to maintain production continuity but experiences longer recovery times after disturbance resolution. Conversely, the low-WIP scenario shows quicker detection of abnormalities and faster system recovery, though with higher sensitivity to disturbance magnitude. Recovery time analysis reveals that the proposed strategy reduces system restoration time by 42% compared to traditional fixed-parameter control methods, demonstrating superior adaptability to dynamic manufacturing conditions.

The multi-objective trade-off analysis indicates that the proposed strategy effectively balances competing objectives by dynamically adjusting control parameters. In the high-WIP scenario, the strategy gradually shifts priority from throughput maintenance to inventory reduction once production stability is assured. In the low-WIP scenario, it initially emphasizes rebuilding critical buffers before transitioning to throughput optimization. This adaptive prioritization mechanism represents a significant advancement over traditional WIP control approaches that typically employ fixed-parameter settings. By continuously rebalancing objectives based on real-time system state, the strategy achieves pareto-optimal operating points that adapt to changing production conditions.

4.4. Sensitivity Analysis

To evaluate the robustness of the proposed MD-VSM framework and validate its practical applicability, we conducted a comprehensive sensitivity analysis examining how parameter variations affect system performance. This analysis provides crucial insights for practitioners implementing the framework in different manufacturing contexts.

Nine key parameters were selected for analysis: WIP cost multiplier, WIP upper limit coefficient, buffer capacity coefficient, multi-objective weight factors (α₁, α₂, α₃), control cycle time, quality variation multiplier, and WIP lower limit coefficient. Each parameter was systematically varied to assess its impact on three primary performance metrics: average production cycle time, total cost, and first-pass yield rate.

Figure 8 presents the tornado diagram illustrating the relative impact of each parameter on total cost. The analysis reveals a clear hierarchy of parameter influence: WIP cost multiplier exhibits the most significant impact with a cost range of 629,817 to 1,101,341 yuan (54.5% variation), followed by WIP upper limit (117,881 yuan impact, 13.6% variation) and buffer capacity (113,413 yuan impact, 13.1% variation). The multi-objective weight factors show moderate influence, with α₃ causing 10.7% variation and α₁ causing 7.6% variation. Notably, the WIP lower limit coefficient shows zero impact on total cost, though it significantly affects other performance dimensions as revealed in the detailed analysis.

The single-factor sensitivity curves (Figure 9) provide detailed insights into parameter behavior. For the WIP upper limit coefficient, total cost increases linearly from 806,639 to 924,519 yuan as the coefficient varies from 0.9 to 1.5, representing a 14.6% cost increase. Simultaneously, cycle time increases modestly from 156.8 to 164.8 min (5.1% increase), while first-pass yield remains constant at 98.13%. This pattern confirms that excess WIP primarily impacts cost without providing quality benefits, while having a minor negative effect on production flow.

The WIP lower limit coefficient demonstrates a contrasting pattern. While total cost remains unchanged at 865,579 yuan across all tested values (0.5 to 1.0), waiting time shows significant sensitivity, decreasing from 12.1 to 8.9 min as the coefficient increases. This 26.4% reduction in waiting time highlights the parameter’s critical role in maintaining production flow stability. Cycle time also decreases from 166.8 to 156.8 min (5.99% reduction), confirming that adequate buffer inventory is essential for smooth operations.

Control cycle analysis reveals important operational trade-offs. As the cycle increases from 1 to 10 min, total cost rises from 854,084 to 879,948 yuan (3.0% increase), while cycle time extends from 154.4 to 168.8 min (9.3% increase). The relatively small cost impact suggests that longer control cycles can be tolerated from a cost perspective, but the significant cycle time deterioration indicates potential responsiveness issues during disturbances.

Quality variation presents a unique pattern where cost impact is minimal (393 yuan range, 0.05% variation), but quality metrics show substantial sensitivity. As the quality variation multiplier increases from 0.5 to 1.5, first-pass yield decreases from 100% to 93.22%, a significant 6.78 percentage point decline. This demonstrates the framework’s cost resilience to quality fluctuations while accurately reflecting their impact on yield metrics.

Parameter interaction analysis revealed significant dependencies between key control parameters. The strongest interaction occurs between WIP upper limit and control cycle (10.4% combined effect on total cost), followed by the interaction between WIP upper and lower limits (9.1%). These interactions suggest that coordinated parameter adjustment is more effective than independent tuning. The relatively weak interactions involving quality and cost parameters indicate these dimensions can be managed independently.

To assess system robustness under uncertainty, we performed Monte Carlo simulation with 100 iterations, assuming ±10% normally distributed variations in all parameters simultaneously. The results, presented in Figure 10, demonstrate excellent stability across most performance metrics. Cycle time shows remarkable consistency with a coefficient of variation (CV) of only 1.7% and a 95% confidence interval of [156.04, 166.41] minutes. Total cost exhibits moderate variability (CV = 8.9%) with a mean of 874,827 yuan and 95% CI of [728,580, 1,023,852] yuan. Quality metrics maintain tight distributions with CVs of 1.1% and 0.9% for first-pass yield and batch yield, respectively.

The analysis of specific parameter variations provides actionable insights. A 25% increase in WIP upper limit (from 1.2 to 1.5) results in a 6.8% cost increase and 2.5% cycle time increase, suggesting diminishing returns from excessive inventory. The WIP cost multiplier shows perfectly linear behavior with ±30% parameter changes resulting in exactly ±27.2% cost changes, confirming the direct pass-through of inventory holding costs. Buffer capacity demonstrates similar linear behavior with ±30% changes yielding ±6.6% cost impacts.

Based on these findings, we provide the following implementation guidelines. First, WIP cost estimation accuracy is paramount given its dominant 54.5% influence on total system cost. Organizations should invest in precise activity-based costing for inventory holding to ensure optimal control decisions. Second, WIP upper limit should be set conservatively between 1.1 and 1.3 times the theoretical requirement, as higher values provide minimal operational benefit while substantially increasing costs. Third, WIP lower limit can be set more aggressively (0.75–0.85) to reduce inventory without compromising quality, though practitioners should monitor waiting time metrics to avoid production disruptions.

For control system design, a cycle time of 3–5 min provides the best balance between responsiveness and computational efficiency. The 3% cost penalty for longer cycles is acceptable if computational resources are limited, but the 9.3% cycle time degradation may be problematic for time-sensitive operations. The multi-objective weights can be adjusted based on strategic priorities, with the framework demonstrating stable performance across a wide range of weight combinations. Quality-focused strategies (α₃ > 0.5) incur approximately 10% additional cost while time-focused strategies (α₁ > 0.5) reduce cycle time by 5–8% with similar cost premiums.

The demonstrated parameter stability, predictable linear relationships, and tight performance distributions under uncertainty validate the MD-VSM framework’s suitability for practical implementation. The absence of threshold effects or catastrophic failure modes within realistic parameter ranges provides confidence for industrial deployment across diverse discrete manufacturing environments.

The robustness demonstrated in this sensitivity analysis has significant implications beyond general discrete manufacturing, particularly for high-stakes sectors like medical device manufacturing. In this domain, strict regulatory compliance (e.g., FDA, GMP standards) demands exceptional process control and complete traceability, which aligns directly with the quality (Q) and cost (C) dimensions of our multi-objective model. The framework’s sensitivity to parameters like buffer capacity and WIP limits is directly analogous to managing sterile component inventories or patient-specific device kits, where stockouts can delay critical procedures and overstocking increases risks of contamination or expiration. The model’s ability to balance cost, time (lead time), and quality (zero-defect goal) is paramount when producing life-sustaining devices such as cardiac stents or orthopedic implants. Therefore, the proposed framework offers a validated methodology that can be adapted to enhance the resilience, efficiency, and safety of healthcare manufacturing supply chains, providing a data-driven approach to navigating the sector’s unique quality, cost, and delivery pressures.

5. Managerial Implications

Before discussing the managerial implications, it is important to contextualize the validation approach of this study. The findings presented are based on a high-fidelity simulation rather than a direct industrial pilot implementation. While a live pilot study represents the ultimate validation and is a crucial next step for future work, the methodology employed here provides a robust and practical assessment of the proposed framework’s potential. The simulation model was parameterized using extensive, real-world operational data—including production schedules, equipment failure logs, cost structures, and quality metrics—sourced directly from our industrial partner’s MES and ERP systems. This data-driven approach ensures that the simulated environment closely mirrors the complexities and variabilities of the actual manufacturing line, lending strong practical relevance to the results and the implications derived from them.

5.1. Implementation Guidelines for Practitioners

The implementation of the proposed MD-VSM-based WIP control strategy requires a structured approach to ensure successful deployment in discrete manufacturing environments. Based on our experimental results, we recommend a three-phase implementation roadmap: assessment, deployment, and continuous improvement. During the assessment phase, manufacturers should conduct a comprehensive evaluation of current WIP distribution patterns similar to our baseline analysis in Figure 2, Figure 3 and Figure 4, identifying critical bottlenecks and inventory accumulation points. Our results revealed significant WIP imbalances across processes, with coating and formation stages showing 3–4 times higher inventory levels than assembly processes. This mapping exercise establishes the foundation for targeted improvements and provides the necessary baseline metrics for measuring progress.

The deployment phase should begin with pilot implementation at critical bottleneck processes, gradually expanding to upstream and downstream operations. As demonstrated in our equipment failure response analysis (Section 5.2), the strategy’s effectiveness stems from its ability to coordinate adjacent processes through collaborative parameter adjustments. For instance, when coating equipment failed, the control system reduced upstream mixing process utilization from 0.97 to 0.52 while increasing downstream calendering utilization from 0.28 to 0.32, maintaining production flow stability. This coordinated response capability requires integration with existing Manufacturing Execution Systems (MESs) and Enterprise Resource Planning (ERP) platforms to enable real-time data exchange and decision support. Early pilot deployments should prioritize high-impact processes with significant WIP accumulation, typically those with utilization rates above 85% as identified in our baseline scenario.

During continuous improvement, manufacturers should implement regular performance reviews using the multi-dimensional metrics framework established in Section 4.2. Our comparative analysis showed that the control strategy can effectively balance competing objectives, with the ability to reduce inventory costs by up to 31% in the low-WIP scenario while maintaining consistent quality performance (first-pass yield variations within ±0.7%). This demonstrated capability to simultaneously optimize multiple performance dimensions requires ongoing calibration of control parameters based on changing production conditions and business priorities. Organizations should establish cross-functional governance teams including production, quality, and financial stakeholders to periodically review performance metrics and adjust strategic priorities as needed.

5.2. Key Success Factors and Potential Barriers

The successful implementation of dynamic WIP control systems depends on several critical factors, with data quality emerging as the most fundamental requirement. Our experimental platform integrated detailed process-specific parameters including quality variation patterns, maintenance schedules, and cost structures (Table 1), enabling accurate system modeling and effective control decisions. In practice, manufacturers must invest in reliable data collection infrastructure, particularly for real-time WIP monitoring and quality testing. The quality of these information inputs directly impacts control effectiveness, as demonstrated in our dynamic event response analysis where prompt detection of equipment failures triggered immediate control adjustments. Organizations with fragmented or delayed data collection systems will face significant challenges implementing such responsive control mechanisms.

Organizational and cultural factors represent another critical success dimension. The proposed control strategy requires cross-functional collaboration and decision-making authority at operational levels. Our comparison across scenarios (Section 5.3) demonstrated that the strategy dynamically shifts priorities between throughput maintenance, inventory reduction, and quality assurance based on real-time conditions. This adaptive prioritization challenges traditional functional silos and fixed performance targets. Potential resistance may emerge from departments accustomed to optimizing their metrics in isolation, particularly when control decisions temporarily reduce local performance to improve system-wide outcomes. As shown in our failure response analysis, the strategy deliberately reduced upstream process utilization to avoid inventory buildup during bottleneck failures, a decision that might face resistance from production teams measured solely on utilization metrics.

A third major challenge, particularly for industries in developing countries, is the intensive technological and capital investment required for full-scale implementation. The proposed digital twin framework relies on a sophisticated and integrated technology stack, including ubiquitous sensor networks for real-time data capture, high-bandwidth communication for data transmission, robust data storage and processing capabilities (potentially cloud-based), and seamless integration between shop floor operational technology (OT) and enterprise-level information technology (IT) systems like MES and ERP. For many manufacturers, especially small- and medium-sized enterprises (SMEs) or those in regions with less developed digital infrastructure, the upfront cost of acquiring, implementing, and maintaining these technologies can be a significant barrier. Furthermore, there is a critical need for a skilled workforce capable of developing, operating, and maintaining these complex systems, a talent pool that may be limited. To mitigate these challenges, a phased implementation strategy is highly recommended. Organizations can begin with a pilot project focused on a single critical bottleneck, using more accessible technologies, and then gradually scale the digital twin’s scope and sophistication as they demonstrate value and build internal capabilities.

5.3. Cost–Benefit Assessment of Implementation

The economic evaluation of MD-VSM-based WIP control implementation reveals compelling returns from investment across multiple performance dimensions. Based on our simulation results, the strategy delivers significant inventory cost reductions, with the low-WIP scenario achieving 31% lower inventory costs compared to the baseline while maintaining consistent production output. For a typical discrete manufacturing operation similar to our experimental setting, this translates to annual inventory carrying cost savings of approximately ¥2.88 million per production line (calculated from the ¥240,000 monthly reduction observed in Figure 5). Additionally, the strategy improves equipment utilization balancing, potentially unlocking 15–20% increased capacity at bottleneck processes through better production flow management without additional capital investment.

Quality-related economic benefits further enhance the value proposition. Our comparative analysis demonstrated that the control strategy maintained high batch qualification rates (87.3%, 86.1%, and 88.5% for baseline, high-WIP, and low-WIP scenarios, respectively) across varied operating conditions. Notably, the low-WIP scenario actually achieved higher qualification rates despite reduced buffer inventory, challenging the conventional assumption that lean operations necessarily increase quality risks. This quality stability translates to reduced scrap and rework costs, estimated at 1.3–1.8 million yuan annually for operations similar to our experimental scale. Furthermore, the improved responsiveness to disturbances (42% faster recovery times compared to traditional fixed-parameter controls) reduces production losses during disruptions, a significant benefit in high-value discrete manufacturing where equipment downtime costs typically range from 5000–15,000 yuan per hour.

Implementation costs must be evaluated against these substantial benefits. The primary investment categories include system development/acquisition, infrastructure enhancement, and organizational change management. Based on industry benchmarks for similar advanced manufacturing systems, implementation costs typically range from 1.5–3.5 million yuan per production line, depending on existing infrastructure maturity and scale of operations. Our experimental results suggest that for manufacturing operations matching our simulation parameters (Table 1 and Table 2), the expected payback period ranges from 8 to 14 months, with larger operations achieving faster returns due to economies of scale. This favorable economic assessment, combined with the strategic benefits of enhanced production flexibility and resilience demonstrated in our disturbance response analysis, presents a compelling case for investment in dynamic WIP control capabilities, particularly for discrete manufacturers facing increasing product customization and market volatility.

It is also beneficial to compare the proposed MD-VSM framework with traditional control systems like Kanban or CONWIP from a deployment perspective. Traditional Kanban systems, particularly physical ones, often have a lower initial deployment cost and require less technical effort, relying on simple visual signals. However, their effectiveness can be limited in highly dynamic, multi-variety environments. The proposed MD-VSM framework requires a more significant upfront investment in terms of both cost and effort. This includes investment in data infrastructure (e.g., sensor integration, MES/ERP connectivity), software for modeling and optimization, and training for personnel. While the initial barrier is higher, the justification lies in the substantial long-term operational benefits. As demonstrated by our simulation results—including a 31% reduction in inventory costs and 42% faster recovery from disruptions—the framework’s ability to perform dynamic, multi-objective optimization provides a level of adaptability and efficiency that can yield a rapid return on this initial investment, particularly for manufacturers facing high product customization and demand volatility.

6. Conclusions

This study introduces and validates an integrated framework to address the critical challenge of dynamic work-in-process (WIP) control in complex discrete manufacturing environments. By synergizing Multi-Dimensional Value Stream Mapping (MD-VSM) with multi-objective optimization, our approach functions as a specialized digital twin, enabling a closed-loop, data-driven system that simultaneously optimizes time, cost, and quality objectives.

The framework’s efficacy and robustness were rigorously evaluated using a high-fidelity simulation platform, which was parameterized with extensive real-world data from our industrial partner’s MES and ERP systems. The evidence demonstrates significant operational and economic benefits, including a 31% reduction in inventory costs and a 42% faster recovery from equipment failures compared to traditional methods. Crucially, a comprehensive new sensitivity analysis confirmed the framework’s stability, showing that key performance metrics remain consistent even under significant parameter uncertainty, thus validating the reliability of our findings.

For manufacturing practitioners, these results offer a validated methodology for enhancing performance. While requiring a greater upfront investment than traditional systems like Kanban or CONWIP, the framework’s superior adaptability and demonstrated financial returns—with an estimated payback period of 8–14 months—present a compelling business case. Moreover, the framework is designed to incorporate heuristic algorithms, addressing practical scalability concerns for large-scale, real-time deployment.

While the simulation provides strong evidence, we acknowledge its limitations. Therefore, a pilot implementation in a live industrial setting represents the most critical direction for future research. Other key avenues include detailed computational studies on heuristic algorithms, including emerging approaches like quantum-inspired optimization and AI-based parameter tuning, a comparative life cycle cost analysis against traditional control systems, and the integration of machine learning for greater self-optimization.