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The poultry processing industry often struggles with demand-supply imbalances due to inherent mismatches in product segmentation. Unlike chicken processing, which benefits from standardized cutting patterns, duck meat processing requires a more complex approach due to variations in carcass weights, consumer preferences, and diverse market demands. This discrepancy results in deviation of demand fulfillment, where some products are overproduced leading to excess inventory and price reductions, while others are underproduced causing shortages and lost revenues. The perishable nature of meat further amplifies this challenge as excess inventory cannot be stored for long periods without spoilage. Keeping a balance between revenue and deviation of demand fulfillment is essential for duck meat processing. Despite its importance, research on this issue in duck meat processing is limited. This paper evaluates three models: Mixed-Integer Programming (MIP), Heuristic, and Hybrid. Each model is tested on structured, real-world datasets to assess its effectiveness in balancing revenue and deviation of demand fulfillment. A comparative analysis highlights the strengths and limitations of each approach and offers insights into their applicability in duck meat processing and broader poultry industries facing similar challenges.
Abstract
The poultry processing industry often struggles with demand-supply imbalances due to inherent mismatches in product segmentation. Unlike chicken processing, which benefits from standardized cutting patterns, duck meat processing requires a more complex approach due to variations in carcass weights, consumer preferences, and diverse market demands. This discrepancy results in deviation of demand fulfillment, where some products are overproduced leading to excess inventory and price reductions, while others are underproduced causing shortages and lost revenues. The perishable nature of meat further amplifies this challenge as excess inventory cannot be stored for long periods without spoilage. Keeping a balance between revenue and deviation of demand fulfillment is essential for duck meat processing. Despite its importance, research on this issue in duck meat processing is limited. This paper evaluates three models: Mixed-Integer Programming (MIP), Heuristic, and Hybrid. Each model is tested on structured, real-world datasets to assess its effectiveness in balancing revenue and deviation of demand fulfillment. A comparative analysis highlights the strengths and limitations of each approach and offers insights into their applicability in duck meat processing and broader poultry industries facing similar challenges.
Keywords
Duck meat processing, mixed-integer programming, heuristic, hybrid
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Abstract ID: 6182
1. Introduction
Duck meat production has seen significant growth in recent years, particularly in Asia, where demand continues to rise. However, the poultry processing industry often struggles with demand-supply imbalances due to inherent mismatches in product segmentation. Unlike chicken processing, which benefits from standardized cutting patterns, duck meat processing requires a more complex approach due to variations in carcass weights, consumer preferences, and diverse market demands. For example, a customer may require one wing, three legs, and one breast, while a single bird yields two wings, two legs, and two breasts. This discrepancy results in deviation of demand fulfillment, where some products are overproduced leading to excess inventory and price reductions, while others are underproduced causing shortages and lost revenues. A key challenge in this sector is to ensure the production aligns with customer demand while reducing inventory surplus and shortages. The perishable nature of meat further amplifies this challenge as excess inventory cannot be stored for long periods without spoilage. Keeping a balance between revenue and deviation of demand fulfillment is essential for duck meat processing.
To address the challenge, this paper proposes three models - Mixed-Integer Programming (MIP), Heuristic, and Hybrid - to determine the number of carcasses allocated to specific cutting patterns for maximizing revenue and minimizing deviation of demand fulfillment. MIP model provides an exact mathematical solution under fixed, deterministic conditions but lacks flexibility in handling diverse demand and supply. Heuristic model, on the other hand, incorporates stochastic elements and heuristic search techniques, enabling adaptability to uncertainties in production and diverse demand but may not always yield an optimal solution. To leverage the strengths of both approaches, a Hybrid model is developed that integrates the tractability of MIP with the flexibility of Heuristic to achieve a more effective balance between revenue and deviation of demand fulfillment.
This paper evaluates the performance of these three models by structured, real-world datasets from historical production and sales data of a duck meat processing company. Two performance metrics, revenue and deviation of demand fulfillment, are used to evaluate the effectiveness of each model. Through a comparative analysis, this study examines the strengths and limitations of each approach and offers insights into their applicability and effectiveness in the duck meat processing environment. The findings contribute to the broader poultry processing industry by offering actionable recommendations for practitioners and researchers seeking to improve the decision-making of demand and supply for perishable meat products.
2. Problem Description
Duck meat processing involves dividing carcasses into various cuts, such as breasts, thighs, wings, and whole duck products. The way carcasses are allocated across different cutting patterns plays a crucial role in determining overall profitability and customer satisfaction. An optimized allocation of carcass will ensure that production aligns with demand while maximizing financial returns.
The problem of balancing revenue and deviation of demand fulfillment in this paper is structured around three key objectives. First, revenue maximization is achieved by assigning carcasses to cutting patterns that yield the highest total revenue. Second, deviation minimization in demand fulfillment focuses on reducing the discrepancies between actual production and demand, ensuring a more balanced and efficient supply chain. Lastly, carcass supply constraints ensure that the total number of carcasses allocated do not exceed available supply, maintaining feasibility within the production system.
This study seeks to identify the most effective approach, whether MIP, Heuristic or Hybrid, to strike the best balance between revenue generation and demand fulfillment. By evaluating these models, the research provides insights into improving decision-making in duck meat processing, contributing to greater efficiency and profitability in the industry.
3. Related Research
Research on optimization in poultry processing has primarily focused on chicken meat, utilizing MIP and heuristic methods to enhance efficiency and maximize profitability [1,5,7,8,12]. Studies have demonstrated MIP's effectiveness in optimizing production schedules and cutting patterns, leading to cost reductions and improved demand fulfillment [2, 6]. However, duck meat processing presents additional challenges due to greater demand variability, differences in carcass composition, and more diverse product segmentation, requiring more flexible allocation strategies to balance revenue and demand fulfillment.
MIP has been widely used in food processing for resource allocation and production scheduling [8], offering precise optimization but struggling with real-world demand and supply fluctuations [2, 4, 9]. In contrast, heuristic models integrate simulation techniques to handle uncertainty, making them better suited for dynamic production environments [3, 5, 10, 12]. While heuristics have been successfully applied in manufacturing and logistics, their use in duck meat processing remains largely unexplored.
Hybrid models, which combine the structured decision-making of MIP with the flexibility of heuristic methods, have proven effective in supply chain and production planning [11]. However, no prior research has evaluated their application in duck meat processing. This study fills the gap by comparing MIP, Heuristic, and Hybrid models, providing practical insights for balancing profitability and demand fulfillment in the duck meat industry.
4. Methodology
4.1 Mixed-Integer Programming Model
MIP model is designed to balance revenue and deviation of demand fulfillment by determining the allocation of duck carcasses across cutting patterns. Cutting patterns refer to predefined methods used to divide duck carcasses into various product types, such as breasts, thighs, wings, and whole duck portions. Each cutting pattern represents a specific way of dividing a carcass to produce a combination of products, influencing both revenue and deviation of demand fulfillment.
In MIP model, cutting patterns and the combination of products are given, which are donated by i and j respectively. Other parameters are all fixed and deterministic that include Pj (revenue per unit of product type j), C (total number of duck carcasses available for processing), (number of units of product type j produced using cutting pattern i), and Dj (demand for product type j). Decision variable represents the number of duck carcasses allocated to cutting pattern i (integer). Decision variable yj denotes the number of units of product type j produced (continuous), d+j and d-j account for overproduction and underproduction, respectively. A crucial element of the model is the weight parameter Л, which controls the trade-off between maximizing revenue and minimizing deviation of demand fulfillment. The model is shown below:
... (1)
... (2)
... (3)
... (4)
The objective function is to balance minimizing total deviation with maximizing revenue. Constraint (1) ensures that the total number of carcasses allocated across different cutting patterns does not exceed the available supply. Constraint (2) captures the difference between actual production and demand for each product. Constraint (3) ensures the number of products generated aligns with the selected cutting patterns. Non-negativity and integer constraint (4) ensures that carcass allocations remain integer values, while deviations of demand fulfillment and production levels are non-negative.
4.2 Heuristic Model
Heuristic model iteratively adjusts the allocation of duck carcasses across cutting patterns to minimize deviation of demand fulfillment while maximizing revenue by the following key steps:
* Initialization: Randomly generate allocations for cutting patterns xi.
* Feasibility check: Ensure Σmi=1 xi ≤ C.
* Production calculation: yj = Σmi=1 aij × j for each product type j.
* Deviation of demand fulfilment: d+j = max (O,yj Dj), d-j = max (0, Dj - yj).
* Evaluation: Evaluate the objective function (same as MIP) for the current allocation.
* Iteration: Adjust allocations iteratively to repeat the evaluation.
* Stop criteria: The iterative process terminates after 500 iterations or when the improvement in the objective function falls below 0.1% for 20 consecutive generations, ensuring computational efficiency and solution stability.
4.3 Hybrid Model: Combining MIP and Heuristic
While MIP provides an exact mathematical solution, it tends to allocate most carcasses to the highest revenue-generating cutting patterns, potentially overlooking demand fulfillment. In contrast, Heuristic explores multiple solutions iteratively, but its heuristic nature may lead to solutions that do not strictly adhere to all constraints and may not always yield the highest revenue.
To overcome these limitations, a Hybrid model is developed to address the limitations of MIP and Heuristic, aiming to minimize deviation of demand fulfillment while maximizing revenue by the following key steps:
* Solve MIP for initial allocation: MIP model is executed first to determine an initial carcass allocation based on fixed constraints.
* Feed MIP results into Heuristic for refinement: MIP solution serves as the initial allocation for Heuristic process, providing a baseline for further refinement.
* Iterative refinement and evaluating through Heuristic: Similar to MIP model, the objective function is used to assess the effectiveness of the current allocation.
* Stop criteria: The iterative process terminates after 500 iterations or when the improvement in the objective function falls below 0.1% for 20 consecutive generations, ensuring computational efficiency and solution stability.
5. Numerical Experiments
5.1 Sensitivity Analysis of Lambda (λ)
In this paper, Lambda (λ) is a weighting parameter which is a control factor to adjust the priority between the two objectives: 1) minimizing deviation of demand fulfillment to ensure production aligns with demand, and 2) maximizing revenue to achieve financial performance. Sensitivity analysis for MIP and Heuristic models was conducted by varying the parameter λ. The results are shown in Figure 1 and Figure 2.
Figure 1 illustrates the impact of X on total revenue and total deviation in MIP model, which suggests the reasonable range of λ ≈ 0.1 to 1.5, where revenue is maximized while keeping deviation at a reasonable level. Selecting a value within this range ensures an effective balance between financial performance and satisfaction in demand. Figure 2 illustrates the impact of λ on total revenue and total deviation in Heuristic model, which suggest a value beyond λ ≈ 0.4, both revenue and deviation fluctuate slightly but remain relatively stable.
5.2 Implementation and Results
To implement these models, historical data in 2021 from an Asian duck meat processing company was used to generate 12 datasets containing demand, price, and carcass supply information. Monthly averages of shipments, market prices, and carcass availability were calculated to create these datasets. The models were fed with eight predefined cutting patterns for 24 products. For MIP model, a best λ value (ranging between 0.1 and 1.5) was determined for each of 12 datasets by running sensitivity analysis that yields the lowest deviation while maintaining the highest possible revenue. For Heuristic and Hybrid models, a fixed value of 1 was used. Table 1 shows the performance of three models - MIP, Heuristic and Hybrid - in terms of Revenue (S) and Deviation of demand fulfillment (Kg) for 12 different datasets.
Table 2 shows the outcomes of paired t-tests on the performance of these models, which confirms all three models yield significant differences in performance statistically. MIP model consistently outperforms Heuristic model in revenue generation as seen by t-statistic values in Table 2. Hybrid model achieves slightly lower revenue than MIP but remains superior to Heuristic. Deviation of demand fulfillment is a key metric for assessing how well these models meet demand. A lower t-statistic deviation value in Table 2 suggests a better allocation of duck carcasses to match demand. Hybrid model outperforms both MIP and Heuristic in minimizing deviation of demand fulfillment, confirming its ability to achieve a more balanced solution.
The comparative analysis and results reveal that MIP model is the best for maximizing revenue, while Hybrid model offers the best trade-off between the performance of revenue and deviation of demand fulfillment. Heuristic model, while flexible, underperforms the other two models. These findings highlight the importance of choosing an effective approach in enhancing operational efficiency in the duck meat processing industry.
6. Conclusions
This study examined three models - Mixed-Integer Programming (MIP), Heuristic and Hybrid - to balance revenue and deviation of demand fulfillment in duck meat processing industry. The goal was to minimize deviation of demand fulfillment while maximizing revenue ensuring efficient resource utilization in duck meat processing. The results highlighted key differences in model performance. MIP model excelled in revenue maximization but had high deviation of demand fulfillment due to its focus on the most profitable cutting patterns. Heuristic model achieved better demand fulfillment but generated lower revenue. Hybrid model maintained high revenue while significantly reduced deviation, making it the most balanced solution. Sensitivity analysis on the parameter Л demonstrated its impact on balancing revenue and deviation of demand fulfillment, underscoring the importance of fine-tuning model parameters for optimal performance. Paired t-tests confirmed significant differences in performance statistically among three models, with the Hybrid approach outperforming both MIP and Heuristic in minimizing deviation of demand fulfillment while achieving revenue close to MIP.
This study contributes to the broader poultry processing industry by demonstrating effective approaches to enhance profitability and demand fulfillment. The findings, including insights from sensitivity analysis, offer actionable recommendations for practitioners and researchers seeking to improve the decision-making of demand and supply for perishable meat products.
References
[1] E. Küçüktopçu, B. Cemek, and H. Simsek, "Modeling environmental conditions in poultry production: Computational fluid dynamics approach," Animals, vol. 14, p. 501, 2024.
[2] R. Bai, G. Kendall, R. Qu, and J. A. Atkin, "An improved mixed-integer programming model for the meat cutting problem," European Journal of Operational Research, vol. 266, no. 1, pp. 253-269, 2018.
[3] J. Banks, J. S. Carson, B. L. Nelson, and D. M. Nicol, Discrete-Event System Simulation, Pearson, 2016.
[4] S. Geramipour, G. Moslehi, and M. Reisi-Nafchi, "Maximizing the profit in customer's order acceptance and scheduling problem with weighted tardiness penalty," Journal of the Operational Research Society, vol. 68, no. l,pp. 89-111,2017.
[5] T. Upachaban, K. Khongsatit, and T. Radpukdee, "Mathematical model and simulation study of a closed poultry house environment," International Journal of Technology, vol. 7, pp. 1246-1252, 2016.
[6] V. M. Albornoz, P. M. Franca, and A. A. Pessoa, "A mixed integer linear program for operational planning in a meat packing plant," Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO), 2013, pp. 221-229.
[7] M. A. S. Jahromi and M. Tavakkoli-Moghaddam, "Optimization modeling of a poultry industry supply chain network," Journal of Industrial and Systems Engineering, vol. 8, no. 3, pp. 34-50, 2015.
[8] M. R. Hassan, T. N. Ahmad, and K. Y. Leong, "Optimizing poultry production through advanced monitoring and control systems," International Journal of Agricultural and Biological Engineering, vol. 15, no. 5, pp. 231-245, 2022.
[9] M. I. Franco, A. V. Babkin, and S. P. Ivanov, "Production optimization in a grain facility through mixed-integer linear programming," Applied Sciences, vol. 12, no. 16, p. 8212, 2020.
[10] A. V. Babkin, S. A. Anosov, and N. E. Serebryakov, "Optimization of food industry production using the Monte Carlo method," Information, vol. 9, no. 1, p. 5, 2020.
[11] Ehsan Badakhshan & Peter Ball (2024) Deploying hybrid modelling to support the development of a digital twin for supply chain master planning under disruptions, International Journal of Production Research, 62:10, 3606-3637, DOI: 10.1080/00207543.2023.2244604
[12] Elena Simona NICOARĂ1, "Simulation-based Optimization Using Genetic Algorithms for Muti-objective Flexible JSSP," Studies in Informatics and Control * December 2011
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