Enhancing Sustainable Herd Structure Management in Thai Dairy Cooperatives Through Dynamic Programming Optimization

Abstract

Herd management plays a vital role in boosting the productivity, profitability, and sustainability of dairy cooperatives, particularly in developing countries where smallholder farmers are prevalent and have limited access to modern farming technologies. This research presents a dynamic programming (DP) model aimed at helping dairy cooperatives optimize decisions regarding herd structure, specifically focusing on strategies for culling and replacement to match milk supply with varying market demands. The model considers essential traits of dairy cows, including age, milk production, and reproductive condition, to ascertain the best transitions within the herd over several periods. Findings indicate that implementing the proposed DP model can effectively align milk output with fluctuating demand, decrease the gap between supply and demand, and enhance overall herd productivity. While this study uses Thai dairy cooperatives as a case study, the developed model and its insights are relevant to similar smallholder dairy systems in other developing countries, thereby aiding improved decision-making and promoting sustainable herd management practices worldwide.

1. Introduction

The dairy industry is an important part of the global agri-food sector and a significant source of food, improving food security, promoting rural development, and fostering income [1], especially in developing countries. In Thailand, the dairy industry is a crucial part of the national economy, particularly in rural areas where dairy production continues to be driven by smallholder farmers [2,3]. One of the key mechanisms is dairy cooperatives, which provide farmers with access to capital, technical know-how, and a reliable marketing channel. This cooperative model has proven effective in enhancing productivity and raising the incomes of smallholder farms while promoting inclusive growth of the rural economy.

Despite the advantages of dairy cooperatives, there remain many operational challenges, especially concerning the variation in milk demand that influences production planning, pricing, and farm income [4]. The volatility in demand is caused by seasonal consumption, changes in consumer tastes, competition from imported dairy, and external shocks (e.g., COVID-19). Without good strategies in place, these fluctuations can lead to an oversupply or shortage of milk on farms or at the processing plant.

Koonawootrittriron et al. [5] used a comparative analysis of cooperative-supported dairy farms and private organization-supported dairy farms in Central Thailand. The data showed that private organizations offered better technical and management support and led to better milk production and revenue; however, despite this, the majority of smallholder dairy farmers stayed within the cooperative system, indicating that cooperatives retain their importance in rural areas where they have a monopoly on milk collection and service provision. Most of these dairy farmers are smallholders working in the cooperative system, which is an important institutional mechanism for integrating smallholders into the dairy value chain [6]. This gap, particularly when found between cooperative-supported and private-supported farms, highlights the challenge and need for more knowledge transfers and improvements to management practices and for producers targeted support based on their capacity and conditions [7,8].

Some of the most promising and transformative approaches to provide solutions to increase farm productivity, operational efficiency, and sustainability in recent years have been smart farming and precision agriculture [9,10]. The application of various technologies, such as Internet of Things (IoT) devices, sensors, automated milking systems, artificial intelligence (AI), and big data analytics, in livestock and dairy farms has been gaining attention and utilization to provide precision feeding, monitoring of herd health, disease detection, and yield prediction [11]. Particularly in the Thai dairy context, some cooperatives have begun using such technologies to boost responsiveness and limit risks associated with changes in market conditions, and flexible milk pricing systems according to milk quality and market demand help to stabilise farm income [11,12].

However, the uptake of smart farming and precision agriculture technology across Thailand’s dairy cooperatives, particularly smallholder farmers, has so far been limited and faces several challenges. Financial limitations, infrastructural challenges, low technical literacy, and fragmented farm structures are some of the critical barriers to technology adoption [13,14]. Furthermore, the potential for data security breaches, privacy concerns, and threats of cyber-attacks, especially in the context of cooperative systems that involve multiple stakeholders but where data ownership and governance are not clearly defined, perpetuate the above-mentioned limitations of digital farming technologies [15].

Additionally, although there is significant potential for technology-driven tools, their effective implementation in the cooperative dairy system relies as much on hardware investment as it does on farmer trust, proper training, and the requirement that new tools reflect the specific socio-economic circumstances faced by smallholders. Given that most of the cost-effective technological solutions that have already been developed will require specific usage pathways and risk inadequate usage, farmer engagement and capacity building will be critical to prevent further horizontal inequities emerging between well-resourced farms and smaller, less well-connected producers [10,14]. Consequently, the accessibility and long-term sustainability of smart farming systems may depend on supportive institutional environments, farmer-centric design, and inclusive policy frameworks [9].

This situation reaffirms the vital contribution of government intervention and cooperative governance in Thailand’s development of the dairy sector. Government policies that facilitate R&D investments, support AI systems, promote precision livestock practices, and keep farmers updated through continual training and education are still indispensable for approaches to upgrade the dairy value chain [6,16]. Moreover, biosecurity, herd health management, strategies for disease prevention, and responsible use of data must be taken into consideration to ensure the future sustainability of Thailand’s dairy industry [15,17].

In summary, consolidating the Thai dairy value chain necessitates multiple strategies, including strengthening dairy cooperatives as vital intermediates [5,6,12], facilitating appropriate technology transfer [9,11], raising awareness of cybersecurity and data governance [15], and promoting collaboration between private entities, cooperatives, and public authorities [5,7,8,12]. An integrated approach also will be key for enhancing milk productivity, quality, and competitiveness, ensuring that smallholders are not left behind in the transition to smart and sustainable dairy farming.

Dairy cows have unique characteristics that change throughout their life stages, and understanding these characteristics is essential for effective dairy management practices. One of the most critical aspects of dairy cow characteristics is their nutritional requirements. During lactation, dairy cows require high levels of energy and protein to support milk production. The nutritional needs of dairy cows vary during their lactation cycle, with peak needs occurring during the early stages of lactation. It is crucial to ensure that cows receive proper nutrition at each stage of their lactation cycle to maintain their health and milk production [18]. Reproduction is another crucial aspect of dairy cow management. Reproductive performance is influenced by various factors, such as age, genetics, nutrition, and environmental conditions. Management practices such as artificial insemination and synchronization protocols can be used to improve reproductive performance and herd productivity. Disease prevention and control are critical components of dairy cow management. Mastitis, a common disease in dairy cows, can significantly impact herd productivity and profitability. Effective disease prevention and control measures, such as proper milking hygiene, vaccination programs, and regular health checks, can minimize the impact of mastitis on the herd [19].

According to the previous work [20], the majority of dairy cattle in Thailand are crossbred between Holstein Friesian and other local breeds, with over 75% of Friesian blood, in order to produce raw milk. The past study [21] noted that in countries with high dairy production, the typical lifespan of dairy cows is relatively short, lasting only around 3 to 4 years, which is considerably shorter compared to their natural lifespan of approximately 20 years. Understanding the different life stages of dairy cows is essential for operating a dairy farm, as pointed out by [18] and briefly discussed below.

During the calf stage, which lasts from birth to 6 months, calves are weaned at around 2–3 months of age. The heifer stage, which lasts around two years, is when female young cows reach breeding age at an average of 15 months and give birth to their first calf at around 2 years old. The lactating cow stage, which refers to a heifer or a milking cow after giving birth and producing raw milk for around 10 months, is followed by a 90–120 day break before new breeding by artificial insemination (AI) resumes. In the dry cow stage, which lasts approximately 6–8 weeks before giving birth, milking is discontinued to allow the cows to rest for new calving. After calving, a newborn female calf enters the calf stage, while a newborn bull is generally culled for veal. The cows then return to the lactating cow stage for milk production of the next parity.

All stages are repeated, and each cow typically calves once a year while producing milk for nine months of the year. By optimizing lactation periods, milk production efficiency can be increased. Lactating cows are usually culled after giving birth to four calves (or lactation periods), while replacement heifers are raised from new-born animals or purchased from other farms. The relationship of a dairy cow in each stage is shown in Figure 1.

The lactation curve of dairy cattle has been studied extensively over the years. Wood proposed the first mathematical expression to represent the Friesian cows’ weekly average milk production in 1967 and 1969 [22,23], and this model is still widely used today. While most lactation curve studies focus on milk yield [24], the conventional lactation curve of dairy cows typically shows a peak or maximum daily yield arriving between 4 and 8 weeks after calving, followed by a constant decrease until around 305 days, at which point milking ceases in preparation for the next lactation phase [25]. Cows that have longer prenatal recovery periods tend to receive more complete nutrition, resulting in greater milk yield in future lactations compared to those with shorter rest periods. A dry period of 45–60 days is recommended, and the lactation cycle is considered to end when the cow’s life cycle in a year or 365 days consists of one lactation phase and one dry period. Recent studies have used advanced lactation curve modelling by integrating physiological factors, energy balance, and feed intake patterns to better reflect cow health and productivity [26]. In addition, perturbation modelling has emerged to capture deviations in milk yield caused by stressors or diseases, allowing quantification of resilience and milk loss [27,28]. These developments enhance precision livestock farming and support more informed dairy management decisions. Figure 2 illustrates the lactation curve separated into three phases, representing the milk yield characteristics of dairy cows.

The study [29] found that the number of gestation cycles (parities) had a significant impact on milk production as illustrated in Figure 3, with young cows in their first lactation producing the least milk. Dobson et al. have shown evidence of decreased reproductive performance in dairy cows over the past few decades despite increased milk yields [30]. The productive lifespan of dairy cows is influenced by various factors, such as fertility, health, nutrition, milk quality, and milk output. Dairy cows in high-producing countries have a typical productive lifespan of only three to four years. Studies have investigated the elements that influence raw milk production and the lactation curve, including the temperature-humidity index (THI) [31,32]. Holstein Friesian dairy cows, known for their high milk production, are the primary breed used by Thailand’s Department of Livestock Development to improve dairy cow quality [33,34]. To predict milk yield and lactation curves, understanding the patterns for the initial yield (IY), peak yield (PY), days to peak (DTP), persistency (PST), and 305-day milk yield (MY) is necessary [35].

In dairy production systems, herd structure management is essential for maintaining the long-term productivity, profitability, and sustainability of livestock farming. Management of breeding, culling, replacement, and resource allocation inform milk yield, reproductive performance, animal welfare, and economic return [36,37,38]. Additional complexities arise as a result of dynamic biological processes, fluctuations in market activities, and operational constraints within the agricultural industry which make these decisions more challenging.

Mathematical optimization tools have become tools of choice to support decision-making about herd-management. Of these, Mixed-Integer Linear Programming (MILP) and Dynamic Programming (DP) are commonly used in livestock production planning and management. Both MILP and DP offer strong capabilities to solve complex optimization under constraints, with MILP being particularly useful for multi-objectives and resource constraints and DP shaping a paradigm for sequential decision problems with uncertain and time-dependent variables.

MILP has successfully been applied for both dairy and poultry. Sarttra, Kittitanasak et al. [39], for example, have used MILP to optimise herd management and milk distribution for Thai dairy cooperatives under constraints involving age structure, lactation cycles, production capacity, and distribution logistics. MILP has shown effectiveness in poultry farming for production planning, inventory planning, and maximizing profit considering resource constraints (e.g., feed availability, labour hours, and transportation costs) [40]. Significant improvements in operational efficiency and profitability were also demonstrated after applying MILP to broiler production planning [41], poultry feed optimization, and logistics operations [42,43].

In contrast DP is specifically useful for livestock management, especially for allowing optimization of culling and replacement of dairy herds. DP was first applied to livestock management through modelling optimal treatment and replacement policies based on animal health, milk yield, and economic factors [44,45]. Dynamic Programming has also been applied to small herd or individual cow management in Markov Decision Processes (MDP) [46] and subsequently adapted for larger herds but can struggle to handle short-termdynamics without modifying the model and losing accuracy [47]. Recent research has widened the application of DP in dairy farming. Shrestha et al. [48]. sought to develop a DP model to assess the Retention Payoff (RPO) in organic dairy herds to support elevated cow longevity and sustainable production practices. Likewise, Seyed Sharifi et al. [49] used dynamic programming (DP) for optimal culling decisions, consequently improving reproductive performance and herd profitability. Individual cow parameters (fertility and health status) and herd-level management style differentiate culling rates in dairy herds [50]. The realization could support the value of dynamic, evidence-based decision-making tools, such as DP, to appropriately manage herd structure.

Dynamic Programming (DP) becomes one of the most appropriate tools for this study due to specific features of herd management problems, involving the necessity of optimizing decisions regarding which animals to cull and which to replace through time, aiming to optimise a biological entity which is influenced by multiple economic and biological dynamics. Though MILP provides sound solutions for static, constrained resource production planning, the dynamic and time-related aspect of dairy herd management seems more favourable for DP, as it captures much of the complexity seen in dairy systems. Hence, in this study, we used a Dynamic Programming approach to develop a decision-support model that optimizes the management of the herd, increases profitability, and is able to foster sustainable dairy farming.

Effective dairy cooperative management relies practically on herd structure management, which has a profound impact upon the efficiency, stability, and development potential of the whole cooperative business, especially in developing countries such as Thailand. Dairy cooperatives play a vital role in the support for small farmers, but they face a host of problems due to fluctuations in milk demand, limited resources, and operational inefficiency. An ever more important task for those in charge of a dairy farm is to decide on the herd size, which cows to cull, and which to keep as replacements. This point becomes more critical still when the farm is pushed into having to meet seasonal demands.

This study seeks to investigate how dynamic programming (DP), an optimisation tool in mathematics terms, can be applied to promote decision-making on herd structure management for Thai dairy cooperatives. Ours is a detailed examination covering various aspects of DP modelling, drawing upon real on-farm data with which to support results. All steps are covered in the decision-making process where herd structure is concretely involved: culling policy, replacement policy. The research objectives are three, as follows:

Firstly, we aim to design a dynamic programming method for herd structure management in dairy cooperatives. Second, the method is then compared with traditional approaches to herd management in so far as performance indicators are concerned and at the same level of technical skills among workers. Lastly, practical solutions for dairy cooperatives are offered to improve the balance between supply and demand as well as the sustainability of their operations. By a dynamic programming approach, herd structure management can be improved considerably for better productivity and for the sustainability of dairy businesses. The results of our work not only contribute to academic theories on model development of herds but also provide advice for practical actions in Thai cooperatives, as well other countries that are facing similar supply demand problems.

2. Methodology

2.1. Problem Description

In a practical case study, the management of raw milk in a medium-size dairy cooperative in Thailand was examined. The Nakhon Pathom Dairy Cooperative Co., Ltd., Nakhon Pathom Province, Thailand, which has a pasteurization processing plant that only produces pasteurized products, was the subject of the study. One of the primary challenges faced by the cooperative was managing the supply of raw milk from its members to correspond to the high fluctuation in product demand. The highest demand with high fluctuation during the year was for pasteurized school milk, which had a predetermined quota and could only be sold during the school year. In contrast, commercial pasteurized products with the cooperative brand had comparatively smooth demand and were locally traded using the cooperative’s selling points or taken care of by middle merchants.

Based on the preliminary study, there is a significant difference between the demand for raw milk and the supply capacity among farmers in the dairy cooperatives. While the monthly supply of raw milk from the farmers remains relatively stable throughout the year, the demand for raw milk exhibits significant fluctuations, particularly during the school term. The demand for school milk, in particular, is high during school periods, and it can result in an undersupply of raw milk. This scenario can be illustrated in Figure 4.

To manage this challenge, the Nakhon Pathom Dairy Cooperative Co., Ltd., in Thailand has implemented various strategies, including optimizing their herd structure management. Thailand’s dairy cooperatives typically operate under semi-intensive production systems. Figure 5 provides an overview of a typical milking parlour in a Thai cooperative, showing the housing and milking equipment used. This visual context allows readers to better understand the scale and infrastructure of smallholder-based dairy production systems. Dynamic programming is used as a mathematical optimization tool in this study. The management of overall herd structure in dairy farming involves many technical farming aspects, including the life cycle of dairy cows, lactation cycle, and other factors affecting milk yield. To simplify the formulation of a mathematical model, the stages of a dairy cow can be classified into five stages based on age and reproductive status. Each stage requires key decisions on whether to buy or cull cows to ensure optimal milk production capacity. Involuntary culling due to factors such as infertility or illness are considered as controlled in this study, while voluntary culling is based on the farmer’s decision to sell cows for dairy purposes.

The proposed model assumes that milk yield curves of Thai Friesians can be empirically estimated based on the number of lactation cycles and are deterministic. Other yield traits, such as fat and protein, are assumed to be insignificant, and the maximum parity is limited to four due to technical issues. Pregnancy rates of Artificial Insemination and abortion rates are also assumed under certain effects, and future demands during the planning horizon are deterministic. The planning horizon is assumed to be within three years, with decisions made on a monthly basis.

It is important to note that to increase the number of heifers or cows for higher expected future milk yield, farmers need to carefully consider investment and raising capacity constraints. The proportion of active milking cows to others, herd size, and increment of herd size are critical factors that need to be determined and mathematically modelled to maintain stable income and sustainability of farmers.

There are several other assumptions made in the proposed model, including a constant number of farmer members, known and constant processing capacity, and no uncontrollable factors such as natural disasters or pathogenesis of dairy cows. The model assumes that dairy cows in Thailand have a productive lifespan comparable to those in the United States. Despite smaller herd sizes and lower automation, cooperative frameworks in Thailand enhance herd management practices, promoting sustained productivity. This assumption is supported by field observations and consultations with cooperative veterinarians. While future studies may consider additional factors, such as genomic-polygenic estimated breeding value and seasonal calving effects, the proposed model provides a foundation for optimizing herd structure management decisions in dairy farming.

2.2. Dairy Herd Management with Dynamic Programming

Based on the case study, dynamic programming was used to help determine an appropriate herd structure for dairy farmers in various situations. The objective was to enable farmers to produce an appropriate amount of raw milk in each period, considering the limitations of their capacity and ability to raise dairy cows. The results included the number of cows to be purchased and culled in each period, which affected the amount of raw milk produced. The objective of the problem is to minimize the gap between monthly demands and supplies of raw milk within 3-year planning horizon. The graphical expressions presented in Figure 6 are used to depict the logical progression of cattle through various stages that can impact both the current and future structure of the herd.

The mathematical expressions presented below demonstrate the key components of dynamic programming, such as decision variables, parameters, stages, state, transformation functions, recursion functions, and constraints. These components work together to create an effective decision-making framework for managing cattle herds, with each element playing a crucial role in determining the future structure and success of the herd.

2.2.1. Notation and Indices

• Indices
• $a$: Index of age of cattle $(a=0,1,\dots ,60)$;
• $t$: Index of month $(t=1,2,\dots ,36)$;
• $l$: Index of lactation Cycle $(l=1,2,\dots ,3)$ $l$ = $l+1wheneverr=1$;
• $r$: Index of month-in-milk number $\left(r=0,1,\dots ,14\right)r=\left\{\begin{array}{c}\ge 1acowisinlactation\\ =0otherwise\end{array}\right.$;
• $b$: Index of gestational age $(b=1,2,\dots ,9,10)$ $b=\left\{\begin{array}{c}\ge 1acowispregnent\\ =0otherwise\end{array}\right.$;

2.2.2. Decision Variables for Heifers Aged Between 0–14 Months Old (State I)

• Main decision variables
• ${AX}_{at}$: Number of heifers with the age of $a$ bought in month $t$;
• ${AY}_{at}$: Number of heifers with the age of $a$ sold in month $t$;
• Corresponding variables
• $A_{at}$: Number of heifers with the age of $a$ at the end of month $t$;
• ${AH}_t$: Number of newborn heifers from first pregnant heifers in month $t$;
• ${AM}_t$: Number of newborn heifers from cows in month $t$;

2.2.3. Decision Variables and Parameters for Heifers Aged Between 15–18 Months Old (State II)

• Main decision Variables
• ${BX}_{at}$: Number of heifers with the age of $a$ bought in month $t$;
• ${BY}_{at}$: Number of heifers with the age of $a$ sold in month $t$.
• Corresponding variables
• $B_{at}$: Number of heifers with the age of $a$ at the end of month $t$;
• ${\overline{Z}}_{at}$: Number of $a$ month-old heifers with pregnancy success in month $t$.
• Parameters
• ${BR}_a$: Pregnancy success rate of heifer at the age $a$.

2.2.4. Decision Variables and Parameters for First Pregnant Heifers Aged Between 16–27 Months Old (State III)

• Main decision variables
• ${CX}_{a,t,b}$: Number of first pregnant heifers at the age of $a$ with the current gestational age of $b$ bought in month $t$;
• ${CY}_{a,t,b}$: Number of first pregnant heifers at the age of $a$ with the current gestational age of $b$ sold in month $t$.
• Corresponding variables
• $C_{a,t,b}$: Number of first pregnant heifers at the age of $a$ with the current gestational age of $b$ at the end of month $t$;
• $D_{a,t,r,l}$: Number of cows at the age of $a$ in month $t$ with milking month $r$ and lactation cycle $l$;
• ${AH}_t$: Expected number of newborn heifers from first pregnant heifers in month $t$;
• ${BH}_t$: Expected number of newborn bulls from first pregnant heifers in month $t$;
• ${HAbort}_{a,t,b}$: Expected number of miscarried heifers at the age of $a$ with the current gestational age of $b$.
• Parameters
• $FR$: Female newborn rate by AI;
• ${HA}_b$: Abortion rate of a heifer with the gestational age of $b$.

2.2.5. Decision Variables and Parameters for Non-Pregnant Milking Cow Aged Between 24–60 Months Old (State IV)

• Main decision variables
• ${DX}_{a,t,r,l}$: Number of cows at the age of $a$ bought in month $t$ with milking month $r$ and lactation cycle $l$;
• ${DY}_{a,t,r,l}$: Number of cows at the age of $a$ sold in month $t$ with milking month $r$ and lactation cycle $l$.
• Corresponding variables
• $D_{a,t,r,l}$: Number of cows at the age of $a$ at the end of month $t$ with milking month $r$ and lactation cycle $l$;
• $E_{a,t,b,r,l}$: Number of cows at the age of $a$ in month $t$ with the current gestational age of $b$, milking month $r$, and lactation cycle $l$;
• ${\overline{ZM}}_{a,t,r,l}$: Number of cows with pregnancy success at the age of $a$ in month $t$ with the current milking month $r$ and lactation cycle;
• ${Cowculled}_t$: Number of cows culled due to infertility or maximal cycle reached in month $t$;
• ${TMA}_{a,t,r,l}$: Total expected number of miscarried cows at the age of $a$ in month $t$ with milking month $r$ and lactation cycle $l$.
• Parameters
• ${DR}_{lr}$: Pregnancy success rate of a cow with parity $l$ in the milking month $r$.

2.2.6. Decision Variables and Parameters for Pregnant Milking Cow Aged Between 27–97 Months Old (State V)

• Decision Variables
• Main decision variables
• ${EX}_{a,t,b,r,l}$: Number of cows at the age of $a$ bought in month $t$ with the current gestational age of $b$, milking month $r$, and lactation cycle $l$;
• ${EY}_{a,t,b,r,l}$: Number of cows at the age of $a$ sold in month $t$ with the current gestational age of $b$, milking month $r$, and lactation cycle $l$.
• Corresponding Variables
• $D_{a,t,r,l}$: Number of cows at the age of $a$ at the end of month $t$ with milking month $r$ and lactation cycle $l$;
• $E_{a,t,b,r,l}$: Number of cows at the age of $a$ in month $t$ with the current gestational age of $b$, milking month $r$, and lactation cycle $l$;
• ${AM}_t$: Expected number of newborn heifers from milking cow in month $t$;
• ${BM}_t$: Expected number of newborn bulls from milking cow in month $t$;
• ${TMA}_{a,t,r,l}$: Total expected number of miscarried cows at the age of $a$ in month $t$ with milking month $r$ and lactation cycle $l$;
• ${MA}_{a,t,b,r,l}$: Expected number of miscarried cows the age of $a$ in month $t$ with the current gestational age of $b$, milking month $r$, and lactation cycle $l$.
• Parameters
• $FR$: Female newborn rate by AI;
• ${MAR}_{bl}$: Milking cow abortion rate at the current gestational age of $b$ and lactation cycle $l$;
• $V_{rl}$: Milk yield of a cow with parity $l$ in the milking month $r$, where $V_{r>10,l}=0$.

2.2.7. Dynamic Programming

• Stage: Month (t).
• State: Number of dairy cows of various ages and stages at a given time, and status of dairy cows at month t.
• Transformation Function: $t=t+1,a=a+1,r=r+1,b=b+1$.
• Recursion Function:

$$\begin{gathered} f_t\left(Setofmaindecisionvariables:{A_{a,t},B}_{a,t},{C_{a,t,b},D}_{a,t,r,l},E_{a,t,b,r,l}\right)=\underset{\mathit{Set\; of\; main\; D}.V.s}{\mathit{min}}[\left|{D_t-H}_t\right|+ \\ {f^{*}}_{t+1}\left(A_{a+1,t+1},B_{a+1,t+1},{C_{a+1,t+1,b+1},D}_{a+1,t+1,r+1,l},E_{a+1,t+1,b+1,r+1,l}\right)] \end{gathered}$$

(1)

where

$$H_t={\sum }_{a=24}^{60}{\sum }_{l=1}^4{\sum }_{r=1}^{13}{\sum }_{b=1}^9\left(V_{a,r,l}(D_{a,t,r,l}+E_{a,t,b,r,l}\right);{\forall }_t$$

(2)

$$\begin{array}{l}Setofmaindecisionvariables\\ ⋲\{{AX}_{at},{AY}_{at},{BX}_{at},{BY}_{at},{CX}_{a,t,b},{CY}_{a,t,b},{DX}_{a,t,r,l},{DY}_{a,t,r,l},{EX}_{a,t,b,r,l},{EY}_{a,t,b,r,l}\}\end{array}$$

(3)

The dynamic programming in the case study is used to determine the optimal number of dairy cows to minimize the differences between milk supply and raw milk demand over the planning horizon. This can be represented as a recursion function in Equation (1), which calculates the absolute value of the difference between monthly demand and milk yield. In Equation (2), $H_t$ is the total raw milk production at each month of cows in different age groups and the current herd structure. Equation 3 presents the primary decision variables, which involve buying and selling cows at various stages of their lifecycles. Detailed formulations for other state transformation functions are provided in Supplementary Materials to improve readability and maintain the focus of the main modelling framework.

• Constraints

$${\sum }_{a=0}^5{AX}_{at}=0;{\forall }_t$$

(4)

$${\sum }_{a=0}^5{AY}_{at}=0;{\forall }_t$$

(5)

$${\sum }_{a=16}^{18}{BX}_{at}=0;{\forall }_t$$

(6)

$${MC}_t={\sum }_{a=24}^{60}{\sum }_{l=1}^4{\sum }_{r=1}^{13}{\sum }_{b=1}^9\left(D_{a,t,r,l}+E_{a,t,b,r,l}\right);{\forall }_t$$

(7)

$$35\le {\displaystyle \frac{\sum _{a=0}^{15}{A}_{at}\times 100}{{MC}_t}}\le 40$$

(8)

$$30\le {\displaystyle \frac{\sum _{a=15}^{18}{B}_{at}\times 100}{{MC}_t}}\le 45$$

(9)

$$20\le {\displaystyle \frac{\sum _{a=16}^{27}{C}_{atb}\times 100}{{MC}_t}}\le 25$$

(10)

$$mincap\le {\sum }_{a=0}^{60}{\sum }_{l=1}^4{\sum }_{r=1}^{13}{\sum }_{b=1}^9{A}_{at}+B_{at}+C_{abt}+D_{atrl}+E_{a,t,b,r,l}\le maxcap$$

(11)

Each iteration of the dynamic programming search is subject to certain constraints that regulate the solution space. For instance, as mentioned in Equations (4) and (5), heifers under the age of 6 months cannot be traded due to cooperative regulations that prohibit the trading of animals that are too young to be weaned. Purchasing a heifer between the ages of 16 and 18 months without a pregnancy is considered risky due to the high chance of infertility, and this is prohibited as per Equation (6). However, there are no restrictions on selling heifers during this time period, as it is considered voluntary culling. This means that if a farmer has a heifer that is not expected to have a successful pregnancy, they may choose to sell it to reduce the size of their herd. Equation (7) calculates the total number of active milking cows as the sum of lactating cows that are not pregnant and newly pregnant lactating cows. In order to maintain a sustainable herd, it is essential to strike a balance between replacement and active milking cows. Replacement cows fall into three categories: (1) heifers under 15 months of age, (2) heifers between 15 and 18 months of age, and (3) heifers with their first pregnancy. Equation (8) states that the proportion of replacement cows in the first category to the total number of active milking cows should fall within arbitrary upper and lower limits of 40% and 30%, respectively. The upper and lower bounds of the proportion of non-pregnant heifers older than 15 months to total active milking cows are presented in Equation (9). The ratio of pregnant heifers to total active milking cows is given by Equation (10). Finally, Equation (11) sets the limit on the total number of cows that can be managed by farmers, ensuring that this value does not exceed the capability requirement. The following sections will explore and solve problems under various scenarios using the proposed dynamic programming method, followed by conclusion and discussion.

3. Computational Experiments

The primary objective of this study is to minimize the discrepancies between raw milk production and demand for raw milk throughout the designated planning horizon by determining the optimal number of cows in each life stage over the plan using the proposed dynamic programming previously mentioned. The developed dynamic programming was coded using the Python 3.8. In the experiment, the current situation was modelled using the existing number of cows for dairy cooperative members and raw milk demands expressed in Supplementary Materials. The problem was then solved optimally based on these parameters. Additionally, potential scenarios will be simulated to explore the potential outcomes and assess the effectiveness of the proposed dynamic programming.

3.1. Experimental Results Based on the Current Scenario

The dynamic programming model was applied to address the herd management problem over a three-year planning period, considering the current conditions of Nakhon Pathom Dairy Cooperative Co., Ltd. The optimal results generated by the dynamic programming approach were then compared with the outcomes produced by the cooperative’s existing procedures. As previously noted in the problem description, the demand for raw milk fluctuates throughout the year due to the school milk campaign. During school term periods, there is a peak in raw milk demand, whereas school break periods lead to a lower demand volume. The current herd management approach appears to be inappropriate for the situation, as there are significant discrepancies between the demand and supply of raw milk each month, along with a substantial overall difference. The systematic dynamic programming approach can produce significantly better results, both in terms of monthly performance and overall outcomes as illustrated in Figure 7.

Based on the experimental results, the proposed dynamic programming approach significantly reduces the absolute difference between raw milk demand and supply compared to the traditional planning method used by the cooperative. Specifically, the proposed approach achieves an absolute difference of 19,500,268 litres, compared to 22,585,588 litres in the traditional approach, marking an improvement of 13.7% in reducing supply–demand imbalances. Additionally, with an optimised trading strategy that dynamically adjusts limits per stage, the Mean Absolute Deviation (MAD) between raw milk demand and supply is reduced to 26.02%, demonstrating greater stability and responsiveness. The proposed DP model effectively minimizes extreme mismatches, enhances demand responsiveness, and smoothens supply variations while preserving herd sustainability. By implementing controlled herd adjustments across all stages, including limited trading of younger heifers, the model ensures gradual, stable supply adjustments without excessive fluctuations. Several months exhibit minimal absolute differences, emphasizing the model’s improved adaptability. Through strategic herd restructuring, the approach enhances long-term supply consistency, ensuring a more efficient, sustainable, and responsive raw milk production system. Full experimental results are show in Table S1.

A quantitative analysis of herd stability indicates substantial improvements brought by the DP-based approach. The maximum change in total herd size reduced from 135 heads (traditional) to 72 heads (DP-based), representing a 46.7% reduction. Moreover, the standard deviation of herd size declined from 45.6 to 23.5, reflecting a 48.5% improvement in stability. In addition, the annual culling rate decreased from 29% to 22%, while the replacement rate reduced from 30% to 25%, suggesting better resource efficiency and lower operational stress.

Table 1. Comparison of herd stability indicators between traditional and DP-based approaches.

Indicator	Traditional	DP-Based	Decrement Percentage (Improvement)
Maximum Change in Total Herd Size	135	72	↓ 46.7%
Standard Deviation of Herd Size	45.6	23.5	↓ 48.5%
Culling Rate per Year	29%	22%	↓ 7%
Replacement Rate per Year	30%	25%	↓ 5%

summarizes the key performance indicators related to herd stability and sustainability implications.

3.2. Experimental Results Based on the Simulated Scenarios

To evaluate the effectiveness of the proposed dynamic programming (DP) approach, multiple demand scenarios are simulated to assess its ability to manage herd structure and milk supply under different market conditions. The objective is to examine how the system responds to varying levels of demand and its capacity to maintain supply–demand balance while ensuring herd sustainability.

Four key scenarios are considered in the analysis. The first scenario tests the system under high raw milk demand, where production must be adjusted to meet increased requirements efficiently. The second scenario examines low raw milk demand, requiring strategic herd adjustments to prevent overproduction and optimise resource use. The third scenario evaluates the impact of high demand variability, where fluctuations in demand necessitate continuous adjustments to maintain stability. Finally, the fourth scenario investigates low demand variability, where a steady market environment allows for more predictable herd and production planning.

By analysing these scenarios, the assessment focuses on the adaptability and effectiveness of the proposed DP model in maintaining an efficient and sustainable raw milk supply.

3.2.1. High-Demand Scenario

In the high-demand scenario, the original raw milk demand was adjusted by increasing all demand values by 20% to simulate periods of heightened market requirements. This scenario represents situations such as seasonal peaks, expanding market opportunities, or sudden increases in consumer demand. The objective is to assess how well the system scales up production while maintaining a balanced herd structure and ensuring efficient resource utilization.

Under the high-demand scenario, where raw milk demand was increased by 20%, the proposed dynamic programming approach demonstrated its ability to scale production while maintaining herd stability. The absolute difference between supply and demand reached 23,106,052 litres, reflecting the challenge of balancing a sudden surge in market requirements. Despite this, the system effectively managed herd restructuring and supply adjustments, achieving a Mean Absolute Deviation (MAD) of 25.69%, slightly higher than in the baseline scenario due to the increased volatility. The DP model ensured a steady supply by optimizing trading decisions, carefully increasing the number of lactating cows while maintaining a sustainable herd structure. Some months exhibited close supply–demand alignment, highlighting the system’s adaptability under pressure. These results indicate that while the system can respond effectively to periods of heightened demand, additional flexibility in trading constraints or long-term herd planning may further enhance performance under extreme market conditions expressed in Figure 8. Complete results are expressed in Table S2.

3.2.2. Low-Demand Scenario

In a declining market, managing raw milk production is crucial to prevent overproduction and inefficiencies. This low-demand scenario reduces all demand values by 20%, simulating market contractions due to seasonal downturns, economic slowdowns, or shifting consumer preferences. Excess supply poses challenges such as increased storage costs, wastage, or forced sales at lower prices. To address this, herd restructuring must focus on gradual reductions in lactating cows while maintaining replacement heifers for future recovery. Trading constraints should also prevent excessive culling that could undermine long-term sustainability. This scenario assesses how effectively the system adjusts to lower demand, optimizing herd management while minimizing disruptions to milk supply

Under the low-demand scenario, where raw milk demand was reduced by 20%, the proposed dynamic programming (DP) approach effectively minimized supply–demand imbalances while ensuring herd sustainability. The total absolute difference between supply and demand was 17,303,181 litres, compared to 22,585,588 litres in the traditional approach, marking an improvement of 23.4% in reducing excess supply. Additionally, the Mean Absolute Deviation (MAD) between raw milk demand and supply was 28.86%, reflecting the challenge of maintaining herd efficiency while preventing overproduction. The DP model gradually adjusted herd size, reducing lactating cows while maintaining replacement heifers to avoid long-term depletion. Some months exhibited close alignment between supply and demand, demonstrating the system’s adaptability to market downturns. These results highlight the system’s ability to optimise herd restructuring, prevent excessive culling, and maintain operational efficiency even in reduced market conditions in Figure 9. Complete results are detailed in Table S3.

3.2.3. High-Variability Demand Scenario

Fluctuating market conditions can lead to unpredictable raw milk demand, requiring a system capable of dynamically adjusting production and herd structure. This high-variability scenario introduces 10% increased variation in demand, simulating external factors such as changing consumer trends, supply chain disruptions, or economic instability. Managing this variability presents challenges, as sudden spikes in demand require rapid herd expansion, while unexpected drops may lead to overproduction and inefficiencies. The system must carefully balance short-term fluctuations while maintaining long-term herd sustainability. This scenario evaluates how effectively the system adapts to higher market volatility, ensuring stable milk production while preventing excessive supply–demand mismatches.

Under the high-variability demand scenario, where demand fluctuations increased by 10%, the system effectively adapted to unpredictable market conditions while maintaining herd stability. The total absolute difference between supply and demand was 21,140,084 litres, with a Mean Absolute Deviation (MAD) of 28.21%, reflecting the challenge of responding to rapid demand changes. The model successfully adjusted herd size dynamically, ensuring supply remained responsive without excessive overcorrections. While some months exhibited minimal differences, extreme demand swings required continuous herd restructuring to maintain balance. These results indicate that the system can effectively manage unpredictable demand patterns while preserving operational stability, though additional flexibility in trading constraints may further enhance responsiveness in highly volatile conditions shown in Figure 10. Full experimental outcomes are delineated in Table S4.

3.2.4. Low-Variability Demand Scenario

In a stable market environment, raw milk demand remains relatively predictable, allowing for more consistent production planning and herd management. This low-variability demand scenario reduces demand fluctuations by 10%, simulating periods of steady market conditions where changes in consumption are minimal. With less demand uncertainty, the focus shifts from rapid adjustments to maintaining an optimised herd structure that ensures long-term sustainability.

Under the low-variability demand scenario, where demand fluctuations were reduced by 10%, the system effectively stabilized supply–demand balance while maintaining long-term herd sustainability. The total absolute difference between supply and demand was 17,805,095 litres, with a Mean Absolute Deviation (MAD) of 23.76%, reflecting improved predictability in milk production. With fewer extreme fluctuations, herd restructuring was more gradual, resulting in stable trading activities and optimised resource allocation. The system effectively minimized supply mismatches while reducing unnecessary herd adjustments. These results demonstrate that under stable market conditions, the system can enhance planning accuracy, lower operational volatility, and maintain herd efficiency with minimal disruptions.

The proposed dynamic algorithm demonstrated robust adaptability across different demand conditions in Figure 11. It was most effective in stable demand environments, where predictable consumption allowed for better planning accuracy and lower supply mismatches. Under high variability, the system required more frequent adjustments, though it successfully prevented severe imbalances. While demand surges and declines were managed effectively, trading constraints limited rapid structural changes, leading to some residual supply mismatches. Future refinements, such as dynamic trading limits or anticipatory herd restructuring, may further improve responsiveness under extreme market shifts. These findings underscore the model’s practical applicability for cooperative milk production planning, ensuring efficient supply–demand balance, herd sustainability, and long-term operational stability. The complete set of results is showcased in Table S5.

These consistent findings for the experiments with different scenarios show the flexibility and robustness of the proposed model in managing dairy herd structure. The results suggest the DP-based model can be used as an effective decision support tool for dairy cooperatives, especially for those in developing countries.

4. Managerial Advantages and Discussion

4.1. Implications for Dairy Cooperatives in Developing Countries

Adaptation of the proposed DP-based approach to other dairy cooperatives requires local adjustment of key model parameters, including herd characteristics, production systems, and market conditions (e.g., feed costs, farm-gate milk prices). Such adjustments involve modifying the lactation curve, assumptions regarding cow longevity, demand patterns, and relevant economic factors such as feed prices, milk prices, or breeding stock transaction costs. Furthermore, collecting accurate data on herd structure and historical milk supply–demand trends is essential to ensure proper model calibration and support effective decision-making.

However, successful adaptation of this model to other settings requires careful consideration of local conditions. These include breed-specific lactation profiles, regional climate factors, cow productivity characteristics, and common farming practices. Dairy cooperatives seeking to implement this model must ensure access to reliable herd data and have a clear understanding of demand fluctuations in their specific markets. Under certain conditions, seasonal calving may also be considered as a management strategy; however, its feasibility should be carefully evaluated based on the characteristics of the cooperative, farmer profiles, and infrastructure availability.

Most importantly, the model’s flexibility, the possibility of parameter customization, and sensitivity to local production dynamics are key to enhancing its practical application. Ensuring effective integration of locally relevant data and collaborative management of production information will ultimately maximize the operational usability and efficiency of this DP-based optimization approach.

4.2. Aspects Impacting Herd Stability and Sustainability

Dairy cow lactation curves have wider variability associated with breed, climatic regions, and farm practices which is an important aspect related to the generalizability of the proposed model. Breeds genetics, feed availability, disease occurrence, and heat stress have been described as factors that affect variations in quantitative traits such as milk yield and thus affect the patterns of lactation cycles in cows. Incorporating these dynamics to future modelling would increase the accuracy and relevance of a model, especially under heterogeneous production systems. The economic aspect is essential to all herd management decisions, and not only biology. Real-world dairy herd decisions are influenced by financial factors (purchase and sale of cows), price of the market, price of food, and veterinary services. Thus, future research should incorporate economic constraints into the optimisation-padding framework to ensure economic feasibility of solution approach for cooperatives with limited financial capital.

4.3. Enabling Smart Farming Integration: Opportunities and Challenges

Smart farming offers innovative solutions that can elevate dairy cooperatives to the next level in herd management. By leveraging data from various mobile applications, precision feeding systems, and health monitoring devices, these solutions provide real-time raw data to facilitate informed decision-making. However, smallholder-based cooperatives often face significant barriers to adopting these technologies, including high investment costs, limited digital literacy, and inadequate ICT infrastructure. To overcome these challenges, cooperative-specific strategies such as co-financing, training programs, and external financial support are essential.

4.4. Limitations of the Model, Feasibility of Implementation, and Areas for Future Development

Although the well-known DP-based representation is feasible in practice, it might not be entirely ideal for current dairy farming practices and economic conditions. The present model does not incorporate several important cost factors, including expenses associated with purchasing and selling animals, veterinary services, fluctuations in feed prices, and volatility in milk prices. Future modelling efforts should consider these variables to improve the model’s realism and applicability. Additionally, the model assumes that the productive lifespan of dairy cows is relatively fixed. Extending the lifespan of cows could lead to less frequent culling and replacement, thereby lowering operational costs. However, this approach could increase risks associated with managing older animals. Conversely, lowering herd intensification would require larger herd sizes to meet milk demand, which may impact feed requirements and challenge sustainability pathways.

The capability of the model may face limitations due to the absence of field testing and validation under real farming conditions, which may affect its practical robustness. The observed gaps between predicted and actual numbers of farmers are likely due to the decomposition of cooperative structural information, such as the number of farmer groups or individual farmers—elements that the model has the potential to address. Incorporating feedback loops from farmers and cooperative managers would provide opportunities to further refine and validate the model using real-world data from dairy cooperatives.

Nevertheless, addressing these complex challenges requires a holistic approach that integrates mathematical optimization, economic feasibility, and technology-enabled collaboration. Establishing a cooperative framework is essential to support smallholder farmers in improving productivity, enhancing resilience, and coping with market and climate-driven uncertainties.

5. Conclusions

This study addressed a critical operational challenge commonly faced by dairy cooperatives, particularly in developing countries, where mismatches between milk supply and market demand threaten farm sustainability and farmer incomes. To tackle this issue, this study developed a dynamic programming (DP)-based model for analysing herd structure management under changing market conditions. The proposed approach offers a structured framework to support strategic decisions related to culling, replacement, and herd composition in response to demand fluctuations and production constraints.

Nevertheless, several key limitations in this study must be acknowledged for the model’s broader applicability. The fixed productive lifespan of dairy cows, together with the relatively intensive farming system, may not perfectly reflect conditions in low-intensity, pasture-based, or health-oriented dairy systems, where cows often live longer (though are not necessarily more productive), with lower culling rates and differing reproductive performance. Extending cow life in such systems would likely reduce the frequency of culling and replacement, limiting herd management flexibility but possibly improving animal health and welfare outcomes.

The current model lacks consideration of key economic factors such as livestock trading costs, veterinary expenses, feed price fluctuations, and milk price volatility, which are essential for realistic decision-making in dairy cooperatives. Future model development should incorporate these variables to enhance economic realism and operational relevance. Additionally, this research utilized a mathematical optimization framework that has not been tested in real farming systems. Future efforts should include pilot trials in cooperative setups to evaluate the model’s feasibility, gather feedback from farm managers, and refine operational parameters.

To ensure its practical utility and broaden adoption, particularly for smallholder-based cooperatives with limited resources, any future development should consider incorporating lactation patterns specific to regional breeds, climate resilience strategies, and environmental considerations, including potential greenhouse gas emissions resulting from changes in herd size. Furthermore, the recent extension of the model toward multi-objective optimization frameworks will enable cooperatives to meet planned output while simultaneously optimizing economic, environmental, and social sustainability goals.

This study offers a fundamental and significant development toward the strategic management of dairy herds by means of a dynamic programming approach; however, real-world application would require customization and validation for regional contexts, along with the incorporation of broader economic and sustainability dimensions, all of which are essential for supporting resilient systems of dairy production across diverse global settings.