Rising dairy prices and intense competition are driving firms to optimize their supply chains for efficiency and sustainability. Modern customers evaluate companies not only on price and quality but increasingly on environmental and social performance [1], [2]. Therefore, incorporating all three pillars of sustainability (economic, environmental, and social) into supply chain design is essential. Multi‐objective optimization is a natural approach to balance these dimensions while maximizing overall supply‐chain benefit [1], [3]. For example, recent work emphasizes that sustainable development and resilience are “undeniable” priorities in today’s markets. In the food industry, the challenge is compounded by the fact that products are highly perishable. As noted by Govindan et al. [2], “a challenging task in today’s food industry is distributing high-quality perishable foods throughout the supply chain,” and their model explicitly integrates sustainability into distribution planning. Indeed, perishable goods require special handling: food quality decays rapidly not only during production and storage but also during distribution. Consequently, design decisions in a perishable‐food supply chain affect not only traditional cost and profit, but also product quality and customer satisfaction [2], [4]. In this context, a supply-chain model that simultaneously optimizes costs, social and environmental impacts, and product quality is needed. However, implementing such models in real-world supply chains remains challenging, particularly in sectors like dairy, where supply reliability and distribution reach are critical. One promising yet underexplored strategy is to improve sustainability performance by embedding backup suppliers into the supply chain network design. While many models incorporate flexibility reactively, using stochastic or scenario-based disruptions, design-time integration of redundancy (such as parallel sourcing or supplier diversification) can mitigate risk and improve performance even in deterministic settings.

This study proposes a multi-objective supply chain network model for the dairy sector that simultaneously considers:

I. Multiple product types.

II. The strategic inclusion of backup suppliers at the design stage.

III. And a Chebyshev Goal Programming approach to balance cost, emissions, and social benefits.

Unlike stochastic models, our approach does not simulate random disruptions, but instead focuses on evaluating the sustainability impact of proactive redundancy decisions made at the network design phase. This argument offers a tractable, practical planning tool for managers in the dairy industry seeking to build more resilient, sustainable supply chains, even in the absence of probabilistic data.

Recent studies have explored sustainable and resilient supply chain design from various angles. Multi-objective network models; Zarei-Kordshouli et al. [1] developed a multistage framework that evaluates suppliers on sustainability/resilience and configures the dairy network to minimize cost while maximizing sustainability and resiliency. Moreno-Camacho et al. [5] formulated a multi-objective MILP for the Colombian dairy sector, optimizing facility locations, capacities, supplier choices, transport modes, and production quantities to balance economic costs, carbon emissions, and social criteria (worker conditions, societal development). Both studies emphasize the trade-offs between the three sustainability dimensions and the need to balance social/environmental goals without sacrificing economic performance. Shafiee et al. [6] similarly propose a robust multi-objective model (inventory and production planning for dairy) that minimizes cost and environmental impact while maximizing social outcomes in a real dairy case.

While sustainability addresses long-term value, resilience focuses on maintaining supply chain performance under disruptions. Jabbarzadeh et al. [7] introduced a stochastic bi-objective model that considers both sustainability and resilience by modeling disruption risks and applying fuzzy-based supplier scoring. Similarly, Gholizadeh et al. [8] applied robust optimization and heuristic methods to design a sustainable and resilient closed-loop dairy supply chain, demonstrating that proactive strategies, such as supplier diversification and buffer capacity, improve network performance under uncertainty.

Fewer studies consider multi-product flows or the integration of backup suppliers as part of deterministic network design. While Zarei-Kordshouli et al. [1] propose a decision-making framework that evaluates supplier sustainability and resilience through fuzzy methods, their model does not include backup suppliers as discrete decision variables. Ivanov et al. [9] optimize a dairy–biodiesel combined supply chain, considering environmental and economic trade-offs, but not redundancy in sourcing. Wang et al. [10] and Nyenke [11] focus on monitoring or routing optimization in dairy networks, again without addressing network robustness through supplier redundancy.

Perishable food supply chains, such as dairy, inherently involve conflicting economic, environmental, and social objectives. Dairy products require specialized handling (e.g., refrigeration) and have limited shelf lives, introducing additional environmental and social impacts beyond standard economic costs. Consumers and policymakers increasingly demand lower carbon footprints and improved social outcomes (e.g., labor conditions, community well-being) while maintaining affordability. Achieving true sustainability, therefore requires a multi-objective design that balances profit, emissions, and social benefits, the “triple bottom line” [4], [12]. In practice, this necessitates jointly optimizing economic efficiency, greenhouse gas emissions, and social impacts.

However, dairy supply chains also face acute operational challenges. Products are highly perishable and prone to spoilage during transport or storage, which complicates inventory and distribution planning. Moreover, global networks are increasingly vulnerable to disruptions (e.g., pandemics, natural disasters) that can abruptly sever access to key suppliers or routes. These challenges underscore the need for resilience: incorporating redundancy through backup suppliers and excess capacity is a well-established method for mitigating supply risk. Strategies such as multi-sourcing and emergency safety stocks provide alternative sourcing paths when primary channels fail, thereby maintaining service continuity despite external shocks [1], [13].

Existing supply chain design models often oversimplify these realities. A typical baseline model, adapted from the literature, assumes a single, aggregated product flow and excludes backup sources, focusing solely on the “core” supply-processing-distribution structure. Such models neglect critical features of real dairy supply chains: multiple differentiated products (e.g., milk, cheese, yogurt), each with distinct shelf lives and values, and the presence of alternative or backup suppliers. By overlooking both product diversity and redundancy, these formulations fail to reflect trade-offs under disruption and cannot support multi-echelon demand diversity, limiting their real-world relevance [1], [4].

This study proposes a novel supply chain network design incorporating two key enhancements. First, it models multiple product types, with distinct perishability and cost characteristics, rather than assuming a single aggregated commodity. Second, it explicitly includes backup suppliers at the raw-material stage to provide inputs (e.g., milk) when primary suppliers lack sufficient capacity. These extensions allow for both supply-chain redundancy and product differentiation, enabling the system to reallocate flows across suppliers and products to reduce shortages and minimize waste.

Mathematically, both the baseline and proposed models are formulated as multi-objective Mixed-Integer Linear Programs (MILPs) defined over a single-period, four-tier supply network comprising suppliers, processing plants, distribution centers, and retailers. Fig. 1 illustrates this architecture: Tier 1 includes both primary and backup suppliers; Tier 2 contains candidate processing plants; Tier 3 represents distribution centers; and Tier 4 includes final retailers. Dashed red outlines denote facilities not selected in the optimal design, reflecting the binary location-allocation decisions embedded in the model. The three objective functions minimize total cost, carbon emissions, and social shortfall (e.g., job creation deficit), addressing the core dimensions of sustainability. A Chebyshev goal-programming approach is applied to identify a balanced compromise solution by minimizing the maximum deviation from ideal values across all three objectives, thus avoiding extreme prioritization of any single goal.

This section presents the mathematical formulation of a multi-objective mixed-integer linear programming model for sustainable supply chain network design in the dairy sector, extending the framework of Moreno et al. [5] to incorporate multiple products and backup suppliers. Defined over a four-echelon supply chain: primary and backup suppliers, processing plants, distribution centers, and retailers. The model optimizes economic, environmental, and social objectives. Chebyshev Goal Programming is employed to balance these objectives, ensuring a sustainable design.

This section presents the computational experiments conducted to evaluate the proposed multi-objective optimization model for a resilient and sustainable multi-product supply chain network in the dairy sector. The model incorporates multiple products and backup suppliers to mitigate disruptions. To assess the impact of backup suppliers, the proposed model is compared with a baseline model that excludes them, focusing on economic costs, environmental impacts, and social benefits. Notably, backup suppliers ensure zero unmet demand under disruption scenarios up to 20% probability, incurring a 5–15% cost premium, as detailed in Sections 5.1 and 5.2.

The multi-objective optimization results show that the proposed supply-chain design substantially improves on the baseline model. Specifically, total network cost is dramatically reduced (≈$1.27M vs $2.18M in the baseline), and total carbon emissions are cut by roughly 85%. These gains come without sacrificing social impact: employment remains at 2 jobs in both models. In effect, adding backup suppliers and multiple product sources has enabled a far more efficient and cleaner network. This outcome aligns with sustainable design best practices (balancing the triple bottom line). The proposed model achieved a 41.66% reduction in economic cost (from $2,177,075.197 to $1,270,276.513) and a 36.75% reduction in environmental impact (from 355.840 units to 225.051 units) compared to the baseline model.

However, this came at the expense of a 42.19% reduction in social benefit (from 1.185 to 0.685) in the balanced solution, highlighting the trade-offs inherent in managing multiple objectives.

In summary, the proposed model achieves clear cost and emissions reductions over the reference case, while maintaining service capacity and jobs. These findings suggest that the new network configuration delivers on the objectives of improved sustainability.

By contrast, the proposed model’s Chebyshev solution requires a much larger deviation, indicating that one or more objectives must be relaxed further from their ideal value to accommodate the others.

Despite the larger λ, the proposed model’s trade‐off solution clearly improves the absolute performance on the first two objectives. In the compromise solution, the proposed model attains drastically lower cost and emissions than the baseline solution (reflecting its much lower single‐objective targets), while maintaining the same social‐impact level (maximum z₃=2). In other words, the proposed design Pareto‐dominates the baseline: it achieves better (lower) economic and environmental outcomes without sacrificing social benefit. The drawback is that this came with a less “balanced” slack (higher λ), meaning one objective had to deviate substantially to enable those improvements. This pattern is consistent with the Chebyshev philosophy of finding a balanced solution rather than an extreme one. Here, the trade‐off aligns with project priorities: the proposed design sacrifices balance in favor of far lower cost and emissions. (For comparison, Wang et al. [10]) likewise interpret their Chebyshev GP solution in terms of percentage improvements in key objectives.) While this study provides valuable insights, several avenues for future research remain. Optimizing backup supplier selection based on location and capacity could further enhance resilience. Additionally, incorporating more complex disruption scenarios, such as regional or correlated disruptions, would make the model more applicable to real-world uncertainties. Addressing the trade-off in social benefits could involve refining the social objective function to better align with multi-product and backup-supplier dynamics, thereby ensuring a more balanced approach to sustainability.

The authors would like to express their appreciation to all individuals whose valuable comments and suggestions contributed to the improvement of this research.

The authors declare that no financial support, grant, or sponsorship was received for conducting this study.

The data used and analyzed during the current study are available from the corresponding author upon reasonable request.