Wheat and flour are central to the global food system, serving a crucial dietary function worldwide. The Supply Chain (SC) for these commodities is characterized by its fragility and complexity, influenced by a combination of intrinsic and extrinsic factors. Bread, a staple food for millions globally, represents the primary output of this SC. The consistent availability of a resource is paramount for global food security. Any disruption or shortage in its supply can precipitate widespread repercussions, impacting not only economic stability but also social and political equilibrium. The significance of the wheat and flour SC is paramount; even minor disruptions within it can precipitate considerable ramifications for both populations and governmental stability. Therefore, meticulous attention to the inherent challenges confronting this SC is imperative to safeguard a consistent food supply and avert severe socio-economic repercussions.

The crucial role of wheat and its derivatives as a national dietary food highlights the necessity for strategic planning for its Supply Chain Management (SCM) and provision. A foundational step toward refining management practices and facilitating informed decision-making, thereby boosting efficiency and productivity, involves comprehending the prevailing trends within this sector. In contemporary times, the nation's wheat requirements are fulfilled by combining internal cultivation and foreign procurement. Part of the domestically produced wheat is utilized by agriculturalists for rural bread production, seed purposes, and livestock feeding. The outstanding quantity is procured by the government through established guaranteed price mechanisms. Following its procurement, wheat is transferred to designated storage facilities. Imported wheat, which typically arrives at the nation's ports, is subsequently distributed throughout the provinces [1]. Each year, a significant quantity of grain is moved from purchasing centers and ports to these storage facilities, then to our mills and end-consumption points. The grain SC can be analyzed from both strategic and operational perspectives. Long-term decisions primarily involve selecting suppliers for imported grain [1]. Conversely, mid-term decisions focus on optimizing the quantity of imports, managing the flow of both domestic and imported wheat, developing storage strategies, overseeing the production of wheat-based products, and allocating resources to meet demand effectively [1-2].

Maintaining the stability of this vulnerable SC demands both rigorous monitoring and strategic foresight. A comprehensive understanding of various influencing factors, both internal and external, is crucial. These factors encompass natural disasters, geopolitical instabilities, economic sanctions, and global market price volatility. To enhance the overall resilience of this system, it is essential to incentivize domestic agricultural production of wheat, thereby mitigating reliance on imported grains for this critical commodity. As previously emphasized, these products are integral to food security, yet their import management is frequently underestimated. By fostering domestic production, we can effectively mitigate the risk of shortages and ensure a consistent supply of essential food products.

This research aims to develop a stochastic programming model for redesigning the wheat and flour SC. The primary objectives are to determine the optimal locations for constructing mills and to optimize the network flow. Notably, this study utilizes a two-stage stochastic modeling approach, which is an infrequent application within this specific research context. The main goals of the paper include:

I. Finding the best locations for mill construction to improve efficiency and lower transportation expenses. II. Catering to two categories of flour customers (essential and non-essential) and wheat customers to satisfy varied market needs; III. Focusing on the use of domestic wheat for mills while restricting imports to certain conditions to decrease reliance on foreign sources and bolster local production.

IV. Implementing the model in a real-world case study in Iran to evaluate its effectiveness in actual market scenarios.

V. Employing scenario-based stochastic programming, backed by historical data on wheat farming and current demand, to deliver the best solutions and mitigate risks; VI. Reducing expected costs and enhancing the sustainability of the SC; VII. Assessing the value of imports and identifying the most efficient import ports to cut expenses and enhance the distribution network's efficiency.

The present study proposes a comprehensive and practical solution to enhance the wheat and flour SC within Iran.

This paper is structured as follows. Section 2 provides a comprehensive overview of the theoretical background of the wheat and flour SC. Section 3 meticulously defines the problem and its underlying assumptions, subsequently presenting the deterministic mathematical model. Following this, a two-stage scenario-based stochastic model for the wheat and flour SC is formulated. Section 4 is dedicated to the analysis and discussion of the model's results. Finally, Section 5 offers managerial recommendations, presents conclusions, and suggests avenues for future research.

Research concerning wheat SC and its derivative products remains limited. To comprehensively address existing knowledge gaps, prior research studies have been categorized into three principal domains: 1) Agricultural food SCs (AFSCs), 2) uncertainty in SCs, and 3) wheat and flour SCM. Each section will provide an in-depth examination of its respective topic, offering insights into the current research landscape and identifying avenues for future investigation.

The wheat and flour SC is fundamental to both food security and economic stability. The model proposed in this research aims to optimize this critical SC by effectively managing its central components, encompassing farms, import points, silos, flour mills, warehouses, and various customer types. A core objective of the model is to identify the optimal locations for new silo construction strategically. Wheat, sourced from either domestic cultivation or international imports, undergoes initial transportation to silos for storage. Following storage, it is distributed to key consumers, including the agricultural sector and animal feed producers. Subsequently, the wheat is transferred to flour mills for processing into flour, which is then held in warehouses. Essential flour consumers, such as bakeries producing staple food products, receive priority in allocation. Any surplus flour is then directed to non-essential consumers, including confectionery manufacturers. A visual representation of this problem overview is provided in Fig. 1.

This model extends beyond merely managing storage and distribution; it comprehensively optimizes the transportation of wheat from its points of origin, including farms and import locations, to silos and subsequently to flour mills situated across various regions. Since flour is a staple food, mills and warehouses are geographically dispersed nationwide. The model ensures that these facilities operate at maximum efficiency to meet demand. Furthermore, it assesses the necessity of constructing new silos to enhance overall storage capacity.

Safaei et al. [37] previously addressed this problem using a deterministic model. Building upon that work, the current study introduces a stochastic model to address the same problem.

Uncertainty in SC and logistics network design can be categorized into two primary categories: “Operational parameter uncertainty” and “network disruption uncertainty.”

Operational parameter uncertainty: This type refers to the typical fluctuations inherent in business processes, such as unpredictable shifts in demand or variations in the raw materials supply. These factors can significantly challenge SCM [38].

Network disruption uncertainty: This type encompasses infrequent events characterized by a low likelihood of occurrence but possessing substantial consequences for network performance. These disruptions can originate from natural disasters, such as floods and earthquakes, or human-induced factors, including wars and terrorist attacks. Such occurrences have the potential to impede the SC severely, thereby underscoring the critical need for strategic planning to bolster network resilience [38].

In contrast to numerous SCs where demand uncertainty significantly impacts operations, specialists in this domain contend that demand volatility is not a primary concern for this particular study. Given that wheat and flour are staple commodities, their consumption is directly correlated with per capita consumption, which is mainly dependent on population size. Consequently, the demand for these products remains relatively stable and is therefore not treated as an uncertain parameter within this model.

Instead, two principal sources of uncertainty considerably influence this SC:

I. Wheat loss rate in the field, which is affected by climatic conditions (such as flood, earthquake, and famine) and internal variables, culminating in fluctuations in domestic wheat production.

II. Import prices, which are influenced by global events (such as wars, climate conditions, economic sanctions, and geopolitical tensions), are a substantial uncertainty variable in the model.

Considering the various sources of uncertainty inherent in the system, this study adopts a two-stage stochastic programming approach. In the first stage, the model specifies the optimal locations for silos. Subsequently, the second stage focuses on optimizing flow allocation decisions across the SC under various scenarios. The objective function in this model aims to minimize the expected total cost, encompassing both operational expenses and initial capital investments across several uncertainty scenarios. The set S denotes the generated scenarios that capture the uncertainty in yield rates and import costs. Table 2 outlines the six probable scenarios taken into account in this study.

Min Z1 = ∑ ∑ fit Piit + ∑ ∑ fjt yjt + ∑ ∑ ∑ Pas fkt ykts + ∑ ∑ flt

i t j t k t s l t

+ ∑ ∑ ∑ ∑ Pas Cijt Xijts + ∑ ∑ ∑ ∑ Pas Cjkt Xjkts

i j t s j k t

+ ∑ ∑ ∑ ∑ Pas Cklt Xklts + ∑ ∑ ∑ ∑ Pas Xklts Ωkt

k l t k l t

4 5 (1)

+ ∑ ∑ ∑ ∑ Pas Clat Xlats + ∑ ∑ ∑ ∑ Pas Clbt Xlbts

l a t s l b t s

+ ∑ ∑ ∑ ∑ Pas Cjwt Xjwts + (∑ ∑ ∑ Cpjt + Ims) ∑ ∑ ∑ PasXpjts

j w t s p j t p j t 1 3 2

+ CC (∑ ∑ ∑ Pas Lats + ∑ ∑ ∑ Pas Lwts) + cb ∑ ∑ ∑ Pas Lbts

a t s w t s b t s

The objective function, as formalized in Eq. (1), is designed to reduce anticipated total costs. These costs encompass both fixed and variable expenditures, such as management expenses per hectare of cultivated land, construction costs for new silos, operational and production costs for active flour mills, warehouse management costs, transportation costs across all network levels, import costs, and shortage costs.

Piit(1 − αis) ≥ ∑ Xijts , for all i, t,

yptsPipt ≥ ∑j Xpjts, for all p, t, s (3)

1 7 6 2

∑i Xijts + ∑p Xpjts ≥ ∑w X + ∑k X , for all j, t, s, (4)

jwts jkts 3 4 5

∑k X ≥ ∑a X + ∑b X , for all l, t, s, (5)

klts lats lbts

rr ∑j X ≥ ∑l X , for all k, t, s, (6)

jkts klts

∑l X = Dat − Lats, for all a, t, s, (7)

lats

∑ Xlbts ≤ Dbt − Lbts, for all b, t, s, (8)

∑j X = Dwt − Lwts, for all w, t, s, (9)

jwts 6 2 T 1

∑w X + ∑k X ≤ Capj ∗ ∑t=1 yjt, for all j, t, s, (10)

jwts jkts

rr ∑j X ≤ Capk, for all k, t, s, (11)

jkts

∑l X ≤ Capl, for all l, t, s, (12)

klts 6 2 T 1

∑w X + ∑k X ≥ SS ∗ ∑t=1 yjt, for all j, t, (13)

jwt jkt

∑t yjt ≤ 2, for all j, (14) ∑j yjt = k, for all t = 1, (15) ∑T−t1 yjt = 0, for all t, (16) ∑s Pas = 1, (17)

1 2 3

yjt, y , ypts ∈ {0,1}, for all i, k, p, t, (18)

kts 1 2 3 4 5 6 7 1 2 3

Xijts, Xjkts, Xklts, Xlats, Xlbts, Xjwts, Xpjts, Lats, Lbts, Lwts ≥ 0, for all i, j, k, l, a,

(19)

b, w, t, s.

The constraints within this mathematical model are formulated to augment the expected value of the wheat and flour SC across various scenarios. These constraints specifically address critical aspects of production, storage, transportation, and processing. Their inclusion ensures the efficient flow of wheat and flour while simultaneously sustaining SC balance and operational feasibility. Eq. (2) represents the farm output constraint for each scenario, which incorporates varying loss rates. This constraint stipulates that the volume of wheat supplied from each farm must be equivalent to the quantity of healthy wheat harvested from the agricultural land. Furthermore, the import constraint Eq. (3) ensures that the total volume of imported wheat does not surpass the annual import quota established by regulatory bodies. This phenomenon occurs when permitted within various scenarios. To maintain consistency in the quantity of goods entering and exiting each SC level, several flow balance constraints are incorporated. Eq. (4) ensures that the wheat dispatched from silos does not surpass the available stock. Similarly, Eq. (5) imposes a comparable constraint on flour, mandating that the outflow from storage cannot exceed the existing inventory level. Constraint regarding the wheat-to-flour conversion Eq. (6) establishes the connection between the quantity of processed wheat and the resulting flour produced, according to the conversion rate.

To satisfy customer needs, the supply of essential flour and non-essential flour and wheat, respectively, is governed by demand fulfillment constraints, Eqs. (7)-(9). Due to the restricted capacity of each SC facility, Eq. (10) guarantees that the total amount of wheat stored in a silo does not surpass its storage limit, provided that the silo was built in the current or prior periods. Moreover, Eq. (11) guarantees that the quantity of wheat processed in flour mills remains within their production capacity. Concurrently, Eq. (12) restricts the volume of flour stored in warehouses to their maximum capacities. To bolster SC resilience, a minimum inventory constraint Eq. (13) mandates that newly built silos sustain a safety stock equivalent to two months' average consumption rate. Furthermore, the restriction on silo construction, Eq. (14), guarantees an even allocation of storage facilities throughout the provinces, adhering to government regulations. The initial condition constraint Eq. (15) specifies the number of silos present at the start of the first period. At the same time, Eq. (16) prohibits the construction of silos in the later stages of the planning timeline. The total probabilities for scenarios must not exceed one, and Eq. (17) regulates this. Ultimately, the nature of the decision variables is precisely defined by variable constraints Eq. (18) and Eq. (19). Eq. (18) designates binary variables (0 or 1), specifying whether a silo is constructed, a flour mill is operational, or wheat imports are allowed. Eq. (19) specifically mandates that all other variables, including quantities of wheat and flour, maintain continuous and non-negative values. Collectively, these constraints are designed to guarantee the efficient wheat and flour SCM, thereby achieving particular objectives, such as cost minimization, enhanced operational efficiency, and the secure and consistent supply of these crucial products.

Scenario 1 High wheat loss rate in the field, high import prices 0.09 Scenario 2 High wheat loss rate in the field, typical import prices 0.21 Scenario 3 Typical wheat loss rate in the field, high import prices 0.15 Scenario 4 Typical wheat loss rate in the field, typical import prices 0.35 Scenario 5 Low wheat loss rate in the field, high import prices 0.06 Scenario 6 Low wheat loss rate in the field, typical import prices 0.14

The present research presents a model designed to optimize the wheat and flour SC network. The model's core function is to determine the optimal quantity of wheat to be imported from various international sources, while simultaneously ensuring the maximal utilization of domestic wheat production. By incentivizing and facilitating increased local wheat cultivation, this model effectively contributes to reducing reliance on imports for this critical grain. The model additionally enhances flour production efficiency and optimizes product distribution across various SC tiers, all while effectively managing uncertainty. The core objective of this model is to satisfy demand at the lowest possible cost, even when confronted with challenging conditions across diverse scenarios. The analysis incorporates multiple variable costs, specifically those associated with wheat cultivation, imports, flour production, transportation, and potential shortages. The model is implemented using GAMS software, thereby precluding the necessity of employing heuristic methods. This study reveals that about 60% of the total SC costs are attributable to distribution, production, transportation, and shortages. The remaining 40% of the costs are associated with silo construction. From a strategic perspective, 40% of the total costs are linked to long-term decisions, whereas 60% pertain to operational expenses. These cost calculations were performed over nine years, offering a comprehensive understanding of the SC's cost structure.

The second aspect of silo construction and distribution focuses on strategically establishing facilities to supply wheat for flour production across all provinces. This distribution plan is crucial for defining the service area of each silo. Despite the considerable transportation distances for some silos, the model's design strategically identifies which provinces, particularly those equipped with two silos, will serve as primary wheat suppliers, thereby ensuring a stable supply network. Consequently, the model recommends the construction of 39 silos for optimal operational efficiency within the SC.

Regarding import strategies, the model demonstrated a clear divergence based on scenario characteristics. In odd-numbered scenarios, characterized by elevated transportation and import costs, the model opted to forego imports and instead manage shortages for non-essential customers. Conversely, in even-numbered scenarios, the decision to import was directly contingent upon the domestic production level. Analysis reveals that the shortages observed in odd-numbered scenarios significantly exceeded those in even-numbered scenarios. Notably, 2015 exhibited a substantially higher shortage volume compared to other years, primarily attributable to the incomplete construction of silos. In contrast, subsequent years experienced relatively consistent levels of shortages. Amirabad Port, situated in northern Iran, and Imam Khomeini Port, located in the south, are determined as the principal import hubs. Wheat imports constitute less than 15% of the total supply, significantly mitigating reliance on foreign sources. This ratio specifically pertains to essential goods, with a minor proportion allocated to non-essential items. This presents a worthy opportunity for private enterprises to supply non-essential flour to the food industry.

This research received no external funding.

Sufficient data is available upon request.

No potential conflict of interest was reported by the authors.