Access to essential medications like metformin in Iran’s healthcare system is enhanced through quantity discounts and government subsidies, ensuring robust cash flow and preventing financial distress. The pharmaceutical supply chain, encompassing production, distribution, and sales, is critical for community health [1]. Effective coordination among interdependent participants is vital to improve profitability and ensure reliable access to medications [2].

In decentralized supply chains, participants often prioritize individual gains, reducing overall efficiency. Notable contracts include buy back [3], revenue sharing [4], sales rebate [5], quantity flexibility [6], trade credit [7], quantity discount [8]. These serve to stimulate demand and manage it effectively. Unlike demand management tools that focus on forecasting, coordination contracts incentivize alignment [9].

Governments are crucial in supply chain coordination, supporting R&D [10], market regulation [11], pricing [12], and welfare [13]. Interventions incentivize members via covering investment costs, subsidizing production, expanding markets through advertising, offering low-interest loans, providing tax exemptions, and paying tariffs as subsidies [13]. In Iran, where drug prices are regulated, multiple retailerss produce metformin, requiring non-pricing strategies like quantity discounts to gain market share [14]. Government subsidies and policies support equitable access, reduce financial burdens, and strengthen the healthcare system [15]. This study examines how quantity discounts and subsidies optimize coordination in Iran’s metformin supply chain, improving accessibility and public health.

preventing financial distress and ensuring robust cash flow through quantity discounts and government subsidies. This study explores a two-tier pharmaceutical supply chain in countries like Iran, involving distributors and retailers, to optimize coordination. Government-insurer collaboration sets medication coverage and reimbursement rates, with subsidies reducing patient costs and boosting equity [16]. Misaligned financial flows between suppliers and insurers can cause bankruptcies, disrupting drug access quantity discounts align stakeholders, enhancing profitability and stability. This paper’s contributions include:

I. Pioneering analysis of quantity discounts and subsidies for supply chain coordination in Iran’s pharmaceutical sector.

II. Incorporating incentive contracts’ impact on demand, considering competing distributors’ terms.

III. Highlighting government-insurer policies ensuring affordable medication access. Analytical models show these strategies foster collaboration, reduce costs, and ensure equitable access to high-quality medications, offering insights for Iran’s supply chain.

Section 2 defines the problem and presents mathematical models for supply chain coordination. Section 3 compares contracts used for coordination. Section 4 conducts numerical experiments and sensitivity analyses on contract parameters, providing managerial insights. Section 5 summarizes findings and concludes.

preventing financial distress and ensuring robust cash flow through quantity discounts and government subsidies. This study analyzes a two-stage pharmaceutical supply chain in countries like Iran, involving a distributor and retailers (pharmacies) for a specific medication. Multiple distributors supply drugs to pharmacies under varying contractual agreements. Government-insurer collaboration sets medication coverage and reimbursement rates, with insurers covering part of the costs and patients paying the rest within a specified timeframe (Fig. 1). Misaligned financial flows between suppliers and insurers can cause financial strain, disrupting drug access and patient health outcomes. This research explores quantity discount contracts to mitigate coordination challenges, enhancing accessibility and supply chain stability. The paper details the assumptions and notations used, and provides additional assumptions and notations as needed.

Access to essential medications like metformin in Iran’s healthcare system is enhanced by preventing financial distress through quantity discounts and subsidies. This section outlines optimizing quantity discount rates in a two-stage pharmaceutical supply chain using the Stackelberg model. It proves solution uniqueness, models retailers-distributor interactions, and validates for accuracy (Fig. 2). The approach, integrating subsidies, maximizes chain profit and ensures equitable drug access in regulated markets.

In this section, a number of numerical examples are solved and the related results are analyzed. Let’s assume T=180 day (≈ 0.49 year), c = $30/unit, w = $50/unit, p = $100/unit, ϑ = 70%, Om = $60/order, Od = $60/order, h = $3 unit/year, α = 565⁄year and m=1 year. Deterioration rate is θ(t) = 0.01 t0.01 and η1 .2 and β1 have uniform distribution on the interval (0,1). It is assumed that there are two substitutions, and λs1, 2 = 80%. Parameter values are hypothetical, based on typical ranges in Iran’s pharmaceutical market, to illustrate the model’s applicability in regulated settings (Centralized and decentralized functions are available upon request).

The sensitivity analysis in Table 1 of the study illustrates the impact of key parameters on profit and order quantity across centralized, non-coordinated, and coordinated (quantity discount) scenarios in Iran’s metformin supply chain. Variations in potential demand (α) significantly influence profit and order quantity (Q*), with a ±50% change in α increasing coordinated scenario profits from $10,875 to $11,125 and Q* from 10,422.67 to 31,268.01 units, highlighting the importance of demand stimulation through marketing. The replenishment period (T) directly affects Q*, with longer periods increasing order quantities but potentially reducing profits due to higher costs (e.g., centralized scenario profit drops from $5,855 to $17,565). Parameters like wholesale price (w) and production cost (c) show limited impact on Q* in centralized and non-coordinated scenarios due to profit balancing between retailers and distributors, while selling price (p), set by the government, linearly boosts profits across all scenarios. The coordinated scenario demonstrates superior flexibility in leveraging quantity discounts, particularly with higher discount sensitivity (β1), though constrained by competitor actions and government regulations, underscoring the need for strategic optimization of manageable variables like α and β1 to enhance profitability and drug accessibility.

preventing financial distress and ensuring robust cash flow quantity discounts and government subsidies. This study demonstrates that not all discounts are profitable; each must be carefully evaluated to avoid mismatched cash flows, which may lead to financial distress and potential bankruptcy. In a two-tier pharmaceutical supply chain involving government, insurers, and companies under price controls, quantity discounts align stakeholders, reducing inefficiencies and boosting profitability. Government subsidies stabilize prices and enhance market access, addressing financial challenges. Analytical models show these strategies optimize supply chain profits and collaboration, ensuring equitable access to high-quality medications. These insights guide policymakers to strengthen public health. Future research could explore dynamic pricing, multi-product supply chains, or digital technologies to further improve coordination and accessibility in Iran’s pharmaceutical sector.