In recent years, the design of sustainable closed-loop supply chain networks has emerged as a major stream of research in the advanced logistics and supply chain management literature. This growing interest is largely driven by increasing environmental concerns, regulatory pressures, resource scarcity, and the need to incorporate reverse flows into conventional supply chain structures. Within this body of research, several studies have attempted to address the integration of sustainability dimensions, uncertainty, and operational complexity across different industrial contexts, including pharmaceutical, steel, and automotive industries. Sazvar et al. [7] proposed a multi-objective programming model for the design of a PSC network under crisis conditions. Their network consisted of three facility levels, namely production plants, warehouses, and demand centers, and the model simultaneously considered economic, environmental, and social objectives. To capture the uncertainty associated with pharmaceutical demand, multiple scenarios were incorporated into the formulation. The proposed model was solved using the epsilon-constraint method, allowing the authors to generate trade-off solutions among the conflicting sustainability objectives.

Similarly, Savadkoohi et al. [8] developed a mathematical programming model for the design of a green and reliable closed-loop PSC network in which environmental sustainability, reverse flows, and uncertainty in demand, return rates, and facility capacity were simultaneously incorporated. To address uncertainty, they adopted an enhanced chance-constrained stochastic programming approach, which provides more effective control over the level of risk in comparison with the classical chance-constrained formulation. Their model included multiple types of facilities, such as collection, recycling, and remanufacturing centers, and captured both strategic location decisions and tactical product flow decisions within a unified framework. Pourjavad et al. [9] investigated closed-loop supply chain network design from a sustainable development perspective by proposing a fuzzy multi-objective mixed-integer linear programming model. Their study focused on minimizing total costs, reducing environmental impacts, and maximizing social benefits over a multi-period planning horizon. To cope with uncertainty in parameters such as return rates and facility capacities, a fuzzy approach was employed. The model was solved using a genetic algorithm, and the quality of the obtained solutions was further validated through comparison with the Non-dominated Ranked Genetic Algorithm (NRGA). The network structure in their study comprised four echelons in the forward logistics process and four echelons in the reverse logistics process, thereby reflecting a relatively comprehensive representation of closed-loop operations. Li et al. [10] examined an integrated location–inventory problem in a closed-loop supply chain that involved a hybrid production–recycling center, distribution–collection centers, and customers. In their stochastic-demand setting, the decisions related to facility location, customer allocation in both forward and reverse channels, and inventory levels were optimized simultaneously. The model explicitly incorporated various cost components, including facility opening costs, transportation costs, inventory holding costs, safety stock costs, return processing costs, and shortage penalties. To solve this complex problem, the authors designed a hybrid heuristic algorithm based on differential evolution and genetic algorithms. Easwaran and Üster [11] presented a mixed-integer programming model for the design of a multi-product closed-loop supply chain network in which forward and reverse flows were integrated under limited facility capacities. In their formulation, hybrid facilities for manufacturing/remanufacturing and distribution/collection were considered, and the model aimed to minimize the total costs of facility location, processing, and transportation. To enhance computational tractability, the authors employed a Benders decomposition approach augmented with strengthened cuts, which improved the efficiency of the solution procedure for large-scale instances. Beyond the pharmaceutical sector, Pourmehdi et al. [12] proposed a multi-objective mathematical model for designing a sustainable closed-loop supply chain network in the steel industry. Their formulation simultaneously addressed economic, environmental, and social dimensions, with environmental criteria including energy consumption, water usage, and CO2 emissions, while social performance was measured through job creation. Using scenario-based stochastic programming and preemptive fuzzy goal programming, the authors modeled uncertainty in market demand and scrap supply. They also investigated the effects of production technology shifts and the conversion of retail facilities into hybrid centers on the overall network configuration. Abbasi et al. [13] developed a mathematical model for the design of a green closed-loop supply chain network in the automotive industry during the COVID-19 pandemic. Their five-echelon structure included suppliers, plants, distribution/collection centers, recycling/disposal centers, and customers. By using a multi-objective integer programming model and the weighted-sum method, they simultaneously optimized conventional and health-related costs while minimizing CO2 emissions in a system characterized by both forward and reverse flows. This study highlights how crisis conditions and public health requirements can alter the priorities and design principles of sustainable supply chain systems.

In the context of pharmaceutical distribution, Jalal et al. [14] proposed an integrated location–transportation model for PSC network design. Their network consisted of production plants, distribution centers, and retailers. By combining multi-scale time planning and robust optimization, the model captured decisions related to facility location, product flows, transportation fleet composition, security requirements, and taxation policies under demand uncertainty. The proposed approach was tested on real-world data using a Fix-and-Optimize algorithm, demonstrating its practical applicability in complex and uncertain decision environments. Abbasi et al. [15] introduced a bi-objective optimization model for the design of reliable supply chain networks in the context of 3PL companies. Their four-level network included suppliers, consolidation hubs, distribution centers, and customers. Considering the perishability of pharmaceutical products and the possibility of disruptions at hubs and distribution centers, the model incorporated resilience strategies such as backup facility deployment, facility fortification, and multiple sourcing. To handle uncertainty related to disruption probabilities, a credibility-based fuzzy programming approach was employed. A noteworthy aspect of this work is the explicit modeling of the direct relationship between facility failures and product deterioration, which adds significant realism to the reliability analysis. Zandkarimkhani et al. [16] developed a bi-objective mixed-integer programming model for the design of a multi-product, multi-period PSC network for perishable drugs. Under demand uncertainty, they simultaneously modeled location, inventory, and routing decisions in a three-echelon network composed of suppliers, distribution centers, and customers. To solve the problem, they proposed a hybrid approach combining fuzzy goal programming and probabilistic constraints. The effectiveness of the model was evaluated using real data from the Avonex pharmaceutical distribution chain in Tehran, thereby providing empirical support for the applicability of the proposed framework. Likewise, Zandieh et al. [17] designed a multi-objective model for a pharmaceutical distribution network based on the three pillars of sustainability: economic, environmental, and social performance. Their model was intended to support managers in making both strategic and technical decisions concerning the pharmaceutical distribution system, particularly with respect to the configuration of central and local distribution centers and the associated product flows. By minimizing costs, maximizing social welfare, and reducing adverse environmental effects, the model aimed to guide decision-makers toward more sustainable network configurations.

Overall, the existing literature demonstrates substantial progress in the development of sustainable and closed-loop supply chain network models. Researchers have increasingly incorporated uncertainty, reverse logistics, resilience, and multi-objective optimization into their formulations. However, despite these valuable contributions, several important research gaps remain. First, while some studies have considered reverse flows in PSCs, the integration of return disposition policies—such as resale, donation, and disposal—into the structural design of the network has received limited attention. Second, although 3PL providers have been recognized as important actors in improving flexibility and responsiveness, their role is often treated either as an external operational option or merely as an evaluation criterion, rather than as an endogenous decision variable within a network design model. Third, the concept of hybrid or multi-purpose facilities, capable of simultaneously supporting forward and reverse operations, has not been sufficiently explored in PSC settings in combination with sustainability and 3PL selection. These gaps indicate the need for a more integrated and realistic modeling framework capable of jointly addressing facility configuration, reverse logistics policy, sustainability objectives, and outsourcing decisions in pharmaceutical closed-loop supply chains.

Despite the significant growth in the literature regarding sustainable, Closed-Loop Supply Chain Network Design (CLSCND), a critical examination of existing methodologies reveals persistent limitations. Most contemporary models rely on static or pre-defined network configurations, or alternatively, treat 3PL providers as exogenous parameters—effectively decoupling them from the core network optimization logic. This research addresses this substantial structural gap by introducing a novel, integrated mathematical framework where the strategic utilization of 3PL services is internalized as an endogenous decision variable, inherently linked to the network’s objective function and operational constraints.

The proposed model transcends conventional formulations by simultaneously optimizing facility location, flow allocation, inventory policies, and transportation routing. Crucially, it provides, for the first time, a dynamic mechanism for operational selection between two distinct logistical paradigms: Leveraging external 3PL-managed warehousing or deploying in-house, multi-purpose facilities equipped with transshipment capabilities. This flexibility allows the network to adapt to fluctuating demand and cost landscapes with unprecedented agility.

Furthermore, our model offers a sophisticated approach to reverse logistics. Rather than reducing the complexities of returned pharmaceuticals to simple recycling or disposal, we evaluate a multi-dimensional disposition strategy. The model incorporates a rigorous trade-off analysis between two conflicting policies: pharmaceutical donation, which generates positive social impact and potential tax advantages, versus secondary market resale, which serves as a vital revenue stream for economic optimization.

Finally, the architecture of our model treats the configuration of hybrid distribution/collection facilities as a primary decision variable. This ensures that the model systematically evaluates the cost-capacity trade-offs inherent in choosing between the capital-intensive construction of dedicated, single-purpose facilities versus the strategic, multi-purpose integration of existing infrastructure. By aligning economic profitability with social imperatives and environmental sustainability, this framework provides decision-makers with a robust, scientifically grounded tool for navigating the complexities of modern PSCs, thereby bridging the divide between theoretical optimization and real-world operational reality.

For modeling the defined network, the symbols are given in Table 1, and the model is written below.

hk Transportation cost of product type ẑ ∈ {i,p} from node z to node z′ using vehicle type Trz,z̀,z ̂,k hₖ operated by 3PL provider k

Techp

Prm,p Unit production cost of pharmaceutical product p at plant m using technology Techₚ

Techp

Fm,p Fixed cost of establishing plant m to produce product family p with technology Techₚ Fz H Fixed establishment cost of facility z ∈ {D, HDCC, CC} with capacity level H Szp Inventory holding cost of product p at facility z ∈ {D, HDCC, WARₖ} Bt Available budget for raw material procurement in period t ∂t Bank interest rate applied to financial loans in period t ABCt Maximum bank credit available for raw material procurement in period t SMSPpt Selling price of pharmaceutical product p in the secondary market during period t HYhdcc Hybridization cost of a distribution center hdcc HPLk Contracting cost for collaboration with 3PL provider k ICz,p Inspection cost of product family p at facility z ∈ {CC, HDCC} DCCdc,p Disposal cost of product p at disposal center dc β Tax rate applied to pharmaceutical product sales SHCc,p,t Shortage penalty cost of product p for customer c in period t SPpt Unit selling price of product p in period t Environmental Parameters hk CO₂ emission rate generated by transporting one unit of product per unit distance using CE vehicle type hₖ of 3PL provider k Operational Parameters TPRi,p Conversion coefficient of raw material i into pharmaceutical product p capH z Capacity of facility z at capacity level H TPRi,s Supply capacity of supplier s for raw material i caph kk Capacity of vehicle type hₖ owned by 3PL provider k dc,p,t Demand of customer c for product p in period t αp,c Return rate of product family p from customer c SSd,p Safety stock level of product p at distribution center d SShdcc,p Safety stock level of product p at hybrid distribution center hdcc γp Proportion of returned pharmaceutical products p that remain usable for donation or secondary market resale M A sufficiently large positive constant (Big-M parameter) Social Parameters FJz H Number of fixed jobs created when facility z is established with capacity level H VJz H Number of variable jobs generated when facility z operates at capacity level H URz Unemployment rate in the region where facility z is located Decision Variables Techp Binary variable equal to 1 if plant m is established to produce product p using xmp technology T echₚ; 0 otherwise yz H Binary variable equal to 1 if facility z is established with capacity level H; 0 otherwise yWark Binary variable equal to 1 if the warehouse of 3PL provider k is utilized; 0 otherwise zhdcc Binary variable equal to 1 if hybridization is applied to distribution center hdcc; 0 otherwise ys Binary variable equal to 1 if supplier s is selected; 0 otherwise yk Binary variable equal to 1 if 3PL provider k is used for transportation; 0 otherwise Iz,p,t Inventory level of usable product p at facility z in period t I ̂z,p,t Inventory level of unusable returned product p at facility z in period t hk Quantity of product type ẑ transported from node z to node z′ by vehicle hₖ of 3PL Qz,z̀,z ̂,k,t provider k in period t BCt Bank credit received for raw material procurement in period t SHc,p,t Unmet demand (backorder) of product p for customer c in period t Techp Techp H1 H1 H2 H2

c1 = ∑ F x + ∑ Fd yd + ∑ Fhdccyhdcc + ∑ Fcc H3ycc H3 (1)

m,p mp m,p,Techp d,h1 hdcc,h2 cc,h3 Wark War

+ ∑ Fk y k + ∑ HYhdcczhdcc + ∑ HPLkyk + ∑ Fsys

k,Wark hdcc k s Wark

+ ∑ SdpId,p,t + ∑ Shdcc,pIhdcc,p,t + ∑ Sp,k Ik,Wark,p,t

d,p,t hdcc,p,t k,Wark,p,t

+ ∑ SccpIcc,p,t

cc,p,t

hk hk (2)

c2 = ∑ ( ∑ ICcc,p (Qcc,md,p,k,t) + ∑ ICcc,p (Qcc,sm,p,k,t)

t,p,k,hk cc,md cc,sm hk hk

+ ∑ IChdcc,p (Qhdcc,md,p,k,t) + ∑ IChdcc,p (Qhdcc,sm,p,k,t)

hdcc,md hdcc,sm hk hk

+ ∑ DCCdc,p (Qcc,dc,p,k,t) + ∑ DCCdc,p (Qhdcc,dc,p,k,t))

dc,cc dc,hdcc Techp Techp,hk

+ ∑ Prm,p Qm,d,p,k,t + ∑ SHCc,p,tSHc,p,t + ∑ BCt ∂t

m,d,p,Techp,k,hk,t c,p,t t h h h Techp,hk h h

c3 = ∑ ( ∑ Tr k Q k + ∑ Tr k Q + ∑ Tr k Q k (3)

s,m,i,k s,m,i,k,t m,d,p,k m,d,p,k,t d,hdcc,p,k d,hdcc,p,k,t t,k,hk i,s,t,m m,d,p,Techp d,hdcc,p hk hk hk hk

+ ∑ Trd,Wark,p,kQd,Wark,p,k,t + ∑ Trhdcc,c,p,kQhdcc,c,p,k,t

d,Wark,p hdcc,c,p hk hk hk hk

+ ∑ TrWark,c,p,kQWark,c,p,k,t + ∑ Trc,hdcc,p,kQc,hdcc,p,k,t

Wark,c,p c,hdcc,p hk hk hk hk

+ ∑ Trc,cc,p,kQc,cc,p,k,t + ∑ Trhdcc,hdcc,p,kQhdcc,hdcc,p,k,t

c,cc,p hdcc,p hk hk hk hk

+ ∑ Trcc,md,p,kQcc,md,p,k,t + ∑ Trcc,sm,p,kQcc,sm,p,k,t

cc,md,p cc,sm,p hk hk hk hk

+ ∑ Trhdcc,md,p,kQhdcc,md,p,k,t + ∑ Trhdcc,sm,p,kQhdcc,sm,p,k,t

hdcc,md,p hdcc,sm,p hk hk hk hk

+ ∑ Trcc,dc,p,kQcc,dc,p,k,t + ∑ Trhdcc,dc,p,kQhdcc,dc,p,k,t)

dc,cc dc,hdcc

Re = ∑ (tap ∑ Qhk + ∑ Qhk ) + (1 − β) ∑ SPptQhk (4)

cc,md,p,k,t hdcc,md,p,k,t hdcc,c,p,k,t p,k,hk,t cc,md hdcc,md hdcc,c,p,k,hk,t hk hk

+ ∑ SPptQWark,c,p,k,t + (1 − β) ∑ SMSPptQcc,sm,p,k,t

k,Wark,c,p,hk,t cc,sm,p,k,hk,t hk

+ ∑ SMSPptQhdcc,sm,p,k,t

hdcc,sm,p,k,hk,t

Max Z1 = Re − c1 − c2 − c3 (5) h Techp,hk h

Min Z2 = ∑ ( ∑ CEhkQ k + ∑ CEhkQ + ∑ CEhkQ k (6)

s,m,i,k,t m,d,p,k,t d,hdcc,p,k,t t,k,hk i,s,t,m m,d,p,Techp d,hdcc,p h hk h hk

+ ∑ CE kQd,Wark,p,k,t + ∑ CE kQhdcc,c,p,k,t

d,Wark,p hdcc,c,p h hk h hk h hk

+ ∑ CE kQWark,c,p,k,t + ∑ CE kQc,hdcc,p,k,t + ∑ CE kQc,cc,p,k,t

Wark,c,p c,hdcc,p c,cc,p h hk h hk h hk

+ ∑ CE kQhdcc,hdcc,p,k,t + ∑ CE kQcc,md,p,k,t + ∑ CE kQcc,sm,p,k,t

hdcc,p cc,md,p cc,sm,p h hk h hk

+ ∑ CE kQhdcc,md,p,k,t + ∑ CE kQhdcc,sm,p,k,t

hdcc,md,p hdcc,sm,p h hk h hk

+ ∑ CE kQhdcc,dc,p,k,t + ∑ CE kQcc,dc,p,k,t)

hdcc,dc,p cc,dc,p

Max Z3 = ∑ URmxTechp(FJTechp + VJTechp) + ∑ URdyd H1(FJd H1 + VJd H1) (7)

mp m,p m,p m,p,Techp d,h1

+ ∑ URhdccyhdcc H2 (FJhdcc H2 + VJhdcc H2 ) + ∑ URccycc H3(FJcc H3 + VJcc H3)

hdcc,h2 cc,h3

+ ∑ URhdcczhdcc(HFJhdcc + HVJhdcc)

hdcc

S.t.

h Techp

Q k ≤ M ∑ x , ∀s, m, i, k, hk, t (8)

s,m,i,k,t mp p,Techp Techp,hk

Qm,d,p,k,t ≤ M ∑H1 yd H1 , ∀m, d, k, p, Techp, hk, t (9)

Qhk ≤ M ∑ yhdcc H2 , ∀hdcc, d, k, p, hk, t (10)

d,hdcc,p,k,t

hk War

Qd,War ,p,k,t ≤ My k , ∀hdcc, d, k, p, hk, Wark, t (11)

Qhk ≤ M ∑ ycc H3 , ∀c, cc, k, p, hk, t (12)

c,cc,p,k,t

Qh c,k hdcc,p,k,t ≤ Mzhdcc , ∀c, hdcc, k, p, hk, t (13)

Qh hdcc k ,z,p,k,t ≤ Mzhdcc , ∀z ∈ {sm, md, dc}, hdcc, k, p, hk, t (14) ∑ Qhk ≤ Mys , ∀s (15)

s,m,i,k,t m,i,k,hk,t

∑ xTechp = 1 , ∀m, p (16)

mp Techp

∑ yd H1 ≤ 1 , ∀d (17)

∑ yhdcc H2 ≤ 1 , ∀hdcc (18)

∑ ycc H3 ≤ 1 , ∀cc (19)

∑ QTechp,hk ≤ capTechpxTechp , ∀m, p, Techp, t (20)

m,d,p,k,t m,p mp d,k,hk ∑ QTechp,hk + ∑ Id,p,t−1 ≤ ∑ capH d1yd H1 , ∀d, t (21)

m,d,p,k,t m,k,hk,p,Techp p H1

∑ Qhk + ∑ Qhk + ∑ Qhk + ∑ Ihdcc,p,t−1 + ∑ I ̂hdcc,p,t−1 (22)

d,hdcc,p,k,t c,hdcc,p,k,t hdcc,hdcc,p,k,t d,k,hk,p c,k,hk,p hdcc,k,hk,p p p

≤ ∑ capH hdcc 2 yhdcc H2 , ∀hdcc, t

∑ Qhk + ∑ IWar ,p,t−1 ≤ capWarkyWark , ∀k, t (23)

d,Wark,p,k,t k d,hk,p p

∑ Qhk + ∑ Icc,p,t−1 ≤ ∑ capH cc3ycc H3 , ∀cc, t (24)

c,cc,p,k,t c,k,hk,p p H3

∑ Qhk ≤ TPRi,s , ∀s, i, t (25)

s,m,i,k,t m,k,hk Techp,hk h h

Id,p,t = Id,p,t−1 + ∑( ∑ Q − ∑ Q k − ∑ Q k ) , ∀d, p, t (26)

m,d,p,k,t d,hdcc,p,k,t d,Wark,p,k,t k,hk m,Techp hdcc Wark

Ihdcc,p,t = Ihdcc,p,t−1 (27)

hk hk hk

+ ∑(∑ Qd,hdcc,p,k,t + ∑ Qhdcc ̀ ,hdcc,p,k,t + ∑ γpQc,hdcc,p,k,t

k,h d hdcc ̀ c hk hk hk

− ∑ Qhdcc,hdcc ̀ ,p,k,t − ∑ Qhdcc,c,p,k,t − ∑ Qhdcc,md,p,k,t

hdcc ̀ c md hk

− ∑ Qhdcc,sm,p,k,t) , ∀hdcc, p, t

sm

I ̂hdcc,p,t = I ̂hdcc,p,t−1 + ∑ (1 − γp)Qhk − ∑ Qhk , ∀hdcc, p, t (28)

c,hdcc,p,k,t hdcc,dc,p,k,t c,k,hk dc

Icc,p,t = Icc,p,t−1 + ∑(∑ γpQhk − ∑ Qhk − ∑ Qhk ) , ∀cc, p, t (29)

c,cc,p,k,t cc,md,p,k,t cc,sm,p,k,t k,hk c md sm

I ̂cc,p,t = I ̂cc,p,t−1 + ∑ (1 − γp)Qhk − ∑ Qhk , ∀cc, p, t (30)

c,cc,p,k,t cc,dc,p,k,t c,k,hk dc

IWar ,p,t = IWar ,p,t−1 + ∑ Qhk − ∑ Qhk , ∀k, Wark, p, t (31)

k k d,Wark,p,k,t Wark,c,p,k,t d,hk c,hk

Id,p,t ≥ SSd,p , ∀d, p, t (32)

Ihdcc,p,t ≥ SShdcc,p , ∀hdcc, p, t (33) ∑ Qhk = ∑ TPR ∑ QTechp,hk , ∀m, i, t (34)

s,m,i,k,t i,p m,d,p,k,t s,k,hk p d,k,hk,Techp

∑ Qhk + ∑ Qhk ≤ ∑ QTechp,hk + I , ∀d, p, t (35)

d,hdcc,p,k,t d,War ,p,k,t m,d,p,k,t d,p,t−1 hdcc,k,hk k,Wark,hk m,k,hk,Techp

∑(∑ Qhk + ∑ Qhk + ∑ Qhk + ∑ Qhk ) (36)

hdcc,c,p,k,t hdcc,hdcc ̀ ,p,k,t hdcc,md,p,k,t hdcc,sm,p,k,t k,hk c hdcc ̀ md sm hk hk hk

≤ ∑(∑ Qd,hdcc,p,k,t + ∑ Qhdcc ̀ ,hdcc,p,k,t + ∑ γpQc,hdcc,p,k,t)

k,h d hdcc ̀ c

+ Ihdcc,p,t−1 , ∀hdcc, p, t ∑ Qhk ≤ ∑ (1 − γ )Qhk + I ̂ , ∀hdcc, p, t (37)

hdcc,dc,p,k,t p c,hdcc,p,k,t hdcc,p,t−1 dc,k,hk c,k,hk

∑ Qhk ≤ ∑ Qhk + I , ∀k, War , p, t (38)

War ,c,p,k,t d,War ,p,k,t Wark,p,t−1 k c,hk d,hk

∑(∑ Qhk + ∑ Qhk ) ≤ ∑ γ Qhk + I , ∀cc, p, t (39)

cc,md,p,k,t cc,sm,p,k,t p c,cc,p,k,t cc,p,t−1 k,hk md sm c,k,hk

∑ Qhk ≤ ∑ (1 − γ )Qhk + I ̂ , ∀cc, p, t (40)

cc,dc,p,k,t p c,cc,p,k,t cc,p,t−1 dc,k,hk c,k,hk

∑ Qhk + ∑ Qhk (41)

c,cc,p,k,t c,hdcc,p,k,t cc,k,hk hdcc,,k,hk

hk hk

≤ αp,c ( ∑ Qhdcc,c,p,k,t + ∑ QWark,c,p,k,t) , ∀c, p, t

hdcc,k,hk Wark,k,hk

∑(∑ Qhk + ∑ Qhk ) + SH = d + SH , ∀c, p, t (42)

hdcc,c,p,k,t War ,c,p,k,t c,p,t c,p,t c,p,t−1 k,hk hdcc Wark

∑ Qhk P − BC ≤ B , ∀t (43)

s,m,i,k,t i,s,t t t s,m,i,k,hk

BCt ≤ ABCt , ∀t (44) y, x, z ∈ {0,1} (45) Q, I, SH, BC ≥ 0 (46) The proposed mathematical formulation is composed of several groups of equations that collectively capture the economic, environmental, and social dimensions of the sustainable PSC network. Eq. (1) represents the fixed investment and operational costs associated with the establishment and operation of the network infrastructure. This includes the fixed costs of opening facilities, the contractual costs of collaborating with 3PL providers, the costs of establishing partnerships with suppliers, and the inventory holding costs for pharmaceutical products stored at distribution facilities. Eq. (2) accounts for operational processing costs within the network. Specifically, it includes the inspection costs incurred when returned pharmaceutical products are evaluated at collection or hybrid facilities, the disposal costs associated with non‑usable medicines sent to disposal centers, and the production costs of pharmaceutical products at manufacturing plants. Eq. (3) captures the transportation costs generated by moving raw materials and pharmaceutical products between different nodes of the supply chain. These costs arise from shipments carried out by 3PLs providers using different transportation modes across multiple echelons of the network. Eq. (4) represents the revenue structure of the supply chain. The total income of the network is generated from three sources: The sale of pharmaceutical products to primary customer markets, the resale of eligible returned medicines in secondary markets, and tax reduction benefits obtained through pharmaceutical donation programs. Eq. (5) defines the first objective function of the model, which aims to maximize the overall profit of the supply chain network. This objective is obtained by maximizing total revenues while subtracting all relevant operational, transportation, and infrastructure costs incurred throughout the network. Eq. (6) formulates the environmental objective of the model. This objective minimizes the total carbon emissions generated by transportation activities across the supply chain, thereby capturing the environmental impact of logistics operations and supporting the development of a greener pharmaceutical distribution system. Eq. (7) represents the social objective of the model, which aims to maximize employment generation resulting from the establishment and operation of new facilities. Both fixed and variable jobs are considered, and the contribution of job creation is weighted according to the unemployment rate of each region in order to reflect the socio‑economic importance of facility location decisions. Constraints (8)–(15) ensure the logical consistency of the network structure. These constraints guarantee that material flows can only occur through facilities that have been established. In other words, pharmaceutical products or raw materials cannot be shipped from a facility unless that facility is selected and activated within the network. Constraints (16)–(19) enforce the selection of only one capacity level for each candidate facility. This ensures that if a facility is established, it operates under a single predefined capacity level rather than multiple simultaneous capacity configurations. Constraints (20)–(25) impose capacity limitations on the facilities. These constraints ensure that the total volume of pharmaceutical products processed or stored at any facility does not exceed its available operational capacity. Constraints (26)–(31) represent the inventory balance equations of the network. These constraints track the inflow, outflow, and storage of pharmaceutical products at each facility over the planning horizon, enabling the model to capture the dynamic evolution of inventory levels across time periods. Constraints (32) and (33) enforce safety stock requirements at distribution facilities. These constraints ensure that a minimum level of inventory is maintained in order to protect the supply chain against demand uncertainty and potential supply disruptions. Eq. (34) determines the amount of raw materials required for pharmaceutical production. This relationship links production quantities with raw material consumption through predefined conversion coefficients. Constraints (35)–(41) represent the flow balance relationships throughout the supply chain network. These constraints maintain material conservation at each node by ensuring that incoming flows, outgoing flows, production, returns, and inventory levels remain consistent across the entire network structure. Eq. (42) corresponds to the demand satisfaction constraint for customer zones. This constraint ensures that customer demand is fulfilled either through direct supply or through backordering mechanisms when shortages occur. Constraints (43) and (44) describe the financial constraints related to raw material procurement. These constraints model the availability of financial resources by incorporating the maximum amount of credit that can be obtained from banks or financial institutions, as well as the borrowing conditions associated with such financing. Finally, Constraints (45) and (46) define the domain of the decision variables. These constraints specify the binary nature of location and selection variables, as well as the non‑negativity conditions for continuous decision variables such as flow quantities, inventory levels, and financial variables.

To solve the proposed multi-objective optimization model, the ε‑constraint method is employed. In this approach, one of the objective functions is selected as the primary objective, while the remaining objectives are transformed into constraints bounded by predefined ε levels. This method enables the systematic generation of Pareto‑optimal solutions and facilitates the analysis of trade‑offs among the economic, environmental, and social dimensions of the supply chain.

In the present study, the economic objective—maximization of the total profit of the PSC—is considered as the primary objective function. Accordingly, the environmental objective (carbon emission minimization) and the social objective (employment maximization) are incorporated into the model as additional constraints with specified ε thresholds. By iteratively adjusting these ε values, different feasible solutions can be obtained, each representing a distinct balance among profitability, environmental impact, and social benefits. Eqs. (47) and (48) present the reformulated structure of the model under the ε‑constraint framework.

max 1 (47)

S.t.

x ∈ χ , −z2 ≤ ε2 , z3 ≤ ε3 (48)

The multi-objective nature of the problem necessitates a careful analysis of the trade-offs between conflicting goals. Fig. 2 illustrates the Pareto-optimal frontier between the total network profit (Economic Objective) and the total CO2 emissions (Environmental Objective).

The results demonstrate a clear conflicting relationship between these two dimensions: an increase in total profit is strictly associated with a rise in carbon emissions. This phenomenon occurs because achieving higher profitability often requires more intensive transportation activities, larger shipment volumes, and the utilization of faster or higher-capacity logistics routes that are typically more carbon-intensive.

Key observations from the Pareto analysis include:

Non-Dominance: All points presented in Fig. 2 are non-dominated solutions. This means that no single solution can improve the economic objective without deteriorating the environmental performance, and vice versa.

Trade-off Sensitivity: The slope of the Pareto front indicates the “marginal cost of environmental protection.” As the model moves towards more eco-friendly solutions (lower CO2 emissions), the supply chain must sacrifice a portion of its profit to accommodate more sustainable (but potentially more expensive or less efficient) logistics and facility configurations.

Managerial Decision Support: The existence of this frontier provides a powerful decision-support tool for supply chain managers. Rather than providing a single “optimal” answer, the model offers a set of efficient alternatives. The final selection among these Pareto solutions depends on the strategic priorities of the policy-makers and the regulatory requirements regarding carbon footprints in the pharmaceutical industry.

To evaluate the operational and strategic implications of different reverse logistics strategies, we define and analyze three distinct scenarios representing alternative pharmaceutical return policies:

Scenario 1 (Resale-Only Policy): All conforming returned pharmaceuticals are directed exclusively to secondary markets to maximize economic recovery.

Scenario 2 (Donation-Only Policy): All eligible returned medicines are donated to charity centers, prioritizing corporate social responsibility (CSR) and tax incentives over direct sales revenue.

Scenario 3 (Hybrid Policy - Proposed): The model dynamically allocates returned pharmaceuticals between secondary market resale and charitable donation based on global network optimization.

Table 2 presents the performance metrics of the supply chain network under these three scenarios.

The numerical results in Table 2 reveal critical trade-offs. The Resale-Only policy yields the highest total profit (950.21monetary units) by commercializing all usable returns. However, this economic dominance comes at a significant cost: it leads to the highest volume of pharmaceutical waste disposal (120.68 units), representing a suboptimal environmental footprint and zero direct social contribution through donations. Conversely, the Donation-Only policy minimizes direct waste (100.47 units) and maximizes social outreach, but results in the lowest profitability (870.49 units) due to the absence of secondary market revenues.

The proposed Hybrid Policy acts as a Pareto-efficient compromise. While it generates slightly less profit (910.54 units) than the purely commercial resale policy, it achieves the minimum waste level (100.47 units)— matching the donation-only policy—while keeping a balanced mix of resale (200.17 units) and donation (300.85 units). By integrating these options, the hybrid policy balances economic viability with social responsibility, proving to be the most sustainable choice for high-level decision-makers.

To analyze how changes in customer behavior affect the network, we conducted a sensitivity analysis on the pharmaceutical return rate, varying it from a low return regime (0.02) to a high return regime (0.20). The resulting trends are illustrated in Fig. 3.

Economic Implications: As the return rate increases, the total profit of the network experiences a positive growth trajectory. This upward trend indicates that the economic value recovered from the returned pharmaceuticals (via secondary market sales and tax exemptions from donations) outweighs the extra logistics costs of collection, inspection, and reverse transport.

Environmental Implications: Simultaneously, a higher return rate leads to a marked increase in total CO2 emissions. This negative environmental impact is a direct consequence of the increased transport workload. Moving returned products from customer zones back to collection and hybrid centers requires more frequent vehicle trips, increasing fuel consumption and greenhouse gas emissions.

Social Implications (Job Creation): A key finding of this sensitivity analysis is the positive impact of the return rate on the social objective. When return volumes rise, the existing network capacity becomes constrained. To handle the larger flow of returned products, the optimization model is forced to either establish new collection centers or upgrade existing distribution centers into hybrid facilities. This physical expansion directly generates new fixed and variable jobs, which significantly boosts employment in regions with high unemployment rates.

These sensitivity trends highlight a core challenge in sustainable supply chain management. Higher return rates improve both economic performance (through asset recovery) and social welfare (through job creation in processing facilities), but worsen the network’s environmental impact (due to transport emissions). Therefore, high-level policy-makers must establish a balanced framework. This can be achieved by using greener transport options, such as low-emission 3PL fleets, to offset the carbon footprint of reverse logistics, while leveraging the economic and social benefits of a robust circular economy.

To investigate the role of 3PL providers in shaping the optimal configuration of the PSC, the selected storage facilities and the extent to which secondary distribution centers were converted into hybrid facilities were examined across the optimal solutions. In the proposed network, a hybrid facility simultaneously supports forward and reverse logistics activities. In addition to storing and distributing pharmaceutical products to customer zones, such a facility can receive returned medicines and facilitate their consolidation, temporary storage, inspection, sorting, and subsequent transfer for resale, donation, recovery, or safe disposal. The computational results indicate that 3PL storage facilities are selected in more than 60% of the optimal solutions. Their selection is particularly frequent in low-demand regions and geographically remote areas located far from manufacturing plants. In these areas, establishing a company-owned warehouse may not be economically justified because the expected throughput is insufficient to offset the associated fixed investment and operating costs. By contrast, outsourcing warehousing activities to 3PL providers allows the pharmaceutical company to access logistics capacity without committing substantial capital to the construction, equipment, and long-term operation of dedicated facilities.

The frequent selection of 3PL warehouses therefore highlights their strategic value as a flexible capacity mechanism rather than merely as an outsourcing alternative. By replacing part of the network’s fixed infrastructure with externally provided capacity, 3PL participation can transform a portion of fixed capital expenditure into more flexible, usage-dependent logistics expenditure. This flexibility is particularly valuable under spatially dispersed or fluctuating demand, where maintaining sufficient internal capacity for peak conditions may lead to low facility utilization during normal periods. Accordingly, the use of 3PL warehouses reduces the risk of overinvestment while improving the network’s ability to respond to changes in regional demand and return volumes.

The results also reveal a noteworthy relationship between the use of 3PL warehouses and the hybridization of logistics facilities. In scenarios in which 3PL warehousing capacity is actively employed, approximately 50% of the selected 3PL warehouses operate as hybrid facilities supporting both forward distribution and reverse product flows. In contrast, the hybridization rate remains below 30% in network configurations that rely primarily on company-owned warehouses. Thus, the observed difference is at least 20 percentage points, indicating that hybrid operation occurs considerably more frequently in 3PL-based network structures.

This result can be explained by the greater operational adaptability of 3PL providers. Compared with dedicated internal warehouses, 3PL facilities often have access to shared transportation resources, scalable storage capacity, specialized handling capabilities, and established regional logistics networks. These capabilities make it easier to consolidate forward and reverse flows at the same location. For example, vehicles that deliver medicines to a customer region may collect eligible returned products on their return journeys, thereby reducing empty vehicle movements and improving vehicle utilization. Similarly, shared warehousing capacity can be reallocated between regular inventory and returned products as flow volumes change over time.

From a reverse-logistics perspective, the hybridization of 3PL warehouses can improve the accessibility and responsiveness of the collection network. Locating hybrid facilities closer to geographically dispersed customer zones shortens the distance over which returned medicines must initially be transported and provides additional consolidation points for low-volume return flows. This feature is especially important in PSCs, where returned products may require controlled storage, traceability, timely inspection, and segregation according to quality status. A geographically distributed network of capable 3PL facilities can therefore help prevent recoverable medicines from being prematurely classified as waste simply because collection or processing capacity is unavailable.

Moreover, integrating forward distribution and reverse collection activities within the same facility can create operational synergies. The network may use common infrastructure, labor, information systems, and transportation resources for both flow directions. Such integration can reduce duplicated facility investment and enhance coordination among delivery, collection, inspection, and recovery operations. Consequently, hybrid facilities may increase the proportion of returned medicines that can be successfully directed toward secondary-market resale or donation rather than disposal.

Nevertheless, the greater use of 3PL and hybrid facilities does not automatically guarantee improved performance across all sustainability dimensions. Although outsourcing can lower infrastructure costs and improve responsiveness, it may introduce additional coordination challenges, dependence on external providers, and difficulties in monitoring service quality. These concerns are particularly important in pharmaceutical logistics because returned medicines require strict compliance with product-safety, traceability, temperature-control, and regulatory requirements. Therefore, 3PL selection should not be based exclusively on cost and available capacity. It should also consider the provider’s technical competence, environmental performance, regulatory compliance, information-sharing capabilities, geographical coverage, and ability to handle pharmaceutical returns safely.

Overall, the findings suggest that 3PL participation and facility hybridization are complementary network-design decisions. The presence of 3PL providers not only reduces the need for capital-intensive internal infrastructure but also enables a more adaptable configuration in which forward and reverse flows can be integrated more effectively. This integration improves the network’s capacity to collect, consolidate, and recover returned medicines, particularly in remote or low-demand regions where dedicated internal facilities would otherwise be economically unattractive. Therefore, 3PL providers should be viewed as strategic enablers of circularity and supply chain resilience rather than solely as instruments for reducing logistics costs.

The results provide several implications for PSC decision-makers:

Selective outsourcing is more beneficial than uniform outsourcing: The superiority of 3PL facilities is particularly evident in remote and low-demand regions. Therefore, managers should adopt a differentiated facility strategy in which internal warehouses serve high-volume and strategically important markets, while 3PL capacity supports geographically dispersed or demand-uncertain regions.

3PL selection should be integrated with facility-role decisions: Decisions concerning the selection of logistics providers and the hybridization of distribution centers should not be made independently. A provider capable of supporting both product delivery and pharmaceutical return collection may generate greater network-wide value than a lower-cost provider offering only conventional warehousing services. Contracts should support scalable and bidirectional operations: Agreements with 3PL providers should include flexible capacity clauses, service-level requirements for return collection, and explicit responsibilities for inspection, segregation, documentation, and temporary storage. Performance-based contracts can encourage providers to improve both delivery efficiency and the recovery rate of returned medicines.

Regulatory and quality requirements remain critical: The use of shared or outsourced infrastructure should not compromise pharmaceutical safety. Managers must verify that selected 3PL providers comply with relevant good distribution practices, traceability protocols, storage conditions, and requirements for handling returned, damaged, or expired medicines.

Environmental performance should be evaluated at the network level: Although hybridization may reduce empty trips and duplicated infrastructure, additional collection activities can increase transportation and processing emissions. Consequently, the environmental benefit of 3PL participation depends on route consolidation, vehicle technology, facility location, and the efficiency of return-processing operations.