Purpose of this paper:

The pharmaceutical industry is currently facing a “Triple Crisis”: proliferating economic costs due to ineffective supply chains, social injustice in medicine acquisition, and environmental issues related to the improper pharmaceutical waste processing. Unlike ordinary products, medicines are characterised by strict perishability constraints and toxicity upon expiration. The World Health Organisation stated that a significant portion of medical waste was caused by mismatches between demand and supply and inefficient inventory management. In response, the Circular Economy (CE) has been proposed to transition the industry to a closed-loop system (Tirkolaee et al., 2022). However, a prerequisite for a viable Closed-Loop Supply Chain is a robust forward logistics network that can precisely manage inventory shelf-life.

The current literature in supply chain network design (e.g., Shah, 2004; Zahiri et al., 2017) usually sees inventories as homogeneous pools or implements simplified decay rates, ignoring the shelf-life (s) of inventory batches (Nahmias, 1982). This oversimplification leads to severe risk underestimations of wastage and stockouts in strategic planning. Hence, our research aims to bridge the gap between microscopic perishable inventory management and macroscopic strategic network design by designing a deterministic Mixed-Integer Linear Programming (MILP) model to determine the optimal network configuration while explicitly minimising end-of-life wastage. Also, we introduce a novel metric, the Value of Age-Information (VoAI), measuring economic losses from neglecting shelf-life conditions of medicines when designing supply chain networks.

Design/methodology/approach:

Our study provides a multi-echelon, product-and-period MILP model with a network structure comprising Wholesalers (L), Stores/Hospitals (N), and Customers (C). Unlike traditional models that only track inventory quantity (y_t), our model introduces the age index (s) to track the physical trajectories of stocks. The logic of the age index is that the inventory of age s at time t physically transitions to age s+1 at time t+1 (y_{l,p,s,t}\rightarrow y_{l,p,s+1,t+1}), unless shipped or sold. A strict boundary condition is applied: when the age s reaches the maximum shelf-life \mathrm{\Theta}_p, the inventory is mathematically forced out of the available pool and recorded as wastage (w).

To validate the model and illustrate the significance of the “Age Information”, a comparison test between two model variations, the Age-Based Model (Model A) with full shelf-life constraints and the Traditional Model (Model B) without age constraints, treating inventory homogeneously with infinite shelf-life, is conducted. Solving Model B to fix the network design structure (service links and facility locations), these strategic decisions are then imported into Model A to compute the “realistic cost”. Finally, this “realistic cost” is compared with the “optimal cost” calculated independently by Model A, with the difference constituting the VoAI. The model is implemented in Python through Pyomo and solved through the CPLEX solver.

Findings:

Tested by the dataset, including 2L, 3N, 6C, 4 product types (P) and 12 time-periods (T), the outputs of the model present three primary findings:

Inevitable Wastage: The optimal solution yielded a total cost of 631,119.11. Contrary to expectations of avoiding waste, the optimisation generated 661 units of waste. Observing locations of waste (e.g., Wholesaler l_2 generates waste for p_3 at early stages; n_3 experiences expirations of p_3 at the third stage), they indicate wastages not randomly appearing but being induced by network constraints.

Physical Capacity vs Shelf-life: As shown, waste occurs when capacity constraints prevent the system from simultaneously storing "aged" inventory and receiving "fresh" inventory needed for future surges in demand. Hence, to prevent stockouts during future peak demand periods, the model removes older (but still valid) inventory to free up cargo capacity, a trade-off that traditional models fail to capture.

Significant VoAI: The positive VoAI calculated by the comparison test demonstrates that Model B underestimates total costs by ignoring potential spoilage. When implementing the strategic network design derived from Model B in the simulation under realistic shelf-life conditions, the actual cost was higher than that of Model A. Since the traditional mode is incapable of foreseeing expirations, it results in passive and urgent reactions and procurements, increasing costs. This confirms that integrating shelf-life constraints at the design phase significantly improves operational efficiency.

Value:

Theoretically, this work bridges gaps between strategic network design and operational perishable inventory management. Unlike models using hypothetical decay rates, this framework evidently traces the shelf-life of inventory, enabling the identification of when, where, and quantities of expired products within the network. Defining VoAI, it also provides a novel methodological tool to quantify the importance of data granularity. Practically, the study offers supply chain managers a decision-support tool to visualise the hidden waste. It shifts the management focus from simple "safety stock" construction (with the risk of expiration) to "flow velocity" management, providing blueprints for the pharmaceutical industry's transition to CE.

Research limitations/implications:

Even validating the "ageing engine" mechanism, this model simplifies the stochastic volatility of actual demands. Therefore, to address spoilage, the model should be extended into a Closed-Loop Supply Chain, adding reverse logistics and waste recycling. Besides, assuring robustness against uncertainty, stochastic programming or fuzzy-based approaches are necessary. Finally, as NP-hard problems, practical implementations require incorporating advanced mathematical methods, optimising the effectiveness and solubility of solvers (Goodarzian et al., 2021).

Practical implications:

The result illustrates the relationship between capacity and economic losses. Limited capacity pushes companies to discard still-usable medicines for incoming stock, meaning that investments in storage and/or logistics may be more effective at reducing waste than simply optimising procurement. Also, the study warns that excessively reducing inventory to avoid expiration may increase stockout risks during demand spikes, highlighting the priority of patients’ drug availability over waste-reduction goals.

References:

Goodarzian, F., Taleizadeh, A.A., Ghasemi, P., Abraham, A., 2021. An integrated sustainable medical supply chain network during COVID-19. Eng. Appl. Artif. Intell. 100, 104188.

Nahmias, S., 1982. Perishable Inventory Theory: A Review. Operations Research 30, 680–708.

Shah, N., 2004. Pharmaceutical supply chains: key issues and strategies for optimisation. Comput. Chem. Eng. 28, 929–941. 、

Tirkolaee, E.B., Goli, A., Mirjalili, S., 2022. Circular economy application in designing sustainable medical waste management systems. Environ Sci Pollut Res Int 29, 79667–79668.

Zahiri, B., Zhuang, J., Mohammadi, M., 2017. Toward an integrated sustainable-resilient supply chain: A pharmaceutical case study. Transportation Research Part E: Logistics and Transportation Review 103, 109–142.

Structured Abstract

Purpose

Minimum-charge provisions are widely used in freight transport contracts to protect carriers against underutilization, but they expose transport buyers to asymmetric downside risk when demand is uncertain. This risk becomes more pronounced when carbon emissions and delivery-time performance are internalized, as shippers face cost trade-offs between cleaner but slower contracted services and faster, more carbon-intensive fallback options. Existing studies on transport contracting and capacity reservation largely adopt risk-neutral perspectives or treat environmental and service-related costs deterministically, offering limited insight into how downside risk interacts with contractual rigidity and sustainability objectives.

The purpose of this paper is to examine how risk aversion, minimum-charge contract structure, and carbon- and time-adjusted transport costs jointly shape long-term capacity commitment decisions under demand uncertainty. Specifically, the paper asks when minimum-charge provisions meaningfully influence risk-aware capacity decisions, and when increased risk aversion instead drives conservative boundary outcomes with limited operational or environmental benefits.

Design / Methodology / Approach

The paper develops a stylized analytical model of a transport buyer who commits to long-term capacity under a minimum-charge contract and relies on a higher-cost fallback option to satisfy excess demand. Demand is uncertain at the time of contracting. Carbon emissions and delivery-time disutility are internalized through linear per-unit cost adjustments, yielding effective generalized transport costs that allow direct comparison across sourcing modes.

Downside risk is modeled using Conditional Value-at-Risk (CVaR), capturing extreme cost realizations arising from both over-reservation in low-demand states and reliance on costly fallback transport in high-demand states. The resulting CVaR minimization problem is analyzed using the Rockafellar–Uryasev framework. Closed-form structural results characterize the optimal contracted capacity and its dependence on risk preferences and contract parameters.

An illustrative sea–air sourcing case, calibrated using empirical freight rates, emission factors, carbon pricing benchmarks, and values of time from the literature, is used to visualize the trade-off between downside risk reduction and regenerative (carbon- and time-saving) performance.

Findings

The analysis identifies two distinct regimes. When minimum-charge exposure contributes to the upper tail of the cost distribution, an interior optimal contract level exists that balances downside risk from unused capacity against protection from high-cost fallback sourcing. In this regime, higher risk aversion and larger effective cost gaps between fallback and contracted transport increase optimal capacity commitments, while greater minimum-charge rigidity reduces them.

When minimum-charge costs do not affect tail outcomes, increased risk aversion strictly reduces CVaR by expanding contracted capacity, leading to boundary solutions at the contractual upper limit. In this case, minimum-charge provisions no longer influence decisions, and risk aversion masks contractual rigidity.

The numerical case study reveals a clear trade-off between downside risk and regenerative performance. Most environmental and service-related gains are achieved at moderate risk levels. Under rigid contracts, extreme conservatism yields diminishing regenerative returns, as reservation decisions saturate at contractual bounds and further risk reduction occurs without meaningful operational adjustment.

Value

This paper positions risk-aware capacity contracting as a form of regenerative supply chain intelligence, clarifying how contractual structure conditions the ability of decision makers to translate risk sensitivity into meaningful environmental and service improvements. By explicitly linking downside risk, minimum-charge rigidity, and carbon- and time-adjusted costs within a single analytical framework, the paper shows when intelligent decision tools enable regenerative outcomes—and when contractual constraints blunt their effectiveness.

Research Implications

The results highlight the importance of modeling downside risk explicitly when studying transport contracts with minimum-charge provisions. Future research could extend the framework to multi-carrier or multi-shipper settings, dynamic contracting with learning, or strategic interactions under asymmetric information regarding demand and risk preferences.

Practical Implications

For practitioners, the findings highlight that regenerative outcomes are more effectively achieved through balanced risk sensitivity combined with contractual flexibility, rather than through extreme conservatism under rigid minimum-charge terms. For policymakers and industry bodies, the results suggest that contract structures and risk-allocation practices play a complementary role to carbon pricing in enabling intelligent, regenerative transport decisions.

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OECD (2023). Effective Carbon Rates 2023: Pricing Greenhouse Gas Emissions through Taxes and Emissions Trading, OECD Publishing, Paris.