Some works incorporate uncertainty or multi-objective optimization, but they do not address the real-world situation where multiple projects simultaneously compete for shared resources and depend on coordinated logistics operations. Additionally, the literature rarely integrates multi-project scheduling, multi-supplier procurement, hub location decisions, and type-specific storage constraints within a unified framework, which is essential for realistic project supply chain planning. These limitations highlight a clear problem: organizations must often plan several projects at the same time while deciding (i) when to order materials, (ii) how to allocate limited storage space, (iii) which hubs to activate, and (iv) how to coordinate shipments from multiple suppliers. The absence of an integrated model that addresses these factors can lead to unreliable schedules, higher logistics costs, and delays in material availability.
Based on this comparative analysis, several research gaps remain:
- The integration of hub-based transportation modeling into project scheduling frameworks is still limited, despite strong evidence of its efficiency in supply chain design.
- Storage capacity constraints are oversimplified in the literature and rarely consider type-specific space requirements.
- Renewable-resource availability and rental decisions are insufficiently represented, even though they directly affect feasibility and cost.
This study addresses these gaps through the following key contributions:
- Integration of hub-location modeling into a multi-project scheduling and procurement framework, enabling coordinated and sustainability-oriented transportation planning.
- Incorporation of renewable-resource rental options, providing operational flexibility under limited internal resource availability.
- Type-specific modeling of storage capacity constraints, ensuring that each material category is associated with its own storage-type requirement and volume coefficient, thereby preventing unrealistic aggregation of storage space.
- Development and evaluation of a multi-objective model, solved using the AEC method for small instances and advanced metaheuristics (NSGA-II and MOSFS) for large-scale cases.
- Validation through a real multi-project case study, demonstrating the model’s practical relevance and the performance advantages of the proposed solution techniques.
This section presents the mathematical formulation of the proposed integrated model combining multi-project scheduling, material procurement, and the hub location problem.
The model incorporates two objective functions: (1) minimizing the total costs related to project sites and logistics, and (2) minimizing the overall project completion time. The first objective function accounts for several cost components associated with project sites, including: Penalties due to activity lateness, Costs of renting renewable resources, Material inventory costs. Additionally, the logistics costs comprise: Fixed costs for establishing hub nodes, Transportation costs for directing materials through the selected hubs, Fixed ordering costs incurred per order cycle. The proposed bi- objective formulation is designed to capture the two core and inherently conflicting managerial dimensions of the integrated multi-project scheduling and logistics problem. The first objective minimizes the total cost, which includes procurement, transportation, storage, rental, and operational components. This reflects the economic rationale and the necessity to manage expenditures across multiple projects and distributed supply networks. The second objective minimizes the overall project completion time (makespan), ensuring timely execution of activities under renewable resource limits, hub–supplier assignments, and material availability constraints. These two dimensions, cost efficiency and timely completion, naturally conflict: accelerating project activities requires higher expenditures, whereas reducing costs often prolongs the projects. Therefore, a bi-objective structure is essential to represent this trade-off rather than aggregating both aspects into a single objective. To facilitate material delivery from suppliers to project sites, a subset of hub nodes is selected based on their capacity and establishment costs. In the transportation cost formulation, three discount factors (α.σ.δ) are incorporated to reflect tier-specific economies of scale across different legs of the hub-and-spoke logistics structure. The factor α represents the cost reduction obtained during shipments from suppliers to hubs, where consolidation typically reduces loading and handling expenses. The factor σ captures the additional discount associated with inter-hub transfers, which commonly benefit from higher shipment volumes and contractual rate advantages. Finally, δ represents the discount applied when distributing consolidated flows from hubs to project sites, where outbound logistics frequently exhibit lower per-unit costs due to bulk dispatching. Including these differentiated discount factors enables the model to more accurately characterize real freight-cost behavior across hierarchical transportation stages and enhances the economic fidelity of the integrated scheduling, procurement and logistics framework. The model also allows the assignment of renewable resources to project activities, considering the possibility of renting such resources to enhance flexibility. Lead times associated with material production are explicitly incorporated, ensuring realistic scheduling of material availability. Storage capacity constraints are modeled for each project site, where each material’s volume coefficient is used to calculate the total storage requirement, preventing storage overflow.
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This study addressed the integrated challenge of multi-project scheduling, material procurement, and hub-location planning under renewable-resource and storage constraints. By combining activity scheduling, material flow decisions, and hub selection within a single mathematical framework, the model offers a more coordinated and realistic approach to planning complex construction projects. Traditional scheduling models often treat logistics and project execution as separate layers, which can lead to inefficiencies, delays, and higher costs. In contrast, this study incorporates hub nodes as consolidation points, considers storage limitations, and includes rental resources to more accurately reflect real-world project management. The case study and sensitivity analyses demonstrated how adjustments in hub capacity, storage space, and rental limits influence overall performance. The results showed clear saturation points beyond which additional investment yields minimal benefit. Furthermore, the comparison of algorithms highlighted that the MOSFS method consistently achieves stronger diversity and convergence -especially for large-scale instances- offering more reliable solutions for practical use. Collectively, these results provide managers with actionable insights on how to balance resource availability, storage policies, and transportation strategies to reduce both cost and completion time. This research has certain limitations. Several simplifying assumptions were made to keep the integrated model solvable and avoid excessive complexity. These include the use of deterministic parameters, simplified interactions between supply-chain elements and project tasks, and rational decision-making assumptions. Such simplifications may overlook uncertainty and behavioral variations that arise in dynamic operational environments. Additionally, the case study relied on historical and incomplete logistical data, which limits the generalizability of the findings and may influence the precision of the results when applied to other industries or regions. While the model demonstrates strong capability as a decision- support tool, its applicability is bounded by its structural assumptions. It is particularly suitable for environments with multiple interdependent activities, hub-based material routing, deterministic resource data, and clear rental and storage constraints. Moreover, the computational complexity grows quickly with problem size, potentially creating scalability challenges when dealing with industries that rely on large, highly variable datasets. Despite these limitations, the proposed model offers a solid foundation for integrated project-logistics planning that can be adapted to broader domains. Future research may expand this work by incorporating uncertainty modeling such as stochastic lead times or variable processing durations, enhancing computational performance through hybrid or parallel metaheuristics, and applying the framework to sectors like large-scale manufacturing, infrastructure development, or multi-site energy projects to test its robustness. Additional future extensions could also focus on embedding sustainability criteria, applying AI-based calibration methods to improve parameter accuracy, and enriching the cost structure by considering dynamic rental-price fluctuations and real-time or risk-based decision rules for rental and storage management, which were not feasible to implement within the deterministic and static structure of the current model.
Referencias:
Mazaheri, S., Ahmadi, M., Heidari, A., Hakimi, M., & Khalilzadeh, M. (2026). An integrated analytics approach to multi-project scheduling and material procurement with coordinated hub location. Supply Chain Analytics, 13. https://doi.org/10.1016/j.sca.2025.100191
