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Fatemeh Mohajernia, Jafar Rahmani, Mohsen Mohajernia,
Volume 17, Issue 1 (5-2026)
Abstract
Extant quantitative models in Resource Allocation and Operational Systems often rely on statistical optimization or behavioral frameworks, frequently failing to model and quantify the deterministic structural conflicts that arise when operational and informational constraints are ignored. This paper addresses a critical analytical gap in Industrial Information Integration: the necessity of a deterministic modeling framework to quantify the systemic risks inherent in resource scarcity and misallocation. We introduce a novel analytical framework, derived from the Generalized Pigeonhole Principle (GPP), to quantify the inevitable consequences of resource imbalance within complex organizational systems. The framework develops a three-tiered conceptual model: (1) the Base Principle (quantifying the inevitable Structural Non-Allocation Rate, (N-M)), (2) the Generalized Principle (modeling Inevitable Operational Congestion, λ min), and (3) the Weighted Principle (quantifying Qualitative Mismatch, f). We demonstrate the model's predictive and explanatory power through scenario-based analytical simulations, providing a foundational validation for its applicability across workforce planning and capacity development contexts. The analysis yields testable propositions linking these mathematical inevitabilities directly to systemic consequences (e.g., structural attrition/turnover, intragroup operational conflict). This research provides a new, parsimonious analytical language for Operational Systems Modeling, fundamentally shifting the focus from optimizing individual performance to managing unavoidable structural pressures. The model serves as a robust quantitative decision-support tool for strategic workforce planning and lays the essential groundwork for future dynamic modeling of operational capacity and resource demand.
Dr Hassan Rostamzadeh, Dr Ali Reza Fakharzadeh,
Volume 17, Issue 1 (5-2026)
Abstract
Existing merger approaches in data envelopment analysis integrate decision-making units in a single stage, but in practice, merging units may not be possible or affordable at once. We propose a finite multi-stage framework for the gradual merger of decision-making units that incorporates practical constraints. The model determines input and output contributions of the merged units at each stage and constructs a strictly increasing efficiency sequence that converges to a Pareto-efficient state. Each new unit is optimized using both input and output orientation while preserving a uniform return to scale type across stages. The framework is validated through a multi-stage merger application on a subset of Iranian banks.
F. Ahmadi, S. Kordrostami, M. Mirzaei Chalakei, L. Khoshandam,
Volume 17, Issue 1 (5-2026)
Abstract
Measuring capacity utilization is an important aspect among processes in order to determine overcapacity or undercapacity. Furthermore, in many situations, the convexity and homogeneity properties are not satisfied. Accordingly, in this paper, meta-frontier free disposal hull (FDH) frameworks are proposed to estimate output-oriented and input-oriented capacity utilization (CU) rates of firms under nonconvexity property and heterogeneity of technology. Also, the introduced technique is applied to assess capacity utilization of some Iranian hospitals. The findings show the presented approach is beneficial to measure capacity utilization rates of systems in the presence of nonconvexity and heterogeneity.
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