A Four-Compartment Dynamic Inventory Model for the Ready-Made Garment Industry With an Inventory Reproduction Number

Hami Jafar Koushik, Md. Riad Hossen and Mohammed Forhad Uddin

Journal of Applied Mathematics, 2026, vol. 2026, 1-12

Abstract: The ready-made garment industry suffers from persistent inventory imbalance across its multistage production line: Some stages run short of materials, whereas others accumulate excess stock. Existing dynamic inventory models for this sector rarely address both problems together. In particular, none combines a compartmental representation of production stages with a single, dimensionless indicator that captures the overall balance between replenishment and consumption along the line. This paper develops such a framework. We formulate a four-compartment dynamic model covering the cutting, sewing, finishing, and disposal sections as a system of four nonlinear ordinary differential equations within the mixing-problem (MP) framework, with a susceptible–infected–recovered (SIR) inspired rework loop from finishing back to sewing. We prove that the model is well posed and solutions remain nonnegative for nonnegative initial data. In addition, the dynamics evolve inside a positively invariant region and the equilibrium is locally asymptotically stable. We define an inventory reproduction number Rin via a next-generation matrix; values below, equal to, and above unity correspond to depletion-prone, balanced, and accumulation-prone regimes, respectively. The stability of the equilibrium is shown. The model is calibrated against 5 months of production data from a Bangladeshi ready-made garment exporter and a normalized-forward sensitivity analysis of inventory reproduction number identifies the rework rate from finishing to sewing and the final-output rate are the two parameters with the largest impact. The framework provides ready-made garments managers with both a time-resolved view of inventory across stages and a compact, interpretable threshold for diagnosing whether intervention is needed to avoid stockouts or surplus accumulation.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:4143352

DOI: 10.1155/jama/4143352

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