An Integrated Inventory Optimization Model for Deteriorating Agricultural Commodities Under Time-Dependent Demand and Trade Credit: Evidence from Marathwada Region

Abstract

This paper develops and validates an integrated Economic Order Quantity (EOQ) model for deteriorating agricultural commodities under linearly time-dependent demand with permissible delay in payments (trade credit). The model is formulated using the Ghare-Schrader differential equation framework and solved analytically, yielding closed-form expressions for the optimal order quantity (Q*), optimal cycle time (T*), and minimum total cost per unit time (TC*). Two cases are distinguished based on the relationship between cycle length and trade credit period, generating distinct optimality conditions for each. Empirical calibration is performed using primary data collected from 180 wholesale traders at Agricultural Produce Market Committees (APMCs) in Aurangabad and Nanded districts of Marathwada, Maharashtra. Numerical results demonstrate that the optimized model reduces total inventory cost by 18.4 to 31.2 percent compared with observed trader practices, with the gains concentrated in reduction of deterioration and holding costs. Sensitivity analysis confirms robustness across a ±30% parameter range. The paper contributes to the deteriorating inventory literature by providing the first region-specific calibrated model for Marathwada, and offers actionable policy guidance for traders, cooperative societies, and the Maharashtra State Agricultural Marketing Board.

Introduction

The paper presents an empirically validated Economic Order Quantity (EOQ) model designed for deteriorating agricultural products under time-dependent demand and trade credit conditions, using real data from Marathwada’s APMC markets.

The model derives optimal inventory policies for two trade-credit scenarios and confirms optimal solutions through analytical and numerical methods. A key result is that the optimal replenishment cycle is 2.81 weeks, which is significantly shorter than the 5.2-week cycle currently practiced by traders, indicating that farmers and traders tend to over-order and hold inventory longer than is economically optimal.

The study also finds that implementing the optimal policy can reduce total inventory costs by about 18.4% (approximately ?366.30 per week per trader for sweet oranges). Sensitivity analysis shows that the model is stable under parameter variations, but demand rate is the most influential factor affecting outcomes.

Importantly, the analysis concludes that operating within the trade credit period (Case 2) is consistently the best strategy, suggesting that well-structured supplier credit terms can improve efficiency for both traders and suppliers.

Based on these findings, the paper recommends several policy actions:

• Training programs for traders on inventory optimization through agricultural marketing boards
• Better use of digital platforms like e-NAM to improve demand forecasting
• Standardizing trade credit periods (around 4 weeks) to align financial incentives
• Increased government investment in cold-chain infrastructure, especially in high-deterioration districts like Beed and Osmanabad

Conclusion

This paper has developed and empirically validated an integrated EOQ model for deteriorating agricultural commodities under linearly time-dependent demand and trade credit, calibrated on primary data from Marathwada\'s APMC markets. The analytical model yields closed-form optimality conditions under two trade-credit cases, with numerical optimization confirming the global optimum in Case 1 and a clean analytical approximation available for Case 2. Key findings are: (i) the optimal cycle length T* = 2.81 weeks is substantially shorter than observed trader practice (5.2 weeks), indicating systematic over-ordering relative to the optimal; (ii) the model yields a 18.4% reduction in total inventory cost per unit time (Rs. 366.30/week per trader) for the sweet orange; (iii) sensitivity analysis confirms robustness across a ±30% parameter range, with demand rate as the most sensitive parameter; and (iv) operating within the trade credit period (Case 2) is unambiguously optimal, suggesting that trade credit extension by suppliers would be mutually beneficial. Policy recommendations arising from this research include: (a) the Maharashtra State Agricultural Marketing Board should facilitate workshops to familiarize traders with basic inventory optimization principles; (b) the e-NAM platform should be leveraged for demand data generation to improve forecast accuracy; (c) supplier organizations should consider standardizing trade credit terms at 4 weeks to align incentives with shorter replenishment cycles; and (d) government cold-chain investment should be prioritized in districts where ? is highest (Beed, Osmanabad) to reduce the baseline deterioration rate and thereby reduce TC* at any replenishment policy. The model and findings of this paper provide a template for region-specific inventory optimization studies in other agro-climatic zones facing similar post-harvest loss challenges across developing economies.

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Copyright

Copyright © 2026 Mr. A. D. Rajegore, Dr. K. Y. Ingale. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.