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All Journal International Journal of Industrial Optimization (IJIO)
Wang, Chih-Hsiung
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Decision Sciences, Operations Research & Management Engineering Industrial & Manufacturing Engineering

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Effect of return rate on optimal order quantity for single-period products: a modified newsboy problem approach Hsiao, Wen-Feng; Tsai, W.C.; Wang, Chih-Hsiung
International Journal of Industrial Optimization Vol. 7 No. 1 (2026)
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12928/ijio.v7i1.11340

Abstract

This paper proposes a modified newsboy problem for single-period fashion products, sold by e-stores, for the case where product returns are allowed during the sales season. This is because, even if an e-store sells high-quality products, returns may still occur due to unpredictable consumer behavior in online sales. In the developed model, the assumption from the literature that the number of returns during the sales period is unlimited has been modified to align with real-world conditions. In formulating the problem, the number of returns is assumed to be bounded by a random variable. The corresponding mathematical model is established and the optimal order quantity investigated. The traditional newsboy model is shown to be a special case of the proposed model for which the return factor is ignored. The numerical results show that the optimal order quantity determined when the return rate is ignored is always overestimated and the resulting expected total profit is thus always underestimated. A sensitivity analysis is performed to determine the effects of the model parameters on the optimal solution. The numerical example demonstrates that, in the case of the product return rate, the order quantity predicted by the traditional newsboy model is overestimated by approximately 10%, which results in a profit reduction of about 1%. The numerical results have shown that when the return rate is ignored, the estimated optimal order quantity is higher than the true optimal order quantity and causes the total profit to be slightly underestimated.
Co-Authors Hsiao, Wen-Feng Tsai, W.C.