University of Tehran Press Interdisciplinary Journal of Management Studies 2981-0795 15 1 2022 01 01 A Lot-Sizing Model for Non-Instantaneous Deteriorating Products Under Advance Payment and Non-Linear Partial Backlogging مدل تعیین اندازه دسته تولید برای محصولات زوال‌پذیر غیر آنی تحت پیش‌پرداخت و پشتیبانی جزئی غیر خطی 85 110 81353 10.22059/ijms.2021.315463.674346 EN Sara Tavassoli School of Industrial and Systems Engineering, College of Engineering, University of Tehran, Tehran, Iran Neda Manavizadeh Department of Industrial Engineering, KHATAM University, Tehran, Iran Aida Rezaei School of Industrial and Systems Engineering, College of Engineering, University of Tehran, Tehran, Iran 0000-0001-5765-2614 Masoud Rabbani School of Industrial and Systems Engineering, College of Engineering, University of Tehran, Tehran, Iran 0000-0001-8756-4922 Journal Article 2020 12 18 In real life conditions, the buyers sometimes pay all or a percentage of the product price before receiving it, and the wholesaler sometimes allows them to prepay it at equal intervals. The present study develops a new mathematical model for products with non-instantaneous deteriorating rates by considering consecutive advance payments. In the proposed inventory model, the shortage is consisting of lost sales along with backorders simultaneously. In addition, the model considers the backlogging as totally dependent on the waiting time for the further cycle. In addition, the appropriate conditions to achieve the optimal solutions have been developed, and numerical instances have been provided to verify and evaluate the results and solution method. The useful methods to effectively reduce the annual total cost are provided according to the results of the sensitivity analysis. https://ijms.ut.ac.ir/article_81353_61b9002f3ed86432952810fa1d25334f.pdf