The Inventory Model for Deteriorating Items under Conditions Involving Cash Discount and Trade Credit

Kun-Jen Chung, Jui-Jung Liao, Shy- Der Lin, Sheng-Tu Chuang and Hari Mohan Srivastava
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Kun-Jen Chung: College of Business, Chung Yuan Christian University, Chung-Li 32023, Taiwan
Jui-Jung Liao: Department of Business Administration, Chihlee University of Technology, Banqiao District, New Taipei 22050, Taiwan
Shy- Der Lin: Department of Applied Mathematics and Business Administration, Chung Yuan Christian University, Chung-Li 32023, Taiwan
Sheng-Tu Chuang: Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li 30323, Taiwan
Hari Mohan Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada

Mathematics, 2019, vol. 7, issue 7, 1-20

Abstract: In the year 2004, Chang and Teng investigated an inventory model for deteriorating items in which the supplier not only provides a cash discount, but also allows a permissible delay in payments. The main purpose of the present investigation is three-fold, as follows. First, it is found herein that Theorem 1 of Chang and Teng (2004) has notable shortcomings in terms of their determination of the optimal solution of the annual total relevant cost Z ( T ) by adopting the Taylor-series approximation method. Theorem 1 in this paper does not make use of the Taylor-series approximation method in order to overcome the shortcomings in Chang and Teng (2004) and alternatively derives all the optimal solutions of the annual total relevant cost Z ( T ) . Secondly, this paper systematically revisits the annual total relevant cost Z ( T ) in Chang and Teng (2004) and presents in detail the mathematically correct ways for the derivations of Z ( T ) . Thirdly, this paper not only shows that Theorem 1 of Chang and Teng (2004) is not necessarily true for finding the optimal solution of the annual total relevant cost Z ( T ) , but it also demonstrates how Theorem 1 in this paper can locate all of the optimal solutions of Z ( T ) . The mathematical analytic investigation presented in this paper is believed to be useful for correct managerial considerations and managerial decisions.

Keywords: inventory modelling and optimization; Trade-credit financing; Cash discounts; permissible delays in payments; Supply chain management; economic order quantity (EOQ); mathematical solution procedure; deteriorating items; mathematical analytic tools and techniques; managerial considerations and managerial decisions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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