The Inventory Model for Deteriorating Items under Conditions Involving Cash Discount and Trade Credit
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 T...
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MDPI AG
2019-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/7/596 |
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| author | Kun-Jen Chung Jui-Jung Liao Shy-Der Lin Sheng-Tu Chuang Hari Mohan Srivastava |
| author_facet | Kun-Jen Chung Jui-Jung Liao Shy-Der Lin Sheng-Tu Chuang Hari Mohan Srivastava |
| author_sort | Kun-Jen Chung |
| collection | DOAJ |
| description | 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>. Secondly, this paper systematically revisits the annual total relevant cost <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> in Chang and Teng (2004) and presents in detail the mathematically correct ways for the derivations of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>. 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>, but it also demonstrates how Theorem 1 in this paper can locate all of the optimal solutions of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>. The mathematical analytic investigation presented in this paper is believed to be useful for correct managerial considerations and managerial decisions. |
| first_indexed | 2024-12-12T11:11:12Z |
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| id | doaj.art-0fa3084b64fb43dda421161b89a8499f |
| institution | Directory Open Access Journal |
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| language | English |
| last_indexed | 2024-12-12T11:11:12Z |
| publishDate | 2019-07-01 |
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| spelling | doaj.art-0fa3084b64fb43dda421161b89a8499f2022-12-22T00:26:17ZengMDPI AGMathematics2227-73902019-07-017759610.3390/math7070596math7070596The Inventory Model for Deteriorating Items under Conditions Involving Cash Discount and Trade CreditKun-Jen Chung0Jui-Jung Liao1Shy-Der Lin2Sheng-Tu Chuang3Hari Mohan Srivastava4College of Business, Chung Yuan Christian University, Chung-Li 32023, TaiwanDepartment of Business Administration, Chihlee University of Technology, Banqiao District, New Taipei 22050, TaiwanDepartment of Applied Mathematics and Business Administration, Chung Yuan Christian University, Chung-Li 32023, TaiwanDepartment of Applied Mathematics, Chung Yuan Christian University, Chung-Li 30323, TaiwanDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaIn 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>. Secondly, this paper systematically revisits the annual total relevant cost <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> in Chang and Teng (2004) and presents in detail the mathematically correct ways for the derivations of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>. 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>, but it also demonstrates how Theorem 1 in this paper can locate all of the optimal solutions of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>. The mathematical analytic investigation presented in this paper is believed to be useful for correct managerial considerations and managerial decisions.https://www.mdpi.com/2227-7390/7/7/596inventory modelling and optimizationTrade-credit financingCash discountspermissible delays in paymentsSupply chain managementeconomic order quantity (EOQ)mathematical solution proceduredeteriorating itemsmathematical analytic tools and techniquesmanagerial considerations and managerial decisions |
| spellingShingle | Kun-Jen Chung Jui-Jung Liao Shy-Der Lin Sheng-Tu Chuang Hari Mohan Srivastava The Inventory Model for Deteriorating Items under Conditions Involving Cash Discount and Trade Credit Mathematics 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 |
| title | The Inventory Model for Deteriorating Items under Conditions Involving Cash Discount and Trade Credit |
| title_full | The Inventory Model for Deteriorating Items under Conditions Involving Cash Discount and Trade Credit |
| title_fullStr | The Inventory Model for Deteriorating Items under Conditions Involving Cash Discount and Trade Credit |
| title_full_unstemmed | The Inventory Model for Deteriorating Items under Conditions Involving Cash Discount and Trade Credit |
| title_short | The Inventory Model for Deteriorating Items under Conditions Involving Cash Discount and Trade Credit |
| title_sort | inventory model for deteriorating items under conditions involving cash discount and trade credit |
| topic | 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 |
| url | https://www.mdpi.com/2227-7390/7/7/596 |
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