Inventory Models for Non-Instantaneous Deteriorating Items with Expiration Dates and Imperfect Quality under Hybrid Payment Policy in the Three-Level Supply Chain
This article considers an inventory model for non-instantaneous deteriorating items with expiration dates, such as seasonal items, first-hand vegetables, and fruits. Interestingly, an inspection will be performed to manage the quality of the items during the state of no deterioration because it is d...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/9/1695 |
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| author | Jui-Jung Liao Hari Mohan Srivastava Kun-Jen Chung Shih-Fang Lee Kuo-Nan Huang Shy-Der Lin |
| author_facet | Jui-Jung Liao Hari Mohan Srivastava Kun-Jen Chung Shih-Fang Lee Kuo-Nan Huang Shy-Der Lin |
| author_sort | Jui-Jung Liao |
| collection | DOAJ |
| description | This article considers an inventory model for non-instantaneous deteriorating items with expiration dates, such as seasonal items, first-hand vegetables, and fruits. Interestingly, an inspection will be performed to manage the quality of the items during the state of no deterioration because it is difficult to purchase items with 100% perfection. Additionally, we assume that the upstream member has the power of controlling or influencing downstream members’ decisions. That is, the supplier asks the retailer for a partial advance payment to avoid cancellation of orders and offers them a credit payment to stimulate sales; in turn, the customer must pay some cash when placing an order and pay the remainder in credit for the retailer. The goal of this article is to determine an optimal replenishment cycle and the total annual cost function, so we explore the functional properties of the total annual cost function and show that the total annual cost function is convex. Theoretical analysis of the optimal properties shows the existence and uniqueness of the optimal solution. Then, we obtain simple and easy solution procedures for the inventory system. Moreover, numerical analysis of the inventory model is conducted, and the corresponding examples are considered with a view to illustrating the application of the supply chain model that we have investigated in this article. Finally, in the concluding section, we have not only provided the motivation and the need for our usages of mathematical analytic solution procedures based upon the convexity, monotonicity (increasing and decreasing) and differentiability properties of the object function (that is, the total annual cost function), which involve some symmetry aspects of the object function, but we have also indicated the limitations and shortcomings in our investigation, which will naturally lead to some potential directions for further research on the supply chain model, which we have considered and mathematically analyzed in this article. |
| first_indexed | 2024-03-10T07:11:04Z |
| format | Article |
| id | doaj.art-eb693fc0d06d40aeb6b0b07b52fc07bf |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T07:11:04Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-eb693fc0d06d40aeb6b0b07b52fc07bf2023-11-22T15:28:37ZengMDPI AGSymmetry2073-89942021-09-01139169510.3390/sym13091695Inventory Models for Non-Instantaneous Deteriorating Items with Expiration Dates and Imperfect Quality under Hybrid Payment Policy in the Three-Level Supply ChainJui-Jung Liao0Hari Mohan Srivastava1Kun-Jen Chung2Shih-Fang Lee3Kuo-Nan Huang4Shy-Der Lin5Department of Business Administration, Chihlee University of Technology, Banqiao District, New Taipei City 22050, TaiwanDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaCollege of Business, Chung Yuan Christian University, Chung Li 320314, TaiwanDepartment of Applied Mathematics, Chung Yuan Christian University, Chung Li 320314, TaiwanDepartment of Industrial Management and Business Administration, St. John’s University, Tamsui District, New Taipei City 25135, TaiwanDepartment of Applied Mathematics and Business Administration, Chung Yuan Christian University, Chung Li 320314, TaiwanThis article considers an inventory model for non-instantaneous deteriorating items with expiration dates, such as seasonal items, first-hand vegetables, and fruits. Interestingly, an inspection will be performed to manage the quality of the items during the state of no deterioration because it is difficult to purchase items with 100% perfection. Additionally, we assume that the upstream member has the power of controlling or influencing downstream members’ decisions. That is, the supplier asks the retailer for a partial advance payment to avoid cancellation of orders and offers them a credit payment to stimulate sales; in turn, the customer must pay some cash when placing an order and pay the remainder in credit for the retailer. The goal of this article is to determine an optimal replenishment cycle and the total annual cost function, so we explore the functional properties of the total annual cost function and show that the total annual cost function is convex. Theoretical analysis of the optimal properties shows the existence and uniqueness of the optimal solution. Then, we obtain simple and easy solution procedures for the inventory system. Moreover, numerical analysis of the inventory model is conducted, and the corresponding examples are considered with a view to illustrating the application of the supply chain model that we have investigated in this article. Finally, in the concluding section, we have not only provided the motivation and the need for our usages of mathematical analytic solution procedures based upon the convexity, monotonicity (increasing and decreasing) and differentiability properties of the object function (that is, the total annual cost function), which involve some symmetry aspects of the object function, but we have also indicated the limitations and shortcomings in our investigation, which will naturally lead to some potential directions for further research on the supply chain model, which we have considered and mathematically analyzed in this article.https://www.mdpi.com/2073-8994/13/9/1695inventory modelingmathematical analytic solution procedureseconomic order quantity (EOQ) modeldeteriorating productsimperfect qualityhybrid payment policy |
| spellingShingle | Jui-Jung Liao Hari Mohan Srivastava Kun-Jen Chung Shih-Fang Lee Kuo-Nan Huang Shy-Der Lin Inventory Models for Non-Instantaneous Deteriorating Items with Expiration Dates and Imperfect Quality under Hybrid Payment Policy in the Three-Level Supply Chain Symmetry inventory modeling mathematical analytic solution procedures economic order quantity (EOQ) model deteriorating products imperfect quality hybrid payment policy |
| title | Inventory Models for Non-Instantaneous Deteriorating Items with Expiration Dates and Imperfect Quality under Hybrid Payment Policy in the Three-Level Supply Chain |
| title_full | Inventory Models for Non-Instantaneous Deteriorating Items with Expiration Dates and Imperfect Quality under Hybrid Payment Policy in the Three-Level Supply Chain |
| title_fullStr | Inventory Models for Non-Instantaneous Deteriorating Items with Expiration Dates and Imperfect Quality under Hybrid Payment Policy in the Three-Level Supply Chain |
| title_full_unstemmed | Inventory Models for Non-Instantaneous Deteriorating Items with Expiration Dates and Imperfect Quality under Hybrid Payment Policy in the Three-Level Supply Chain |
| title_short | Inventory Models for Non-Instantaneous Deteriorating Items with Expiration Dates and Imperfect Quality under Hybrid Payment Policy in the Three-Level Supply Chain |
| title_sort | inventory models for non instantaneous deteriorating items with expiration dates and imperfect quality under hybrid payment policy in the three level supply chain |
| topic | inventory modeling mathematical analytic solution procedures economic order quantity (EOQ) model deteriorating products imperfect quality hybrid payment policy |
| url | https://www.mdpi.com/2073-8994/13/9/1695 |
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