Abstract
Utilizing carbon emission regulations helps firms to develop a sustainable supply chain. In a two-echelon supplier-retailer-customer relationship, offering a trade credit period can manage the inventory level. However, there will be a risk of settling the accounts during the trade credit period. Therefore, a portion of purchasing cost is charged as prepayment to mitigate some risk of payment delays. Moreover, obtaining the optimal price for perishable items with expiration dates has become a challenge because of their perishing process. Despite the importance of these challenges, very few papers have concentrated on sustainability considerations for perishable items. Also, the contribution of these issues to the credit risk buyers has never been studied. To address the mentioned gap in the literature, this elaboration investigates a supplier-retailer-customer economic order quantity model for perishable items when two levels of partial delay in payment are permissible and a carbon cap and tax policy is regulated to mitigate the impact of emissions on the two-echelon supply chain. The developed model is applicable in food industries to outline the challenges associated with deterioration, payments, and carbon emissions. This paper determines the optimal replenishment and selling price taking into account the following: (a) perishable items have their specific expiration dates, (b) a prepayment is charged from the buyer when offering a permissible delay in payment, (c) a carbon cap and tax policy is applied to approach the sustainability. Necessary and sufficient conditions of optimality are provided as the solution approach. A case study is presented, and numerical examples and sensitivity analyses are illustrated for validation. Finally, managerial applications are exposed, and results are concluded using future research insights.
Similar content being viewed by others
References
Aggarwal S, Jaggi C (1995) Ordering policies of deteriorating items under permissible delay in payments. J Oper Res Soc 46:658–662
Aljazzar SM, Gurtu A, Jaber MY (2018) Delay-in-payments-A strategy to reduce carbon emissions from supply chains. J Clean Prod 170:636–644
Bouchery Y, Ghaffari A, Jemai Z, Dallery Y (2012) Including sustainability criteria into inventory models. Eur J Oper Res 222:229–240
Cambini A, Martein L (2008) Generalized convexity and optimization: theory and applications vol 616. Springer Science & Business Media
Cárdenas-Barrón LE, Shaikh AA, Tiwari S, Treviño-Garza G (2020) An EOQ inventory model with nonlinear stock dependent holding cost, nonlinear stock dependent demand and trade credit. Comput Ind Eng 139:105557
Dye C-Y, Yang C-T (2015) Sustainable trade credit and replenishment decisions with credit-linked demand under carbon emission constraints. Eur J Oper Res 244:187–200
Feng L, Chan Y-L, Cárdenas-Barrón LE (2017) Pricing and lot-sizing polices for perishable goods when the demand depends on selling price, displayed stocks, and expiration date International. J Prod Econ 185:11–20
Goyal SK (1985) Economic order quantity under conditions of permissible delay in payments. J Oper Res Soc 36:335–338
He P, Zhang W, Xu X, Bian Y (2015) Production lot-sizing and carbon emissions under cap-and-trade and carbon tax regulations. J Clean Prod 103:241–248
Hovelaque V, Bironneau L (2015) The carbon-constrained EOQ model with carbon emission dependent demand. Int J Prod Econ 164:285–291
Hua G, Cheng T, Wang S (2011) Managing carbon footprints in inventory management. Int J Prod Econ 132:178–185
Huang Y-F (2003) Optimal retailer’s ordering policies in the EOQ model under trade credit financing. J Oper Res Soc 54:1011–1015
Huang Y-F (2007) Economic order quantity under conditionally permissible delay in payments. Eur J Oper Res 176:911–924
Jaggi CK, Goyal S, Goel SK (2008) Retailer’s optimal replenishment decisions with credit-linked demand under permissible delay in payments. Eur J Oper Res 190:130–135
Khan MA-A, Shaikh AA, Panda GC, Konstantaras I, Taleizadeh AA (2019) Inventory system with expiration date: pricing and replenishment decisions. Comput Ind Eng 132:232–247
Min J, Zhou Y-W, Zhao J (2010) An inventory model for deteriorating items under stock-dependent demand and two-level trade credit. Appl Math Model 34:3273–3285
Mishra U, Wu J-Z, Tseng M-L (2019) Effects of a hybrid-price-stock dependent demand on the optimal solutions of a deteriorating inventory system and trade credit policy on re-manufactured product. J Clean Prod 241:118282
Mishra U, Wu J-Z, Sarkar B (2020a) A sustainable production-inventory model for a controllable carbon emissions rate under shortages. J Clean Prod 256:120268
Mishra U, Wu J-Z, Tsao Y-C, Tseng M-L (2020b) Sustainable inventory system with controllable non-instantaneous deterioration and environmental emission rates. J Clean Prod 244:118807
Ren S-D, Zhao Y-W, Lou J-J, Hong H-H, Wang H-W (2018) Multifactor correlation analysis and modeling for product low-carbon design. J Ind Prod Eng 35:432–443
Sarkar B (2012) An EOQ model with delay in payments and time varying deterioration rate. Math Comput Model 55:367–377
Sekar T, Uthayakumar R (2018) Optimization of an imperfect manufacturing system for deteriorating items with rework and shortage under inflation. Process Integr Optim Sustain 2:303–320
Shi Y, Zhang Z, Chen S-C, Cárdenas-Barrón LE, Skouri K (2019) Optimal replenishment decisions for perishable products under cash, advance, and credit payments considering carbon tax regulations. Int J Prod Econ 107514
Tai AH, **e Y, He W, Ching W-K (2019) Joint inspection and inventory control for deteriorating items with random maximum lifetime. Int J Prod Econ 207:144–162
Teng J-T (2009) Optimal ordering policies for a retailer who offers distinct trade credits to its good and bad credit customers. Int J Prod Econ 119:415–423
Teng J-T, Cárdenas-Barrón LE, Chang H-J, Wu J, Hu Y (2016) Inventory lot-size policies for deteriorating items with expiration dates and advance payments. Appl Math Model 40:8605–8616
Tiwari S, Ahmed W, Sarkar B (2018a) Multi-item sustainable green production system under trade-credit and partial backordering. J Clean Prod 204:82–95
Tiwari S, Cárdenas-Barrón LE, Goh M, Shaikh AA (2018b) Joint pricing and inventory model for deteriorating items with expiration dates and partial backlogging under two-level partial trade credits in supply chain. Int J Prod Econ 200:16–36
Tiwari S, Cárdenas-Barrón LE, Shaikh AA, Goh M (2020) Retailer’s optimal ordering policy for deteriorating items under order-size dependent trade credit and complete backlogging. Comput Ind Eng 139:105559
Toptal A, Özlü H, Konur D (2014) Joint decisions on inventory replenishment and emission reduction investment under different emission regulations. Int J Prod Res 52:243–269
Tsao Y-C, Sheen G-J (2008) Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payments. Comput Oper Res 35:3562–3580
Wang W-C, Teng J-T, Lou K-R (2014) Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime. Eur J Oper Res 232:315–321
Wang Q, Wu J, Zhao N, Zhu Q (2019) Inventory control and supply chain management: a green growth perspective. Resour Conserv Recycl 145:78–85
Wu J, Chan Y-L (2014) Lot-sizing policies for deteriorating items with expiration dates and partial trade credit to credit-risk customers. Int J Prod Econ 155:292–301
Wu J, Ouyang L-Y, Cárdenas-Barrón LE, Goyal SK (2014) Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing. Eur J Oper Res 237:898–908
Wu J, Chang C-T, Teng J-T, Lai K-K (2017) Optimal order quantity and selling price over a product life cycle with deterioration rate linked to expiration date. Int J Prod Econ 193:343–351
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
The authors declare no competing interests.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Sepehri, A. Optimizing the Replenishment Cycle and Selling Price for an Inventory Model Under Carbon Emission Regulation and Partially Permissible Delay in Payment. Process Integr Optim Sustain 5, 577–597 (2021). https://doi.org/10.1007/s41660-021-00164-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41660-021-00164-9