Smart Economic Production Quantity Model with Circularity Index, Shortages, and Waste Management by 3D Printing

Document Type : Research Paper


1 Department of Mathematics, Maharaj Singh College, Saharanpur, UP (India) (Affiliated to MSU, Saharanpur)

2 Department of Mathematics, Deva Nagri College, Meerut, UP(India) (Affiliated to CCSU, Meerut)

3 Department of Mathematics Vardhaman College Bijnor (U.P.) India


In modern business, industries like electronics, aircraft, automobiles, etc., keep products in circulation through processes like reuse, remanufacture, and recycling to produce the original products while keeping environmental sustainability at the centre. Therefore, circularity index directly affects the demand and selling price of the products. Further, these industries are also applying 3D printing techniques to reduce the level of waste from the process as much as possible. 3D printing continues to evolve, it promises to reshape manufacturing, healthcare, and various other sectors, unlocking new possibilities for innovation and customization. So, to address all these issues, a smart production inventory model is proposed in the current study considering shortages, 3D printing technique, production rate depended wastage, green investment technology, and a circularity index. Demand rate of product is considered as the function of the circularity index. Objective of current study is to obtain the optimal values of production rate, production period, and cycle time so that overall inventory cost is minimum. In current study, calculus-based optimization technique has been used to obtain the optimal solution.  Finally, numerical analysis is provided to validate the proposed inventory model. The results show that circularity and 3D printing technique help to reduce waste from the system. In addition to this, emitted carbon level from the system is dropped from the production system. Managerial insights based on key parameters is also provided. At the end, future extension of the current model along with concluding remarks is incorporated.


Alamri, A. A. (2011). Theory and methodology on the global optimal solution to a General Reverse Logistics Inventory Model for deteriorating items and time-varying rates. Computers & Industrial Engineering60(2), 236-247.
Asiedu, Y., & Gu, P. (1998). Product life cycle cost analysis: state of the art review. International journal of production research36(4), 883-908.
Bachar, R. K., Bhuniya, S., Ghosh, S. K., AlArjani, A., Attia, E., Uddin, M. S., & Sarkar, B. (2023). Product outsourcing policy for a sustainable flexible manufacturing system with reworking and green investment. Math. Biosci. Eng20, 1376-1401.
Benjaafar, S., Li, Y., & Daskin, M. (2012). Carbon footprint and the management of supply chains: Insights from simple models. IEEE transactions on automation science and engineering10(1), 99-116.
Benkherouf, L., Skouri, K., & Konstantaras, I. (2016). Optimal control of production, remanufacturing and refurbishing activities in a finite planning horizon inventory system. Journal of Optimization Theory and Applications168(2), 677-698.
Bhatnagar, P., Kumar, S., & Yadav, D. (2022). A single-stage cleaner production system with waste management, reworking, preservation technology, and partial backlogging under inflation. RAIRO-Operations Research56(6), 4327-4346.
Christy, A. Y., Fauzi, B. N., Kurdi, N. A., Jauhari, W. A., & Saputro, D. R. S. (2017, June). A closed-loop supply chain under retail price and quality dependent demand with remanufacturing and refurbishing. In Journal of Physics: Conference Series (Vol. 855, No. 1, p. 012009). IOP Publishing.
Chung, C. J., & Wee, H. M. (2011). Short life-cycle deteriorating product remanufacturing in a green supply chain inventory control system. International Journal of Production Economics129(1), 195-203.
Daryanto, Y., Wee, H. M., & Astanti, R. D. (2019). Three-echelon supply chain model considering carbon emission and item deterioration. Transportation Research Part E: Logistics and Transportation Review122, 368-383.
Datta, T. K. (2017). Effect of green technology investment on a production-inventory system with carbon tax. Advances in operations research2017.
Dey, B. K., Park, J., & Seok, H. (2022). Carbon-emission and waste reduction of a manufacturing-remanufacturing system using green technology and autonomated inspection. RAIRO-Operations Research56(4), 2801-2831.
Giri, B. C., & Sharma, S. (2015). Optimizing a closed-loop supply chain with manufacturing defects and quality dependent return rate. Journal of Manufacturing Systems35, 92-111.
Hua, G., Cheng, T. C. E., & Wang, S. (2011). Managing carbon footprints in inventory management. International Journal of Production Economics132(2), 178-185.
Jaber, M. Y., Zanoni, S., & Zavanella, L. E. (2014). A consignment stock coordination scheme for the production, remanufacturing and waste disposal problem. International Journal of Production Research52(1), 50-65.
Jauhari, W. A., & Wangsa, I. D. (2022). A Manufacturer-Retailer Inventory Model with Remanufacturing, Stochastic Demand, and Green Investments. Process Integration and Optimization for Sustainability6(2), 253-273.
Jauhari, W. A., Adam, N. A. F. P., Rosyidi, C. N., Pujawan, I. N., & Shah, N. H. (2020). A closed-loop supply chain model with rework, waste disposal, and carbon emissions. Operations Research Perspectives7, 100155.
Jauhari, W. A., Hendaryani, O., & Kurdhi, N. A. (2018). Inventory decisions in a closed-loop supply chain system with learning and rework. Int J Procure Manag11(5), 551-585.
John, E. P., & Mishra, U. (2024). Integrated multitrophic aquaculture supply chain fish traceability with blockchain technology, valorisation of fish waste and plastic pollution reduction by seaweed bioplastic: A study in tuna fish aquaculture industry. Journal of Cleaner Production434, 140056.
King, A. M., Burgess, S. C., Ijomah, W., & McMahon, C. A. (2006). Reducing waste: repair, recondition, remanufacture or recycle?. Sustainable development14(4), 257-267.
Kumar, S., Sami, S., Agarwal, S., & Yadav, D. (2023). Sustainable fuzzy inventory model for deteriorating item with partial backordering along with social and environmental responsibility under the effect of learning. Alexandria Engineering Journal69, 221-241.
Kumar, S., Singh, S. R., Agarwal, S., & Yadav, D. (2023). Joint effect of selling price and promotional efforts on retailer’s inventory control policy with trade credit, time-dependent holding cost, and partial backlogging under inflation. RAIRO-Operations Research57(3), 1491-1522.
Lewandowski, M. (2016). Designing the business models for circular economy—Towards the conceptual framework. Sustainability8(1), 43.
Li, J., Lai, K. K., & Li, Y. (2024). Remanufacturing and low-carbon investment strategies in a closed-loop supply chain under multiple carbon policies. International Journal of Logistics Research and Applications27(1), 170-192.
Lok, Y. W., Supadi, S. S., & Wong, K. B. (2023). Optimal investment in preservation technology for non-instantaneous deteriorating items under carbon emissions consideration. Computers & Industrial Engineering183, 109446.
Lou, G. X., Xia, H. Y., Zhang, J. Q., & Fan, T. J. (2015). Investment strategy of emission-reduction technology in a supply chain. Sustainability7(8), 10684-10708.
Manna, A. K., Dey, J. K., & Mondal, S. K. (2017). Imperfect production inventory model with production rate dependent defective rate and advertisement dependent demand. Computers & Industrial Engineering104, 9-22.
McKenna, R., Reith, S., Cail, S., Kessler, A., & Fichtner, W. (2013). Energy savings through direct secondary reuse: an exemplary analysis of the German automotive sector. Journal of cleaner production52, 103-112.
Mishra, U., Wu, J. Z., & Sarkar, B. (2020). A sustainable production-inventory model for a controllable carbon emissions rate under shortages. Journal of Cleaner Production256, 120268.
Mohammed, M., Mohan, M., Das, A., Johnson, M. D., Badwal, P. S., McLean, D., & Gibson, I. (2017, January). A low carbon footprint approach to the reconstitution of plastics into 3D-printer filament for enhanced waste reduction. In DesTech 2016: Proceedings of the International Conference on Design and Technology (pp. 234-241). Knowledge E.
Peter John, E., & Mishra, U. (2023). Sustainable circular economy production system with emission control in LED bulb companies. Environmental Science and Pollution Research30(21), 59963-59990.
Rabta, B. (2020). An Economic Order Quantity inventory model for a product with a circular economy indicator. Computers & Industrial Engineering140, 106215.
Rana, K., Singh, S. R., Saxena, N., & Sana, S. S. (2021). Growing items inventory model for carbon emission under the permissible delay in payment with partially backlogging. Green Finance3(2), 153-174.
Richter, K., & Dobos, I. (1999). Analysis of the EOQ repair and waste disposal problem with integer setup numbers. International journal of production economics59(1-3), 463-467.
Robotis, A., Bhattacharya, S., & Van Wassenhove, L. N. (2005). The effect of remanufacturing on procurement decisions for resellers in secondary markets. European Journal of Operational Research163(3), 688-705.
Sarkar, M., Dey, B. K., Ganguly, B., Saxena, N., Yadav, D., & Sarkar, B. (2023). The impact of information sharing and bullwhip effects on improving consumer services in dual-channel retailing. Journal of Retailing and Consumer Services73, 103307.
Shahpasand, R., Talebian, A., & Mishra, S. S. (2023). Investigating environmental and economic impacts of the 3D printing technology on supply chains: The case of tire production. Journal of Cleaner Production, 135917.
Shree, M. V., Dhinakaran, V., Rajkumar, V., Ram, P. B., Vijayakumar, M. D., & Sathish, T. (2020). Effect of 3D printing on supply chain management. Materials Today: Proceedings21, 958-963.
Singh, R., Yadav, D., Singh, S.R., Kumar, A., and Sarkar, B. (2023). Reduction of carbon emissions under sustainable supply chain management with uncertain human learning. AIMS Environmental Science,10(4): 559-592.
Singh, S. R., Sarkar, M., & Sarkar, B. (2023). Effect of Learning and Forgetting on Inventory Model under Carbon Emission and Agile Manufacturing. Mathematics11(2), 368.
Su, R. H., Weng, M. W., Yang, C. T., & Li, H. T. (2021). An imperfect production–inventory model with mixed materials containing scrap returns based on a circular economy. Processes9(8), 1275.
Taleizadeh, A. A., Haghighi, F., & Niaki, S. T. A. (2019). Modeling and solving a sustainable closed loop supply chain problem with pricing decisions and discounts on returned products. Journal of cleaner production207, 163-181.
Thomas, A., & Mishra, U. (2022). A sustainable circular economic supply chain system with waste minimization using 3D printing and emissions reduction in plastic reforming industry. Journal of Cleaner Production345, 131128.
Tissayakorn, K., & Akagi, F. (2014, February). Green logistics management and performance for Thailand's logistic enterprises. In 2014 IEEE International Conference on Industrial Technology (ICIT) (pp. 707-711). IEEE.
Voulvoulis, N., Kirkman, R., Giakoumis, T., Metivier, P., Kyle, P., & Midgley, C. (2020). Examining Material Evidence: The Carbon Fingerprint. Imperial College London7, 1-15.
Yadav, D., Chand, U., Goel, R., & Sarkar, B. (2023). Smart production system with random imperfect process, partial backordering, and deterioration in an inflationary environment. Mathematics11(2), 440.