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Optimization of a price break policy and advertisement effort based non-instantaneous deteriorating inventory problem with partial backlogged via metaheuristic algorithms

Author

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  • Mondal, Rajan
  • Manna, Amalesh Kumar
  • Akhtar, Md
  • Bhunia, Asoke Kumar

Abstract

Repeated advertisements of an item in different media, displayed stock in a decorated showroom, and also price break policies play a vital role in an inventory control system. Also, the relationship between products’ selling price and market demand is conflicting when all other factors are fixed. Thus, the incorporation of advertisement policy and price break facility in a business is more realistic. This work investigates an inventory problem for non-instantaneous deteriorating items with advertisement and displayed inventory level dependent demand under price break facility. Moreover, partially backlogged shortages and transportation cost for replenishing items are considered in the proposed inventory model. Based on the customer’s demand and storage space of the shop, several cases and sub-cases are considered. In this study, different metaheuristic algorithms are considered for maximizing the average profit in each scenario. Then, considering one numerical example, the proposed model is justified. Finally, the sensitivity analysis is carried out to investigate the impact of model parameters on the policy of optimality and a fruitful conclusion is drawn.

Suggested Citation

  • Mondal, Rajan & Manna, Amalesh Kumar & Akhtar, Md & Bhunia, Asoke Kumar, 2025. "Optimization of a price break policy and advertisement effort based non-instantaneous deteriorating inventory problem with partial backlogged via metaheuristic algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 236(C), pages 221-247.
    • Handle: RePEc:eee:matcom:v:236:y:2025:i:c:p:221-247
    DOI: 10.1016/j.matcom.2025.04.007
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    1. Komeyl Baghizadeh & Nafiseh Ebadi & Dominik Zimon & Luay Jum’a, 2022. "Using Four Metaheuristic Algorithms to Reduce Supplier Disruption Risk in a Mathematical Inventory Model for Supplying Spare Parts," Mathematics, MDPI, vol. 11(1), pages 1-19, December.
    2. R. Sundararajan & M. Palanivel & S. Vaithyasubramanian, 2023. "On the EOQ Models with Advertisement-Price-Dependent Demand and Quantity Discount with Expiration Date Under Shortage," SN Operations Research Forum, Springer, vol. 4(4), pages 1-31, December.
    3. Li, Guiping & He, Xiuli & Zhou, Jing & Wu, Hao, 2019. "Pricing, replenishment and preservation technology investment decisions for non-instantaneous deteriorating items," Omega, Elsevier, vol. 84(C), pages 114-126.
    4. Al-Amin Khan, Md. & Shaikh, Ali Akbar & Konstantaras, Ioannis & Bhunia, Asoke Kumar & Cárdenas-Barrón, Leopoldo Eduardo, 2020. "Inventory models for perishable items with advanced payment, linearly time-dependent holding cost and demand dependent on advertisement and selling price," International Journal of Production Economics, Elsevier, vol. 230(C).
    5. Nguyen Duy Tan & Hwan-Seong Kim & Le Ngoc Bao Long & Duy Anh Nguyen & Sam-Sang You, 2024. "Optimization and inventory management under stochastic demand using metaheuristic algorithm," PLOS ONE, Public Library of Science, vol. 19(1), pages 1-25, January.
    6. Maihami, Reza & Nakhai Kamalabadi, Isa, 2012. "Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand," International Journal of Production Economics, Elsevier, vol. 136(1), pages 116-122.
    7. Ajoy Hatibaruah & Sumit Saha, 2023. "An inventory model for two-parameter Weibull distributed ameliorating and deteriorating items with stock and advertisement frequency dependent demand under trade credit and preservation technology," OPSEARCH, Springer;Operational Research Society of India, vol. 60(2), pages 951-1002, June.
    8. Pankaj Narang & Pijus Kanti De, 2023. "An imperfect production-inventory model for reworked items with advertisement, time and price dependent demand for non-instantaneous deteriorating item using genetic algorithm," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 24(1), pages 53-77.
    9. Madadi, Alireza & Kurz, Mary E. & Ashayeri, Jalal, 2010. "Multi-level inventory management decisions with transportation cost consideration," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(5), pages 719-734, September.
    10. Chandan Mahato & Gour Chandra Mahata, 2023. "Sustainable partial backordering inventory model under linked-to-order credit policy and all-units discount with capacity constraint and carbon emissions," Flexible Services and Manufacturing Journal, Springer, vol. 35(3), pages 896-944, September.
    11. Chandra K. Jaggi & Priyanka Verma, 2010. "Two-warehouse inventory model for deteriorating items with linear trend in demand and shortages under inflationary conditions," International Journal of Procurement Management, Inderscience Enterprises Ltd, vol. 3(1), pages 54-71.
    12. M. Palanivel & M. Suganya, 2022. "Partial backlogging inventory model with price and stock level dependent demand, time varying holding cost and quantity discounts," Journal of Management Analytics, Taylor & Francis Journals, vol. 9(1), pages 32-59, January.
    13. W. J. Baumol & H. D. Vinod, 1970. "An Inventory Theoretic Model of Freight Transport Demand," Management Science, INFORMS, vol. 16(7), pages 413-421, March.
    14. M. Palanivel & R. Uthayakumar, 2015. "Finite horizon EOQ model for non-instantaneous deteriorating items with price and advertisement dependent demand and partial backlogging under inflation," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(10), pages 1762-1773, July.
    15. Ali Akbar Shaikh & Abu Hashan Md Mashud & Md. Sharif Uddin & Md. Al-Amin Khan, 2017. "Non-instantaneous deterioration inventory model with price and stock dependent demand for fully backlogged shortages under inflation," International Journal of Business Forecasting and Marketing Intelligence, Inderscience Enterprises Ltd, vol. 3(2), pages 152-164.
    16. Yang, Liu & Liu, Kanglin & Zhang, Juan & Zelbst, Pamela J., 2024. "Inventory management with actual palletized transportation costs and lost sales," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 184(C).
    17. J. Viswanath & R. Thilagavathi, 2024. "A study of two warehouse inventory dynamism for non-instantaneous deteriorating item with Weibull demand considering trade credit policy," OPSEARCH, Springer;Operational Research Society of India, vol. 61(4), pages 1906-1926, December.
    18. Shah, Nita H & Soni, Hardik N & Patel, Kamlesh A, 2013. "Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates," Omega, Elsevier, vol. 41(2), pages 421-430.
    19. Zhang, Jianxiong & Wang, Yu & Lu, Lihao & Tang, Wansheng, 2015. "Optimal dynamic pricing and replenishment cycle for non-instantaneous deterioration items with inventory-level-dependent demand," International Journal of Production Economics, Elsevier, vol. 170(PA), pages 136-145.
    20. Pal, A.K. & Bhunia, A.K. & Mukherjee, R.N., 2006. "Optimal lot size model for deteriorating items with demand rate dependent on displayed stock level (DSL) and partial backordering," European Journal of Operational Research, Elsevier, vol. 175(2), pages 977-991, December.
    21. Sunil Tiwari & Chandra K. Jaggi & Asoke Kumar Bhunia & Ali Akbar Shaikh & Mark Goh, 2017. "Two-warehouse inventory model for non-instantaneous deteriorating items with stock-dependent demand and inflation using particle swarm optimization," Annals of Operations Research, Springer, vol. 254(1), pages 401-423, July.
    22. Md Akhtar & Amalesh Kumar Manna & Avijit Duary & Asoke Kumar Bhunia, 2022. "A hybrid tournament differential evolution algorithm for solving optimisation problems and applications," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 45(3), pages 300-343.
    23. José A. Ventura & Boaz Golany & Abraham Mendoza & Chenxi Li, 2022. "A multi-product dynamic supply chain inventory model with supplier selection, joint replenishment, and transportation cost," Annals of Operations Research, Springer, vol. 316(2), pages 729-762, September.
    24. Nita H. Shah & Mamta Keswani & Uttam Kumar Khedlekar & Naisargi M. Prajapati, 2024. "Non-instantaneous controlled deteriorating inventory model for stock-price-advertisement dependent probabilistic demand under trade credit financing," OPSEARCH, Springer;Operational Research Society of India, vol. 61(1), pages 421-459, March.
    25. S. Anily & A. Federgruen, 1990. "One Warehouse Multiple Retailer Systems with Vehicle Routing Costs," Management Science, INFORMS, vol. 36(1), pages 92-114, January.
    26. Tiwari, Sunil & Cárdenas-Barrón, Leopoldo Eduardo & Khanna, Aditi & Jaggi, Chandra K., 2016. "Impact of trade credit and inflation on retailer's ordering policies for non-instantaneous deteriorating items in a two-warehouse environment," International Journal of Production Economics, Elsevier, vol. 176(C), pages 154-169.
    27. Rajan Mondal & Subhajit Das & Md Akhtar & Ali Akbar Shaikh & Asoke Kumar Bhunia, 2024. "A two-warehouse inventory model for deteriorating items with partially backlogged demand rate under trade credit policies," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(7), pages 3350-3367, July.
    28. Swati Agrawal & Snigdha Banerjee, 2011. "Two-warehouse inventory model with ramp-type demand and partially backlogged shortages," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(7), pages 1115-1126.
    29. San-José, Luis A. & Sicilia, Joaquín & Cárdenas-Barrón, Leopoldo Eduardo & González-de-la-Rosa, Manuel, 2024. "A sustainable inventory model for deteriorating items with power demand and full backlogging under a carbon emission tax," International Journal of Production Economics, Elsevier, vol. 268(C).
    30. Pal, Brojeswar & Sana, Shib Sankar & Chaudhuri, Kripasindhu, 2012. "Multi-item EOQ model while demand is sales price and price break sensitive," Economic Modelling, Elsevier, vol. 29(6), pages 2283-2288.
    31. Dipak Kumar Jana & Barun Das, 2017. "A two-storage multi-item inventory model with hybrid number and nested price discount via hybrid heuristic algorithm," Annals of Operations Research, Springer, vol. 248(1), pages 281-304, January.
    32. Duan, Lisha & Ventura, José A., 2019. "A Dynamic Supplier Selection and Inventory Management Model for a Serial Supply Chain with a Novel Supplier Price Break Scheme and Flexible Time Periods," European Journal of Operational Research, Elsevier, vol. 272(3), pages 979-998.
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