Optimal Production Inventory Model with Preservation Technology, Recycling, and Partial Backlogging under Level Dependent Demand

Abstract

This paper proposes a production inventory model for deteriorating items with level-dependent demand, explicitly incorporating preservation technology. Demand increases with on-hand inventory, reflecting visibility and display effects, while deterioration is reduced through a controllable preservation effort at an additional cost. The model allows shortages, where unmet demand is partially backlogged and partially lost. A comprehensive total cost function is formulated by accounting for production, holding, deterioration, preservation, setup, backlog, and lost-sales costs over a finite production cycle. Owing to the nonlinear and interdependent nature of the system, the optimal production quantity and preservation effort are obtained using numerical optimization techniques. Sensitivity analysis is conducted to examine the impact of key parameters on total cost and decision variables. Numerical results demonstrate that moderate investment in preservation significantly reduces deterioration and overall cost, whereas excessive preservation yields diminishing economic returns. The model provides practical insights for managing production systems dealing with perishable or quality-sensitive products.

Keywords

• Perishable Inventory
• Level-Dependent Demand
• Cost optimization
• Decay Cost
• Preservation technology

How to cite

Mohammad Ekramol Islam, Md. Asrafi Al Mamun (2026). Optimal Production Inventory Model with Preservation Technology, Recycling, and Partial Backlogging under Level Dependent Demand. Sonargaon University Journal, 6(I), 39–52.

@article{islam20264,
  title   = {Optimal Production Inventory Model with Preservation Technology, Recycling, and Partial Backlogging under Level Dependent Demand},
  author  = {Mohammad Ekramol Islam and Md. Asrafi Al Mamun},
  journal = {Sonargaon University Journal},
  volume  = {6},
  number  = {I},
  pages   = {39--52},
  year    = {2026},
  issn    = {2518-3125},
  url     = {https://su.edu.bd/journal/volume-6-issue-1/optimal-production-inventory-model-with-preservation-technology-recycling-and}
}