Industrial Innovations

Industrial Innovations

Inventory Control Planning of Economic Production Quantity for Perishable Products under Stochastic Demand

Document Type : Original Article

Authors
Reza Mirzaie
Heibatolah Sadeghi
Department of Industrial Engineering, University of Kurdistan, Sanandaj, Iran.
10.66224/jii.3.2.99
Abstract
One of the key issues in contemporary economics and inventory management is the determination of the economic production quantity for perishable products. This problem holds particular significance due to challenges such as product deterioration, imperfect production, stochastic demand, and its dependency on price, which complicate optimal decision-making in real-world supply chains.
In this research, the economic production quantity problem for perishable items under stochastic demand is examined, incorporating realistic assumptions including a constant deterioration rate for products, rework of defective items, full backordering of shortages, demand dependency on selling price under Brownian motion behavior, and an exponentially declining production rate to simulate the progressive deterioration of production equipment over time.
In this problem, the production system manufactures perishable products, a portion of which are defective due to imperfect processes. The system performs rework on defective items to convert them back to perfect-quality products, while also accounting for the gradual decline in production rate resulting from equipment aging. To maximize long-run average profit and prevent excessive costs associated with holding, shortages, and deterioration, the production lot size, backorder level, cycle parameters, and dynamic pricing policy must be optimally determined through joint optimization.
For this purpose, a comprehensive nonlinear stochastic mathematical model is developed with an infinite planning horizon to capture long-term behavior. The model is solved using a hybrid approach combining Monte Carlo simulation for handling stochastic elements and gradient descent for efficient optimization and is executed with a numerical example to demonstrate its applicability. Numerical results indicate that the production decline rate and non-reworkable defective items exert the most significant negative impact on profitability, whereas demand price elasticity dominates the deterioration rate in influencing optimal policies, and gradual price reduction in price-sensitive markets substantially increases profit by stimulating demand and mitigating losses from deterioration.
Keywords
Brownian demand
Perishable items
Economic production system
Monte Carlo simulation
Gradient descent
[1] Braglia M, Castellano D, Marrazzini L, Song D. A continuous review,(Q, r) inventory model for a deteriorating item with random demand and positive lead time. Computers & Operations Research. 2019;109:102-21.
[2] Federgruen A, Wang M. Monotonicity properties of a class of stochastic inventory systems. Annals of Operations Research. 2013;208:155-86.
[3] Kogan K. Manufacturing under uncertainty: offsetting the inability to instantaneously adjust production with dynamic pricing. IIE Transactions. 2012;44:419-30.
[4] Sadeghi H, Farughi H, Kalevandi F, Solgi M. Production Planning System with Variable Demand and Stochastic Machine Breakdown. Journal of Industrial Management Perspective. 2023;13:93-126.
[5] Sadeghi H, Golpîra H, Khan SAR. Optimal integrated production-inventory system considering shortages and discrete delivery orders. Computers & Industrial Engineering. 2021;156:107233.
[6] Lin H-J. An economic production quantity model with backlogging and imperfect rework process for uncertain demand. International Journal of Production Research. 2021;59:467-82.
[7] Wei B, Yao D. Ergodic inventory control with diffusion demand and general ordering costs. Operations Research Letters. 2021;49:578-85.
[8] Yao D, Chao X, Wu J. Optimal control policy for a Brownian inventory system with concave ordering cost. Journal of Applied Probability. 2015;52:909-25.
[9] Yao D. Joint pricing and inventory control for a stochastic inventory system with Brownian motion demand. IISE Transactions. 2017;49:1101-11.
[10] Chen H, Wu OQ, Yao DD. On the benefit of inventory‐based dynamic pricing strategies. Production and Operations Management. 2010;19:249-60.
[11] He S, Yao D, Zhang H. Optimal ordering policy for inventory systems with quantity-dependent setup costs. Mathematics of Operations Research. 2017;42:979-1006.
[12] Avinadav T. Stochastic periodic-review models with duration-and quantity-dependent inventory costs: Properties and approximations. Asia-Pacific Journal of Operational Research. 2016;33:1650030.
[13] Lin H-J. Two-critical-number control policy for a stochastic production inventory system with partial backlogging. International Journal of Production Research. 2017;55:4123-35.
[14] Kitaeva AV, Stepanova NV, Zukovskaya AO. Pricing and lot-sizing for continuously decaying items with stochastic demand. IFAC-PapersOnLine. 2017;50:10160-5.
[15] Germs R, Foreest ND. Optimal control of production-inventory systems with constant and compound poisson demand: University of Groningen, Faculty of Economics and Busisness, 2013.
[16] Cao P, Yao D. Optimal drift rate control and impulse control for a stochastic inventory/production system. SIAM Journal on Control and Optimization. 2018;56:1856-83.
[17] Gong M, Lian Z, Xiao H. Inventory control policy for perishable products under a buyback contract and Brownian demands. International Journal of Production Economics. 2022;251:108522.
[18] Sato K, Yagi K, Shimazaki M. A stochastic inventory model for a random yield supply chain with wholesale-price and shortage penalty contracts. Asia-Pacific Journal of Operational Research. 2018;35:1850040.
[19] Violi A, De Maio A, Fattoruso G. Inventory management and delivery of perishable products with stochastic demands and risks consideration. Procedia Computer Science. 2024;232:2941-9.
[20] Cruz JAd, Salles-Neto LLd, Schenekemberg CM. A Rolling Horizon Approach for a Production Planning and Inventory Management Problem Under Stochastic Demand. Process Integration and Optimization for Sustainability. 2025:1-26.
[21] Tshinangi K, Adetunji O, Yadavalli S. A Two-Echelon Supply Chain Inventory Model for Perishable Products with a Shifting Production Rate, Stock-Dependent Demand Rate, and Imperfect Quality Raw Material. AppliedMath. 2025;5:50.
[22] Nwoba P, Osisiogu U, Okoro C, Nduka U. An Inventory Model Under Exponential Demand and Weibull Deterioration Rates with Shortage-Dependent Partial Backlogging. American Journal of Mathematical and Management Sciences. 2025;44:49-68.
[23] Mukherjee AK, Roy SK, Seshadri R, Hana T, He S. Economic production quantity model with shortages under price-and green-sensitive demand in uncertain environment: AK Mukherjee et al. Operational Research. 2025;25:89.
[24] Siriruk P, Kotekangpoo A. Order quantity optimization model for perishable products under continuous review (Q, r) inventory policy with stochastic demand and positive lead time. Omega. 2026;138:103392.
[25] Ugbosu C, Apanapudor JS. OPTIMIZING PERISHABLE INVENTORY SYSTEMS: A DOUBLE-ORDER POLICY WITH WEIBULL-DISTRIBUTED DEMAND. Science World Journal. 2025;20:659-65.
[26] Sethi G, Yadav AS, Singh C. OPTIMIZATION OF PERISHABLE INVENTORY IN TWO-WAREHOUSE SYSTEM USING GENETIC ALGORITHMS WITH LOG-GAMMA DECAY AND NONLINEAR DEMAND. Reliability: Theory & Applications. 2025;20:813-23.
[27] Shaikh AA, Ali H, Ekren B, Das SC, Alrasheedi AF. Sustainable Inventory Optimization for Perishable Goods: A Metaheuristic Approach Considering Price Elasticity, Green Demand, and Carbon Taxation. Green Demand, and Carbon Taxation.
[28] Sadeghi H, Farughi H, Sayedi R. Determining the Optimal Replenishment Policy in an Integrated Vendor–Buyer with Multiple Delivery Policy. 2023.
[29] Atan Z, Honhon D, Pan XA. Displaying and discounting perishables: Impact on retail profits and waste. Management Science. 2025.
[30] Zwierzchowski T, Adamiak K. Desired Trajectory Based Sliding Mode Control for Multiple Perishable Inventory Systems. IEEE Access. 2025.
[31] Kitaeva AV, Cao Y. Shortages of perishables control for a stochastic inventory system in retail through dynamic pricing. Вестник Томского государственного университета Управление, вычислительная техника и информатика. 2025:82-92.
[32] Jagadeesan V, Gopal R, Thanji K, Cep R, Schindlerova V, Elangovan M. A Stochastic Deteriorated Single Product Inventory System Sustaining in Heterogeneous Environments with Restricted Compulsory Waiting Period in reordering. International Journal of Applied and Computational Mathematics. 2025;11:171.
[33] Sadeghi H, Mahmoodi A. Multi-objective inventory model for material requirements planning with uncertain lead-time. International journal of operational research. 2022;43:391-415.
[34] Jain M, Indoria H, Chaudhary A, Singh P. Effects of memory on inventory control and pricing policy for imperfect production with rework process. RAIRO-Operations Research. 2025;59:77-99.
[35] Ceylan M, Aydemir E. A New Sustainable Economic Production Quantity Model with Imperfect Production and Shortage. Arabian Journal for Science and Engineering. 2025:1-12.
 

  • Receive Date 03 December 2025
  • Revise Date 28 December 2025
  • Accept Date 30 December 2025