Please enter verification code
Special Issues
Improved Preservation Technology for Non-Instantaneous Deteriorating Inventory Using Boundary Condition Estimation
Applied and Computational Mathematics
Volume 9, Issue 4, August 2020, Pages: 118-129
Received: Jun. 10, 2020; Accepted: Jun. 30, 2020; Published: Jul. 17, 2020
Views 238      Downloads 88
Ihsan Hishamuddin, Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia
Siti Suzlin Supadi, Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia
Mohd Omar, Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia
Article Tools
Follow on us
Various forms of preservation technology nowadays allow businesses to handle valuable perishable items with greater flexibility. Even with a wide variety of preservation techniques, the mathematical modelling of its implementation in EOQ literature remains rigid. The paper aims to integrate an improved preservation technology in a non-instantaneous deteriorating inventory model for businesses maximizing their average total cycle profit. The improved preservation technology furthers the delay to the time within the cycle where deterioration begins and enhances the durability of inventory that allows operators to employ a less prudent holding facility. Another improvement in this area is the accurate accumulation of preservation cost depending on the inventory level at hand. The conventional EOQ method of forming the objective function before choosing the optimal values for our two decision variables (Cycle time and level of preservation) is undertaken. The cycle time is split in two, differing in their inventory process (deterioration beginning in the second period). The time when deterioration begins is derived using the model's boundary conditions, a first attempt within the area. The optimal solution set is solved for a numerical example using an algorithm to demonstrate the model and prove the global nature of the solution. An investigation into the gains from the improved preservation technology is conducted by dissecting the effects within each individual component within the objective function. 3 separate channels by which this improved preservation technology modelling benefits the business model is found namely shifting to the higher profitable period, effects towards preservation affected costs and the returns to scale from successively increasing preservation levels. Sensitivity analysis is conducted to demonstrate and confirm the findings. The paper discovers great benefits from such an improved modelling that warrants further attention within the scope of preserved inventory models, especially on how levels of preservation could influence the traditional decision variable optimized such as cycle time or ordering frequency. Findings of the paper would have significant benefits to different inventory models with its own delay before deterioration and holding facility requirement.
Operational Research, Mathematical Modelling, Inventory, Preservation, Non-Instantaneous
To cite this article
Ihsan Hishamuddin, Siti Suzlin Supadi, Mohd Omar, Improved Preservation Technology for Non-Instantaneous Deteriorating Inventory Using Boundary Condition Estimation, Applied and Computational Mathematics. Vol. 9, No. 4, 2020, pp. 118-129. doi: 10.11648/j.acm.20200904.12
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A. A. Taleizadeh, An economic order quantity model for a deteriorating item in a purchasing system with multiple prepayments. Applied Mathematical Modelling (2014).
A. K Bhunia, C. K Jaggi, A. Sharma and R. Sharma, A two-warehouse inventory model for deteriorating items under permissible delay in payment with partial backlogging. Applied Mathematics and Computation (2014).
A. K Bhunia and A. A Shaikh, An application of PSO in a two-warehouse inventory model for deteriorating item under permissible delay in payment with different inventory policies. Applied Mathematics and Computation (2015).
B. Sarkar and S. Sarkar, An Improved Inventory Model with Partial Backlogging, Time Varying Deterioration and Stock-Dependent Demand, Economic Modelling, 30 (2013), 924-932.
B. Sarkar, A Production-Inventory Model with Probablilistic Deterioration in Two-Echelon Supply Chain Management, Applied Mathematical Modelling, 37 (2013), 3138-3151.
B. Sarkar and S. Sarkar, Variable Deterioration and Demand-An Inventory Model, Economic Modelling, 31 (2013), 548-556.
B. C. Giri and K. S. Chaudhuri, Deterministic Models of Perishable Inventory With Stock-Dependent Demand Rate and Nonlinear Holding Cost, European Journal of Operational Research, 105 (1998), 467-474.
B. C. Giri, A. Goswami and K. S. Chaudhuri, An EOQ Model for Deteriorating Items with Time Varying Demand and Costs. Journal of the Operational Research Society, 47 (1996), 1398.
C. K. Chan, W. H. Wong, A. Langevin and Y. C. E. Lee, An integrated production-inventory model for deteriorating items with consideration of optimal production rate and deterioration during delivery. International Journal of Production Economics, 189 (2017), 1, 1-13.
C. T Yang, C. Y Dye and J. F Ding, Optimal dynamic trade credit and preservation technology allocation for a deteriorating inventory model, Computers & Industrial Engineering, 87, September (2015), 356-369.
C. Y Dye, The effect of preservation technology investment on a non-instantaneous deteriorating inventory model, Omega, Volume 41 (5) (2013), 872–880.
C. Y Dye, C. T Yang and C. C Wu, Joint dynamic pricing and preservation technology investment for an integrated supply chain with reference price effects, Journal of the Operational Research Society, 69 (2017), Issue 6, 811-824.
C. Y. Dye, The effect of preservation technology investment on a non-instantaneous deteriorating inventory model. Omega 41 (2013), 5, 872.
G. Li, X. He, J. Zhou and H. Wu, Pricing, Replenishment and Preservation Technology Investment Decision for Non-Instantaneous Deteriorating Items, Omega, 84 (2019), 114-126.
H. Huang, Y. He and D. li, Pricing and Inventory Decisions in the Food Supply Chain with Production Disruption and Controllable Deterioration, Journal of Cleaner Production, 180 (2018), 280-296.
H. K. Alfares, Inventory model with stock-level dependent demand rate and variable holding cost. International Journal of Production Economics, 108 (2007), 259-265.
J. T. Teng, M. S. Chern, H. L. Yang and Y. J. Wang, Deterministic lot-size Inventory Models With Shortages and Deterioration for Fluctuating Demand, Operations Research Letters, 24 (1999), 65-72.
J. Zhang, Q. Wei, Q. Zhang and W. Tang, Pricing, Service and Preservation Technology Investment Policy for Deteriorating Items Under Common Resource Constraints, Computers and Industrial Engineering, 95 (2016), 1-9.
J. T. Teng, L. Eduardo C. Barron, H. J. Chang, J. Wu and Y. Hu, Inventory Lot-Sizes for Deteriorating Items With Expiration Dates and Advance Payments, Applied Mathematical Modelling, 40 (2016), 8605-8616.
K-J Chung, J-J Liao, P-S Ting, S-D Lin and H. M Srivastava, The algorithm for the optimal cycle time and pricing decisions for an integrated inventory system with order-size dependent trade credit in supply chain management. Applied Mathematics and Computation (2015).
L. Liu, L. Zhao and X. Ren, Optimal preservation technology investment and pricing policy for fresh food, Computers & Industrial Engineering, 135, September (2019), 746-756.
M. Rabbani, N. Pourmohammad and H. Rafiei, Joint optimal dynamic pricing and replenishment policies for items with simultaneous quality and physical quantity. Applied Mathematics and Computation (2016).
P. M. Ghare, G. F. Schrader, A Model for an Exponential Decaying Inventory. Journal of Industrial Engineering, 14 (1963), 283-243.
P. H. Hsu, H. M. Wee, H. M. Teng, Preservation technology investment for deteriorating inventory, International Journal of Production Economics, 124 (2010), 2, 388.
R. Maihami and I. N. K. Abadi, Joint Control of Inventory and Its Pricing for Non-Instantaneously Deteriorating Items Under Permissible delay in Payments and Partial Backlogging, Mathematical and Computer Modelling, 55 (2012), 1722-1733.
R. Maihami and B. Karimi, Optimizing the Pricing and Replenishment Policy for Non-Instantaneous Deteriorating Items with Stochastic Demand and Promotional Efforts, Computers & Operations Research, 51 (2014), 302-312.
R. Covert and G. C. Philip, An EOQ Model for Items with Weibull Distribution. AIIE Transactions, 5 (1973), 323-326.
S. R. Singh and S. Sharma, A Global Optimizing Policy for Decaying Items with Ramp-Type Demand Rate under Two-Level Trade Credit Financing Taking Account of Preservation Technology, Advances in Decision Sciences, (2013), Article ID 126385.
S. R. Singh, S. Jain and H. Dem, Two Storage Production Model With Imperfect Quality For Decaying Items Under Preservation, International Conference on Computational Intelligence: Modelling, Techniques and Applications, Procedia Technology 10 (2013), 208-215.
S. Saha, I. Nielsen and I. Moon, Optimal Retailer Investments in Green Operations and Preservation Technology for Deteriorating Items, Journal of Cleaner Production, 140 (2017), 1514-1527.
S. Pal, A. Goswami and K. S. Chaudhuri, A deterministic inventory model for deteriorating items with stock-dependent demand rate. International Journal of Production Economics, 32 (1993), 291-299.
T. P. Hsieh and C. Y. Dye, Optimal dynamic pricing for deteriorating items with reference price effects when inventories stimulate demand, European Journal of Operational Research, 262 (2017), Issue 1, 136-150.
T. Singh, P. J. Mishra and H. Pattanayak, An Optimal Policy for Deteriorating Items with time-proportional Deterioration Rate and Constant and Time-Dependent Linear Demand Rate, Journal of Industrial Engineering, 13 (2017), 455-463.
U. Mishra, J. Z. Wu, Y. C. Tsao and M. L. Tseng, Sustainable Inventory System with Controllable Non-Instantaneous Deterioration and Environment Emission Rates, Journal of Cleaner Production (2019).
V. M. Kumar, Deteriorating Inventory Model With Controllable Deterioration Rate For Time- Dependent Demand and Time-Varrying Holding Cost, Yugoslav Journal of Operations Research. 24 (2014), Issue 1, 87-98.
V. M. Kumar, Deteriorating Inventory Model Using Preservation Technology with Salvage Value and Shortages, Advances in Production Engineering & Management, 8 (3) (2014), 185-192.
Y. Yang, H. Chi, O. Tang, W. Zhou and T. Fan, Cross Perishable Effect on Optimal Inventory Preservation Control, European Journal of Operational Research, 276 (2018), 998-1012.
Y. P Lee and C. Y Dye, An inventory model for deteriorating items under stock-dependent demand and controllable deterioration rate, Computers & Industrial Engineering, 63 (2) (2012), 474–482.
Y. He and H. Huang, “Optimizing Inventory and Pricing Policy for Seasonal Deteriorating Products with Preservation Technology Investment,” Journal of Industrial Engineering, Article ID 793568, 7 (2013).
Z. Tao, Z. Zhang, D. Peng, Y. Shi and Y. Shi, Joint Advertising and Preservation Service Decision in a Supply Chain of Perishable Products with Retailer's Fairness Concerns. 11th CIRP Conference on Industrial Product-Service Systems, Procedia CIRP 83 (2019), 461-466.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186