Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2022;45(Suppl 1):395-424.
doi: 10.1007/s40840-022-01316-x. Epub 2022 Jun 9.

An EPQ Model for Delayed Deteriorating Items with Two-Phase Production Period, Exponential Demand Rate and Linear Holding Cost

M L Malumfashi  1   2 , Mohd Tahir Ismail  1 , Majid Khan Majahar Ali  1
Affiliations

An EPQ Model for Delayed Deteriorating Items with Two-Phase Production Period, Exponential Demand Rate and Linear Holding Cost

M L Malumfashi et al. Bull Malays Math Sci Soc. 2022.

Abstract

The economic production quantity (EPQ) model for delayed deteriorating items considering two-phase production periods, exponential demand rate and linearly increasing function of time holding cost is proposed to solve a production problem similar to the one caused by the Covid-19 pandemic. Without shortages, the necessary and sufficient conditions for optimality of this model are characterized through a theorem and lemmas while a solution methodology based on differential calculus is adopted. This paper determines the best replenishment cycle length corresponding to the optimal total variable cost and production quantity of imperfect production industry. To illustrate this model, a numerical experiment is conducted. The results demonstrate that a higher carrying charge decreases the production quantity and a longer demanding period decreases the total variable cost of an industry with a distracted production period. Finally, managerial insights are discussed using sensitivity analysis and future research directions are exposed.

Keywords: Cycle length; Delayed deterioration; EPQ; Exponential demand; Holding cost.

PubMed Disclaimer

Figures

Fig. 1
Fig. 1
The inventory system of delayed deteriorating items
Fig. 2
Fig. 2
Effect of change in A on Z and EPQ
Fig. 3
Fig. 3
Effect of change in C on Z and EPQ
Fig. 4
Fig. 4
Effect of change in ρ on Z and EPQ
Fig. 5
Fig. 5
Effect of change in λ on Z and EPQ
Fig. 6
Fig. 6
Effect of change in π on Z and EPQ
Fig. 7
Fig. 7
Effect of change in θ on Z and EPQ
Fig. 8
Fig. 8
Effect of change in P3 on Z and EPQ
See this image and copyright information in PMC

References

    1. Harris F. How many parts to make at once, factory. Mag. Manag. 1913;10(2):135–136.
    1. Silver EA, Meal HC. A simple modification of the EOQ for the case of a varying demand rate. Prod. Invent. Manag. 1969;10(4):52–65.
    1. Silver EA, Meal HC. A heuristic for selecting lot size quantities for the case of a deterministic time varying demand rate and discrete opportunities for replenishment. Prod. Invent. Manag. 1973;14(1):64–74.
    1. Goswami A, Chaudhuri KS. An EOQ model for deteriorating items with a linear trend in demand. J. Oper. Res. Soc. 1991;42(12):1105–1110.
    1. Chakrabarti T, Chaudhuri KS. An EOQ model for deteriorating items with a linear trend in demand and shortages in all cycles. Int. J. Prod. Econ. 1997;49(3):205–213.

LinkOut - more resources