An EOQ Inventory Model for Time-varying Deteriorating Items with Cubic Demand under Salvage Value and Shortages
Issue:
Volume 5, Issue 4, December 2020
Pages:
36-42
Received:
3 October 2020
Accepted:
17 October 2020
Published:
11 November 2020
Abstract: In this paper, an Economic Order Quantity (EOQ) inventory model is developed for time-varying deteriorating items. Researchers are constantly developing deteriorating inventory models to become more realistic. Many items like paddy, wheat, potato, onion, radioactive substance etc. are becoming damage over time. So time dependent deterioration is more realistic than a constant rate of deterioration of goods used in the present market. The assumption of constant demand rate may not be always appropriate for many inventory items like milk, vegetables etc, the age of these items has a negative impact on demand dure to loss of quality of such products, on the other hand, demand is becoming increased initially when new branded fashionable products like cosmetics, mobile, computer etc are launched in the market. So the demand rate is considered as a cubic function of time and time dependent holding cost. We also want to give importance on salvage value of an inventory system. The model is solved with salvages value associated to the units deteriorating during the cycle. Shortages are allowed and fully backlogged. Finally the model is illustrated with the help of a numerical example, some particular cases are derived and a comparative study of the optimal solutions towards different nature of demand is also presented graphically.
Abstract: In this paper, an Economic Order Quantity (EOQ) inventory model is developed for time-varying deteriorating items. Researchers are constantly developing deteriorating inventory models to become more realistic. Many items like paddy, wheat, potato, onion, radioactive substance etc. are becoming damage over time. So time dependent deterioration is mo...
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Modelling and Optimal Control of Ebola Virus Disease in the Presence of Treatment and Quarantine of Infectives
Herick Laiton Kayange,
Estomih Shedrack Massawe,
Daniel Oluwole Makinde,
Lathika Sunil Immanuel
Issue:
Volume 5, Issue 4, December 2020
Pages:
43-53
Received:
30 October 2020
Accepted:
11 November 2020
Published:
23 November 2020
Abstract: In this paper, a non-linear mathematical model for the dynamics of Ebola virus diseases is formulated and analysed. The model has five classes namely susceptible human, exposed human, infected human, treated human and recovered human. Invariant region and positivity solution of the model are determined. Local stability analyses of disease free Equilibrium and endemic equilibrium are examined. The disease free equilibrium analysis is determined using Routh-Hurwitz criteria, whereby it is found to be locally stable if the reproduction number is less than one. Two control measures: control measure due to quarantine of exposed and susceptible individuals and control measure due to efficacy of treatment drug, used for treating Ebola virus disease Ebola victim are incorporated to the Ebola virus disease model. The control problem is then analysed in order to determine the optimal control. Numerical simulations for the model in the presence of control measures are finally performed. The results show that in the presence of optimal control, the Ebola virus disease can be eliminated in the Society. Furthermore, to minimize infections of Ebola virus disease, quarantine centres with skilled manpower must be prepared in advance so as to accommodate the significant number of exposed and susceptible individuals, in order to avoid further transmission in other areas out of quarantine centres. Also tracing of exposed and infected individuals must be efficiently done in order to quarantine the affected population and educate people on the transmission of the disease, symptoms and prevention measures in order to minimize human to human transmissions. Investing more on researches on new drugs which are effective in treating the Ebola virus disease victim is inevitable.
Abstract: In this paper, a non-linear mathematical model for the dynamics of Ebola virus diseases is formulated and analysed. The model has five classes namely susceptible human, exposed human, infected human, treated human and recovered human. Invariant region and positivity solution of the model are determined. Local stability analyses of disease free Equi...
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