The original online version of this article ( Isiyaku Aliyu, Babangida Sani (2018)  An Inventory Model for Deteriorating Items with Generalised Exponential Decreasing Demand, Constant Holding Cost and Time-Varying Deterioration Rate. AJOR, 8, 1-16. doi: 10.4236/ajor.2018.81001.) was published as some results data reported mistakenly. The author wishes to correct the errors to:

Erratum
4. Numerical Example

Example

To illustrate the model developed an example is considered based on the following values of parameters: N0 = ₦5000 per order, K = 250, C = ₦2.50 per unit, β= 1, a= 0.8, b= 2, i = 0.1 per Naira per unit time, Ac= ₦3.00, and h = 0.5, taking some parameter values from Dash et al. (2014) . Substituting and simplifying the above parameters into Equation (21), gives T ∗ = 1.34247 (490 days). On substitution of this optimal value T ∗ in Equations (19) and (8), we obtain the minimum total cost per unit time T C ∗ = ₦4578.88 and economic order quantity I 0 * = 852.6601216 units. Note that the T ∗ value satisfies

d 2 T C ( T ) d T 2 > 0 .

5. Sensitivity Analysis

A sensitivity analysis was carried out to study the effect of changes in the values of the system parameters N0, K, β, a, b, C, i, Acand h on the optimal length of the cycle ( T ∗ ), the economic order quantity ( I 0 * ) and the minimum total cost per unit time ( T C ∗ ). The sensitivity analysis was performed for each of the parameters by changing its value by 50%, 25%, 5%, 2%, −2%, −5%. −25%, −50%, while keeping the remaining parameters at their original values. The analysis showed the following:

1) With increase in the value of the parameter a, the values of T ∗ decrease while T C ∗ and I 0 * increase. This is because when a increases, deterioration increases and so to avoid much deterioration the model forces T ∗ to decrease. I 0 * increases probably to compensate for the deteriorated units. T C ∗ increases due to the cost of deterioration. The increase/decrease in the values is moderate hence the decision variables are moderately sensitive to changes in a.

2) With increase in the value of parameter b, the values of T ∗ and I 0 * decrease while the value of T C ∗ increases. This is expected because when b increases, deterioration with respect to time also increases and so the model forces T ∗ and I 0 * to decrease. T C ∗ increases due to the cost of deterioration. The decreases/increase in the values are moderate hence the decision variables are moderately sensitive to changes in b.

3) With increase in the value of parameter Ac, the values of T ∗ and I 0 * decrease while T C ∗ increases. This is also expected since when the cost of a deteriorated unit increases then the model will avoid much quantity in a supply and so both T ∗ and I 0 * decrease. T C ∗ increases because of the cost of deteriorated items. The increase/decrease in the values is moderate hence the decision variables are moderately sensitive to changes in Ac

4) With increase in the value of the parameter β,the values of T ∗ and I 0 * increase while T C ∗ is not stable. This is not expected because when β increases, it is expected that T ∗ and I 0 * should decrease. The fact that T C ∗ is not stable indicates that the model tries to adjust T C ∗ to the minimum value, at the expense of increasing T ∗ and I 0 * . The increases/decrease in the values are low hence the variables are lowly sensitive to changes in β.

5) With increase in the value of the parameter N0, the values of T ∗ , T C ∗ and I 0 * increase. This is also expected since when ordering cost increases then the model will avoid more orders and so both T ∗ and I 0 * increase. T C ∗ will however increase due to increase in stockholding cost. The increases in the values are high hence the decision variables T ∗ , T C ∗ and I 0 * are highly sensitive to changes in N0.

6) With increase in the value of parameter K, the values of T C ∗ and I 0 * increase while T ∗ decreases. This is because when K increases, there will be more demand and so the economic order quantity ( I 0 * ) will increase. This will result in increase in the optimal total cost ( T C ∗ ). The cycle period ( T ∗ ) decreases probably as a result of the model trying to avoid much deterioration. The increases/decrease in the values are moderate hence the decision variables are moderately sensitive to changes in K.

7) With increase in the value of parameter h, the values of T C ∗ and I 0 * increase while T ∗ decreases. This is because as the demand increases the economic order quantity also increases, hence the total variable cost, T C ∗ also increases. On the other hand however, the cycle period decreases which is probably due to higher demand. The increase in the values is moderate hence the decision variables are moderately sensitive to changes in h.

8) With increase in the value of parameteri, the values of T ∗ and I 0 * decrease while T C ∗ increases. This is expected because when the inventory carrying charge, i is increased there will be more stockholding cost so the model will avoid that by reducing quantity in an order which results in decreasing I 0 * and T ∗ . T C ∗ increases due to the increase in the carrying charge (i). The increase/decrease in the values is moderate hence the decision variables are moderately sensitive to changes ini.

With increase in the value of parameter C, the values of T ∗ and I 0 * decrease while T C ∗ increases. This is also expected because when the unit cost of an item, C, is increased there will be more stockholding cost so the model will avoid that by reducing quantity in an order, which results in decreasing I 0 * and T ∗ . T C ∗ increases due to the increase in the unit cost. The increase/decrease in the values is moderate hence the decision variables are moderately sensitive to changes in C.

Cite this paper

Aliyu, I. and Sani, B. (2021) Erratum to “An Inventory Model for Deteriorating Items with Generalised Exponential Decreasing Demand, Constant Holding Cost and Time-Varying Deterioration Rate” [American Journal of Operations Research 8 (2018) 1-16]. American Journal of Operations Research, 11, 100-109. https://doi.org/10.4236/ajor.2021.112006

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