The Convergence of Gallego’s Iterative Method for Distribution-Free Inventory Models
Abstract
:1. Introduction
- (a)
- The construction of new inventory models: Qi et al. [2], Şen and Talebian [3], Wang et al. [4], Kumar and Goswami [5], Sarkar et al. [6], Yu and Zhai [7], Qin and Kar [8], Yu and Zhen [9], Moon et al. [10], Tajbakhsh [11], Gallego and ŞAhin [12], Perakis and Roeis [13], Ahmed et al. [14], Levin et al. [15], Mostard et al. [16], Alfares and Elmorra [17], Lin [18], Hariga and Ben-Daya [19], Talluri and Van Ryzin [20], and Gallego [21].
- (b)
- (c)
- (d)
2. Notation and Assumptions
- average demand per unit of time.
- inventory carrying cost per item per unit of time.
- the fixed ordering cost per order.
- order quantities per order.
- reorder point.
- unit shortage cost.
- mean of the lead time demand.
- the variance of the lead time demand.
- Backorder cost is proportional to the number of items back ordered and not to the time for which they are outstanding.
- is the cumulative distribution of the lead time demand. has known finite first and second moments with mean and variance and then makes no assumptions on the distribution form of .
- The inventory model is continuously reviewed. Replenishments are made when the inventory level drops to the reorder point .
3. Recap of Three Related Papers
4. Our Improvement
5. Numerical Examples
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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750 | 150 | 124.499 | 123.122 | 123.044 | 123.040 | 123.039 | 123.039 |
750 | 150 | 124.498996 | 123.121659 | 123.044093 | 123.039467 | 123.039453 | 123.039452 |
0 | 109.544512 | 122.258644 | 122.995305 | 123.036959 | 123.039311 | 123.039444 | 123.039452 |
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Hu, T.-C.; Hung, K.-C.; Yang, K.-L. The Convergence of Gallego’s Iterative Method for Distribution-Free Inventory Models. Mathematics 2019, 7, 484. https://doi.org/10.3390/math7050484
Hu T-C, Hung K-C, Yang K-L. The Convergence of Gallego’s Iterative Method for Distribution-Free Inventory Models. Mathematics. 2019; 7(5):484. https://doi.org/10.3390/math7050484
Chicago/Turabian StyleHu, Ting-Chen, Kuo-Chen Hung, and Kuo-Lung Yang. 2019. "The Convergence of Gallego’s Iterative Method for Distribution-Free Inventory Models" Mathematics 7, no. 5: 484. https://doi.org/10.3390/math7050484
APA StyleHu, T.-C., Hung, K.-C., & Yang, K.-L. (2019). The Convergence of Gallego’s Iterative Method for Distribution-Free Inventory Models. Mathematics, 7(5), 484. https://doi.org/10.3390/math7050484