Exploring the potential use of the Birnbaum-Saunders distribution in inventory management. (English) Zbl 1394.90057
Summary: Choosing the suitable demand distribution during lead-time is an important issue in inventory models. Much research has explored the advantage of following a distributional assumption different from the normality. The Birnbaum-Saunders (BS) distribution is a probabilistic model that has its genesis in engineering but is also being widely applied to other fields including business, industry, and management. We conduct numeric experiments using the R statistical software to assess the adequacy of the BS distribution against the normal and gamma distributions in light of the traditional lot size-reorder point inventory model, known as (\(Q\), \(r\)). The BS distribution is well-known to be robust to extreme values; indeed, results indicate that it is a more adequate assumption under higher values of the lead-time demand coefficient of variation, thus outperforming the gamma and the normal assumptions.
MSC:
| 90B05 | Inventory, storage, reservoirs |
References:
| [1] | Braglia, M.; Grassi, A.; Montanari, R., Multi-attribute classification method for spare parts inventory management, Journal of Quality in Maintenance Engineering, 10, 1, 55-65, (2004) · doi:10.1108/13552510410526875 |
| [2] | Cai, H.; Yu, T.; Xia, C., Quality-oriented classification of aircraft material based on SVM, Mathematical Problems in Engineering, 2014, (2014) · doi:10.1155/2014/273906 |
| [3] | Namit, K.; Chen, J., Solutions to the inventory model for gamma response time demand, International Journal of Physical Distribution & Logistics Management, 29, 138-154, (1999) |
| [4] | Porras, E.; Dekker, R., An inventory control system for spare parts at a refinery: an empirical comparison of different re-order point methods, European Journal of Operational Research, 184, 1, 101-132, (2008) · Zbl 1278.90033 · doi:10.1016/j.ejor.2006.11.008 |
| [5] | Wanke, P. F., Consolidation effects and inventory portfolios, Transportation Research Part E: Logistics and Transportation Review, 45, 1, 107-124, (2009) · doi:10.1016/j.tre.2008.03.003 |
| [6] | Hillier, F.; Lieberman, G. J., Introduction to Operational Research, (2005), New York, NY, USA: McGraw Hill, New York, NY, USA |
| [7] | Eaves, A., Forecasting for the ordering and stock-holding of consumable spare parts [Ph.D. dissertation], (2002), Lancaster, UK: Lancaster University, Lancaster, UK |
| [8] | Huiskonen, J., Maintenance spare parts logistics: special characteristics and strategic choices, International Journal of Production Economics, 71, 1–3, 125-133, (2001) · doi:10.1016/s0925-5273(00)00112-2 |
| [9] | Ballou, R. H.; Burnetas, A., Planning multiple location inventories, Journal of Business Logistics, 24, 2, 65-89, (2003) · doi:10.1002/j.2158-1592.2003.tb00046.x |
| [10] | Nahmias, S., Production and Operations Analysis, (2001), New York, NY, USA: McGraw-Hill, New York, NY, USA |
| [11] | Lee, H. L.; Nahmias, S.; Graves, S. C.; Kahn, A. H. G.; Zipkin, P. H., Single-product, single-location models, Logistics of Production and Inventory, 3-55, (1993), Amsterdam, The Netherlands: North-Holland, Amsterdam, The Netherlands |
| [12] | Yan, X.; Wang, Y., An EOQ model for perishable items with supply uncertainty, Mathematical Problems in Engineering, 2013, (2013) · Zbl 1299.90043 · doi:10.1155/2013/739425 |
| [13] | Min, J.; Ou, J.; Zhong, Y.-G.; Liu, X.-B., EOQ model for deteriorating items with stock-level-dependent demand rate and order-quantity-dependent trade credit, Mathematical Problems in Engineering, 2014, (2014) · Zbl 1407.90028 · doi:10.1155/2014/962128 |
| [14] | Ballou, R. H., Expressing inventory control policy in the turnover curve, Journal of Business Logistics, 26, 2, 143-164, (2005) · doi:10.1002/j.2158-1592.2005.tb00209.x |
| [15] | Silver, E. A.; Peterson, R.; Pyke, D. F., Inventory Management and Production Planning and Scheduling, (1998), New York, NY, USA: Wiley, New York, NY, USA |
| [16] | Eaves, A. H. C.; Kingsman, B. G., Forecasting for the ordering and stock-holding of spare parts, Journal of the Operational Research Society, 55, 4, 431-437, (2004) · Zbl 1095.90505 · doi:10.1057/palgrave.jors.2601697 |
| [17] | Syntetos, A. A.; Boylan, J. E.; Croston, J. D., On the categorization of demand patterns, Journal of the Operational Research Society, 56, 5, 495-503, (2005) · Zbl 1095.90510 · doi:10.1057/palgrave.jors.2601841 |
| [18] | Boylan, J. E.; Syntetos, A. A.; Karakostas, G. C., Classification for forecasting and stock control: a case study, Journal of the Operational Research Society, 59, 4, 473-481, (2008) · Zbl 1153.90488 · doi:10.1057/palgrave.jors.2602312 |
| [19] | Disney, S. M.; Potter, A. T.; Gardner, B. M., The impact of vendor managed inventory on transport operations, Transportation Research Part E: Logistics and Transportation Review, 39, 5, 363-380, (2003) · doi:10.1016/S1366-5545(03)00014-0 |
| [20] | Rojas, F.; Leiva, V.; Wanke, P.; Marchant, C., Optimization of contribution margins in food services by modeling independent component demand, Colombian Journal of Statistics, 38, 1, 1-30, (2015) · Zbl 1436.62691 · doi:10.15446/rce.v38n1.48799 |
| [21] | Johnson, N. L.; Kotz, S.; Balakrishnan, N., Continuous Univariate Distributions, 1, (1994), New York, NY, USA: Wiley, New York, NY, USA · Zbl 0811.62001 |
| [22] | Johnson, N. L.; Kotz, S.; Balakrishnan, N., Continuous Univariate Distributions, 2, (1995), New York, NY, USA: Wiley, New York, NY, USA · Zbl 0821.62001 |
| [23] | Moors, J. J. A.; Strijbosch, L. W. G., Exact fill rates for (R, s, S) inventory control with gamma distributed demand, Journal of the Operational Research Society, 53, 11, 1268-1274, (2002) · Zbl 1139.90317 · doi:10.1057/palgrave.jors.2601441 |
| [24] | Mentzer, J. T.; Krishnan, R., The effect of the assumption of normality on inventory control/customer service, Journal of Business Logistics, 6, 1, 101-120, (1985) |
| [25] | Eppen, G. D.; Martin, R. K., Determining safety stock in the presence of stochastic lead time and demand, Management Science, 34, 11, 1380-1390, (1988) · Zbl 0661.90025 · doi:10.1287/mnsc.34.11.1380 |
| [26] | Leiva, V.; Santos-Neto, M.; Cysneiros, F. J. A.; Barros, M., A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution, Applied Stochastic Models in Business and Industry, (2015) · Zbl 1411.90028 · doi:10.1002/asmb.2124 |
| [27] | Barros, M.; Leiva, V.; Ospina, R.; Tsuyuguchi, A., Goodness-of-fit tests for the birnbaum-saunders distribution with censored reliability data, IEEE Transactions on Reliability, 63, 2, 543-554, (2014) · doi:10.1109/tr.2014.2313707 |
| [28] | Burgin, T. A., The gamma distribution and inventory control, Operational Research Quarterly, 26, 3, 507-525, (1975) · Zbl 0326.90019 · doi:10.1057/jors.1975.110 |
| [29] | Tadikamalla, P. R., The inverse Gaussian approximation to the lead-time demand in inventory control, International Journal of Production Research, 19, 213-219, (1981) |
| [30] | Lau, H. S., Toward an inventory control system under non-normal demand and lead-time uncertainty, Journal of Business Logistics, 10, 88-103, (1989) |
| [31] | Wanke, P. F., The uniform distribution as a first practical approach to new product inventory management, International Journal of Production Economics, 114, 2, 811-819, (2008) · doi:10.1016/j.ijpe.2008.04.004 |
| [32] | Cobb, B. R.; Rumí, R.; Salmerón, A., Inventory management with log-normal demand per unit time, Computers & Operations Research, 40, 7, 1842-1851, (2013) · Zbl 1348.90023 · doi:10.1016/j.cor.2013.01.017 |
| [33] | Pan, A.; Hui, C.-L.; Ng, F., An optimization of (Q, r) inventory policy based on health care apparel products with compound Poisson demands, Mathematical Problems in Engineering, 2014, (2014) · Zbl 1407.90031 · doi:10.1155/2014/986498 |
| [34] | Birnbaum, Z. W.; Saunders, S. C., A new family of life distributions, Journal of Applied Probability, 6, 319-327, (1969) · Zbl 0209.49801 · doi:10.2307/3212003 |
| [35] | R Team, R: A Language and Environment for Statistical Computing, (2014), Vienna, Austria: R Foundation for Statistical Computing, Vienna, Austria |
| [36] | Jin, X.; Kawczak, J., Birnbaum-Saunders and lognormal kernel estimators for modelling durations in high frequency financial data, Annals of Economics and Finance, 4, 1, 103-124, (2003) |
| [37] | Podlaski, R., Characterization of diameter distribution data in near-natural forests using the Birnbaum-Saunders distribution, Canadian Journal of Forest Research, 38, 3, 518-527, (2008) · doi:10.1139/x07-190 |
| [38] | Bhatti, C. R., The Birnbaum-Saunders autoregressive conditional duration model, Mathematics and Computers in Simulation, 80, 10, 2062-2078, (2010) · Zbl 1195.62136 · doi:10.1016/j.matcom.2010.01.011 |
| [39] | Lio, Y. L.; Tsai, T.-R.; Wu, S.-J., Acceptance sampling plans from truncated life tests based on the Birnbaum-Saunders distribution for percentiles, Communications in Statistics. Simulation and Computation, 39, 1, 119-136, (2010) · Zbl 1182.62221 · doi:10.1080/03610910903350508 |
| [40] | Paula, G. A.; Leiva, V.; Barros, M.; Liu, S., Robust statistical modeling using the Birnbaum-Saunders-t distribution applied to insurance, Applied Stochastic Models in Business and Industry, 28, 1, 16-34, (2012) · Zbl 06292429 · doi:10.1002/asmb.887 |
| [41] | Marchant, C.; Bertin, K.; Leiva, V.; Saulo, H., Generalized Birnbaum-Saunders kernel density estimators and an analysis of financial data, Computational Statistics & Data Analysis, 63, 1-15, (2013) · Zbl 1468.62133 · doi:10.1016/j.csda.2013.01.013 |
| [42] | Leiva, V.; Marchant, C.; Saulo, H.; Aslam, M.; Rojas, F., Capability indices for Birnbaum-Saunders processes applied to electronic and food industries, Journal of Applied Statistics, 41, 9, 1881-1902, (2014) · Zbl 1352.62170 · doi:10.1080/02664763.2014.897690 |
| [43] | Leiva, V.; Saulo, H.; Leão, J.; Marchant, C., A family of autoregressive conditional duration models applied to financial data, Computational Statistics & Data Analysis, 79, 175-191, (2014) · Zbl 1506.62105 · doi:10.1016/j.csda.2014.05.016 |
| [44] | Fox, E.; Gavish, B.; Semple, J., A general approximation to the distribution of count data with applications to inventory modeling, Working Paper, (2008) · doi:10.2139/ssrn.979826 |
| [45] | Shapiro, A.; Dentcheva, D.; Ruszczynski, A., Lectures on Stochastic Programming: Modeling and Theory, (2009), Philadelphia, Pa, USA: SIAM, Philadelphia, Pa, USA · Zbl 1183.90005 |
| [46] | Thangaraj, R.; Pant, M.; Bouvry, P.; Abraham, A.; Panigrahi, B. K.; Das, S.; Suganthan, P. N.; Dash, S. S., Solving multi objective stochastic programming problems using differential evolution, Swarm, Evolutionary, and Memetic Computing. Swarm, Evolutionary, and Memetic Computing, Lecture Notes in Computer Science, 6466, 54-61, (2010), New York, NY, USA: Springer, New York, NY, USA · Zbl 1295.90034 · doi:10.1007/978-3-642-17563-3_7 |
| [47] | Storn, R.; Price, K., Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization, 11, 4, 341-359, (1997) · Zbl 0888.90135 · doi:10.1023/A:1008202821328 |
| [48] | Price, K. V.; Storn, R. M.; Lampinen, J. A., Differential Evolution: A Practical Approach to Global Optimization, (2006), Berlin, Germany: Springer, Berlin, Germany |
| [49] | Silver, E. A.; Peterson, R., Decision Systems for Inventory Management and Production Planning, (1985), New York, NY, USA: Wiley, New York, NY, USA |
| [50] | Silver, E. A., Operations research in inventory management: a review and critique, Operations Research, 29, 4, 628-645, (1981) · doi:10.1287/opre.29.4.628 |
| [51] | Wanke, P. F., Product, operation, and demand relationships between manufacturers and retailers, Transportation Research Part E: Logistics and Transportation Review, 48, 1, 340-354, (2012) · doi:10.1016/j.tre.2011.07.010 |
| [52] | Holland, J. H., Adaptation in Natural Artificial Systems, (1976), Ann Arbor, Mich, USA: University of Michigan Press, Ann Arbor, Mich, USA |
| [53] | Mullen, K. M.; Ardia, D.; Gil, D. L.; Windover, D.; Cline, J., DEoptim: an R package for global optimization by differential evolution, Journal of Statistical Software, 40, 6, 1-26, (2011) |
| [54] | Qu, H.; Wang, L.; Zeng, Y.-R., Modeling and optimization for the joint replenishment and delivery problem with heterogeneous items, Knowledge-Based Systems, 54, 207-215, (2013) · doi:10.1016/j.knosys.2013.09.013 |
| [55] | Qu, H.; Wang, L.; Liu, R., A contrastive study of the stochastic location-inventory problem with joint replenishment and independent replenishment, Expert Systems with Applications, 42, 4, 2061-2072, (2015) · doi:10.1016/j.eswa.2014.10.017 |
| [56] | Wang, L.; Qu, H.; Liu, S.; Chen, C., Optimizing the joint replenishment and channel coordination problem under supply chain environment using a simple and effective differential evolution algorithm, Discrete Dynamics in Nature and Society, 2014, (2014) · doi:10.1155/2014/709856 |
| [57] | Ardia, D.; Boudt, K.; Carl, P.; Mullen, K.; Peterson, B., Differential evolution with DEoptim: an application to non-convex portfolio optimization, R Journal, 3, 27-34, (2011) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
