Facing uncertainty in demand, companies try to avoid stock-outs by holding safety inventories, depending on a pre-set customer service level. The knowledge of the demand distribution during lead-time serves to determine the safety inventory level. Many times the distribution is not fully known, except maybe for its range, mean or variance. However literature shows that the performance of holding safety stock strongly depends on the characteristics of the distribution. One option is to protect against the worst case distribution given some information like range or moments. But this worst case is a two-point distribution, bringing unbelief to managers that such an occurrence would ever appear. Mostly they share the opinion that the demand distribution is unimodal. This research develops a technique to derive the safety stock for unimodal demand distributions of which the mode either is known or can be estimated. In this way, the managers obtain solutions to the decision problem including a higher belief that the related type of distribution might appear in practice.
Keywords: Inventory management, linear programming, partial information, demand distribution
@article{RO_2021__55_S1_S1207_0,
author = {Janssens, Gerrit K. and Verdonck, Lotte and Ramaekers, Katrien},
title = {Service-oriented performance of inventory models with partial information on unimodal demand lead-time distributions},
journal = {RAIRO. Operations Research},
pages = {S1207--S1228},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
doi = {10.1051/ro/2020026},
mrnumber = {4223117},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2020026/}
}
TY - JOUR AU - Janssens, Gerrit K. AU - Verdonck, Lotte AU - Ramaekers, Katrien TI - Service-oriented performance of inventory models with partial information on unimodal demand lead-time distributions JO - RAIRO. Operations Research PY - 2021 SP - S1207 EP - S1228 VL - 55 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2020026/ DO - 10.1051/ro/2020026 LA - en ID - RO_2021__55_S1_S1207_0 ER -
%0 Journal Article %A Janssens, Gerrit K. %A Verdonck, Lotte %A Ramaekers, Katrien %T Service-oriented performance of inventory models with partial information on unimodal demand lead-time distributions %J RAIRO. Operations Research %D 2021 %P S1207-S1228 %V 55 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2020026/ %R 10.1051/ro/2020026 %G en %F RO_2021__55_S1_S1207_0
Janssens, Gerrit K.; Verdonck, Lotte; Ramaekers, Katrien. Service-oriented performance of inventory models with partial information on unimodal demand lead-time distributions. RAIRO. Operations Research, Tome 55 (2021), pp. S1207-S1228. doi: 10.1051/ro/2020026
[1] , and , Measuring the impact of asymmetric demand distributions on inventories. Int. J. Prod. Econ. 60–61 (1999) 395–404. | DOI
[2] and , A robust optimization approach to inventory theory. Oper. Res. 54 (2006) 150–168. | MR | Zbl | DOI
[3] , and , Evaluation of inventory control systems in practice. Tijd. Econ. Manage. 25 (1980) 19–39.
[4] , and , The replenishment policy of agri-products with stochastic demand in integrated agricultural supply chains. Expert Syst. App. 48 (2016) 55–66. | DOI
[5] , Forecasting and stock control for intermittent demands. Oper. Res. Q. 23 (1972) 289–303. | Zbl | DOI
[6] , The mode – a neglected statistical parameter. J. R. Stat. Soc. (Ser. A) 128 (1965) 110–117. | MR | DOI
[7] and , Upper and lower bounds on stop-loss premiums in case of known expectation and variance of the risk variable. Mitt. Ver. Schweiz. Versicherungsmathematiker 1 (1982) 149–164. | MR | Zbl
[8] and , Fuzzy period review system with fuzzy random variable demand. Eur. J. Oper. Res. 198 (2009) 113–120. | Zbl | DOI
[9] and , Unimodality, Convexity, and Applications. Academic Press, Boston, MA (1988). | MR | Zbl
[10] , An Introduction to Probability Theory and its Applications. Wiley and Sons, New York, NY (1971). | MR | Zbl
[11] , A minimax distribution free procedure for the (Q, R) inventory model. Oper. Res. Lett. 11 (1992) 55–60. | MR | Zbl | DOI
[12] , and , Statistical methods for eliciting probability distributions. J. Am. Stat. Assoc. 100 (2005) 680–701. | MR | Zbl | DOI
[13] , and , Numerical best bounds on stop-loss premiums. Insur. Math. Econ. 1 (1982) 287–302. | MR | Zbl | DOI
[14] , Some direct estimates of the mode. Ann. Math. Stat. 36 (1965) 131–138. | MR | Zbl | DOI
[15] , and , An inventory model: what is the influence of the shape of the lead time demand distribution. Z. Oper. Res. 30 (1986) B1–B14. | MR | Zbl
[16] , The accuracy of the means and standard deviations of subjective probability distributions. J. R. Stat. Soc. (Ser. A) 141 (1978) 79–85. | DOI
[17] and , On the use of bounds on the stop-loss premium for an inventory management decision problem. J. Interdiscip. Math. 11 (2008) 115–126. | MR | Zbl | DOI
[18] and , A linear programming formulation for an inventory management decision problem with a service constraint. Expert Syst. App. 38 (2011) 7929–7934. | DOI
[19] , and , Linear programming models to support inventory decision-making in the case of incomplete information on demand during lead-time. East West J. Math. 15 (2013) 109–126. | MR | Zbl
[20] , and , Impact of the shape of demand distribution in decision models for operations management. Comput. Ind. 64 (2013) 765–775. | DOI
[21] and , Three-point approximations for continuous random variables. Manage. Sci. 29 (1983) 595–609. | Zbl | DOI
[22] , , , and , A belief-rule-based inventory control method under nonstationary and uncertain demand. Expert Syst. App. 38 (2011) 14997–15008. | DOI
[23] , , and , Application of a technique for research and development program evaluation. Oper. Res. 7 (1959) 646–669. | Zbl | DOI
[24] , Sensitivity to distributions in inventory systems. Manage. Sci. 24 (1978) 1769–1772. | DOI
[25] , Production and Operations Analysis. Irwin, Homewood, IL (1993).
[26] and , Regret in the newsvendor model with partial information. Oper. Res. 56 (2008) 188–203. | MR | Zbl | DOI
[27] and , Estimating the mean and variance of subjective distributions in PERT and decision analysis. Manage. Sci. 21 (1975) 1477–1480. | DOI
[28] , , and , Replenishment planning for stochastic inventory systems with shortage cost, edited by and . In: Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. Springer Berlin-Heidelberg, Berlin (2007) 229–243. | Zbl
[29] , A min–max solution of an inventory problem, edited by , and . In: Studies in the Mathematical Methods of Inventory and Production. Stanford University Press, Redwood City, CA (1958) 201–209.
[30] , and , Inventory Management and Production Planning and Scheduling, 3rd edition. Wiley and Sons, New York, NY (1998).
[31] and , The accuracy of intermittent demand estimates. Int. J. Forecast. 21 (2005) 303–314. | DOI
[32] and , Demand forecasting adjustments for service-level achievement. IMA J. Manage. Math. 19 (2008) 175–192. | Zbl
[33] , and , Eliciting expert judgments about a set of proportions. J. Appl. Stat. 41 (2014) 1919–1933. | MR | DOI
Cité par Sources :
