×

zbMATH — the first resource for mathematics

Estimating the demand distributions of single-period items having frequent stockouts. (English) Zbl 0912.90108
Summary: Very often, the service level of a single-period newsboy-type product is set at such a low level that: (i) stockouts occur in the majority of the periods, and (ii) a large right-hand side of the empirical demand distribution is never observable. This paper reports a practical approach for estimating the periodic-demand distribution of such a product. The approach has three components: (i) using the non-parametric ‘product limit’ method to estimate the fractiles of the observable left-hand side of the empirical distribution; (ii) using a subjective approach and an ‘extrapolation of hourly sales’ approach to ‘fill in’ the missing right-hand side of the empirical distribution; (iii) fitting the estimates obtained in the preceding two components to a Tocher curve – which can handle the diversity of shapes of a realistic demand distribution and is also computationally very convenient for subsequent calculations for production/inventory decisions. The entire approach is shown to be simpler but more powerful than existing alternatives for the problem.

MSC:
90B05 Inventory, storage, reservoirs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alpert, M.; Raiffa, H., A progress report on the training of probability assessors, ()
[2] Bell, P., A new procedure for the distribution of periodicals, Journal of the operational research society, 29, 427-434, (1978) · Zbl 0383.90069
[3] Bell, P., Adaptive sales forecasting with many stockouts, Journal of the operational research society, 32, 865-873, (1981)
[4] Bopp, A., On combining forecasts: some extensions and results, Management science, 31, 1492-1498, (1985)
[5] Cohen, A., Maximum likelihood estimation in the Weibull distribution based on complete and on censored samples, Technometrics, 7, 579-588, (1965)
[6] Conrad, S., Sales data and the estimation of demand, Operational research quarterly, 27, 123-127, (1976) · Zbl 0318.90020
[7] Crowder, M.; Kimber, A.; Smith, R.; Sweeting, T., Statistical analysis of reliability data, (1991), Chapman & Hall London
[8] Hadley, G.; Whitin, T., Analysis of inventory systems, (1963), Prentice-Hall Englewood Cliffs, NJ · Zbl 0133.42901
[9] Harter, H., Maximum likelihood estimation of the parameters of a four-parameter generalized gamma population for complete and censored samples, Technometrics, 9, 159-165, (1967)
[10] Herd, G., Estimation on reliability from incomplete data, ()
[11] Hill, R., Parameter estimation and performance measurement in lost sales inventory systems, International journal of production economics, 28, 211-215, (1992)
[12] Johnson, L., The statistical treatment of fatigue experiments, (1964), Elsevier New York
[13] Kaplan, E.; Meier, P., Nonparametric estimation from incomplete observations, Journal of the American statistical association, 53, 457-481, (1958) · Zbl 0089.14801
[14] Lau, H.; Lau, A., The newsstand problem: A capacitated multi-product newsboy problem, European journal of operational research, (1995), submitted to
[15] Lawless, J., Statistical models and methods for lifetime data, (1982), Wiley New York · Zbl 0541.62081
[16] Lawrence, M.; Edmundson, R.; O’Connor, M., The accuracy of combining judgmental and statistical forecasts, Management science, 32, 1521-1532, (1986)
[17] Lock, A., Integrating group judgments in subjective forecasts, ()
[18] Malcolm, D.; Rosebloom, J.; Clark, C.; Fazar, W., Application of a technique for research and development program evaluation, Operations research, 7, 646-669, (1959) · Zbl 1255.90070
[19] Moder, J.; Rodgers, E., Judgement estimates of the moments of PERT type distributions, Management science, 15, B76-B83, (1968)
[20] Nahmias, S., Production and operations analysis, (1993), Irwin Homewood, IL
[21] Nelson, W., Life data analysis, (1981), Wiley-Interscience New York
[22] Pearson, K., Skew variation in homogeneous material, Philosophical transactions of the royal society, 186, 343-414, (1985)
[23] Ramberg, J.; Schmeiser, B., An approximate method for generating asymmetric random variables, Communications of the ACM, 17, 78-82, (1974) · Zbl 0273.65004
[24] Schmeiser, B.; Deutsch, S., A versatile four parameter family of probability distributions suitable for simulation, IIE transactions, 9, 176-181, (1977)
[25] Selvidge, J., Assessing the extremes of probability distributions by the fractile method, Decision sciences, 11, 493-502, (1980)
[26] Solomon, I., Probability assessment by individual auditors and audit teams: an empirical investigation, Journal of accounting research, 20, 689-710, (1982)
[27] Tocher, K., The art of simulation, (1963), English University Press London
[28] Wecker, W., Predicting demand from sales data in the presence of stockouts, Management science, 24, 1043-1054, (1978) · Zbl 0385.62088
[29] Wilson, J.; Allison-Koerber, D., Combining subjective and objective forecasts improve results, Journal of business forecasting, 11, 3, 3-8, (1992)
[30] Winkler, R.; Makridakis, S., The combination of forecasts, Journal of the royal statistical society. series A, 146, 150-157, (1983)
[31] Winterfeldt, D.; Edwards, W., Decision analysis and behavioral research, (1986), Cambridge University Press Cambridge
[32] Wright, G.; Ayton, P., Judgmental forecasting, (1987), Wiley New York
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.