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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.

90B05 Inventory, storage, reservoirs
Full Text: DOI
[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
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