Pay phones, parking meters, vending machines, and optimal Bayesian decisions on collection times

• 成果类型: Article
• 署名作者: Maitra, R; Dalal, SR
• 署名单位: University System of Maryland; University of Maryland Baltimore; Ericsson; Telcordia Technologies
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214501753168190
• 发表日期: 2001
• 页码: 476-487
• 关键词: markov-chains

摘要

Payphones, parking meters, and vending machines illustrate the modem business practice of substituting machinery for manpower. They do nor eliminate manual labor completely, because full coin-boxes still must be replaced and vending machines still must be stocked. Deciding when to replace a coin-box is important, with unequal losses resulting from underestimation and overestimation. This article derives optimal methodology for this problem by incorporating collection history and specifying common prior distributions over average daily fill rate and standard deviation at each box. The approach is implemented and analyzed on collection records from 11,308 pay phones over a large geographical region. When the loss from overestimation is 19 times that from underestimation, our methods outperform the one in current use at least 69.9% of the time, translating into average potential collection-cost reductions exceeding 21%.