Steady state probabilistic characteristics of the on/off production rate control production-inventory system with MMPP demand arrivals

Approximate steady state probability distribution of the stock level for the single product production-inventory system when the demand is a Markov-modulated Poisson process (MMPP) with finite number of states under the on/off production rate control is obtained. The control causes the stock level to fluctuate around a given value by reducing the production rate when the stock exceeds this value. The asymptotic distributions of the stock-out and overproduction periods are also obtained. Exact steady state distribution of the stock level for MMPP demand arrivals with two states and exponential batch size distribution is compared with the approximate one

A Critical History of Individual and Collective Ethics in the Lineage of Lellouch and Schwartz

The notions of individual and collective ethics were first explicitly defined in the biostatistical literature in 1971 to motivate a mathematical solution to a posed ethical dilemma. This paper reviews key antecedents to these concepts and traces explicit references to them over time, primarily in the biostatistical literature. Following a historical exposition of these texts, a critical thematic analysis shows the following: the normative force of these concepts has not been adequately argued. Individual and collective ethics do not solve the problem of how to use accumulating data to inform ethical action. The notions of the individual and the collective are too vague to prompt clear moral imperatives, especially in difficult cases. These concepts have not been successfully linked to a standard ethical framework. Finally, the paper concludes with the observation that a systematic, comprehensive ethical framework must be identified to fulfill the intuitions behind individual and collective ethics