Calculation of the average travel distance in a low-level picker-to-part system considering any distribution function within the aisles

The estimation of the average travel distance in a low-level picker-to-part order picking system can be done by analytical methods in most cases. Often a uniform distribution of the access frequency over all bin locations is assumed in the storage system. This only applies if the bin location assignment is done randomly. If the access frequency of the articles is considered in the bin location assignment to reduce the average total travel distance of the picker, the access frequency over the bin locations of one aisle can be approximated by an exponential density function or any similar density function. All known calculation methods assume that the average number of orderlines per order is greater than the number of aisles of the storage system. In case of small orders this assumption is often invalid. This paper shows a new approach for calculating the average total travel distance taking into account that the average number of orderlines per order is lower than the total number of aisles in the storage system and the access frequency over the bin locations of an aisle can be approximated by any density function.

Assessing the Relevance of Anomie Theory for Explaining Spatial Variation in Lethal Criminal Violence: An Aggregate-Level Analysis of Homicide within the United States

One of the most influential statements in the anomie theory tradition has been Merton’s argument that the volume of instrumental property crime should be higher where there is a greater imbalance between the degree of commitment to monetary success goals and the degree of commitment to legitimate means of pursing such goals. Contemporary anomie theories stimulated by Merton’s perspective, most notably Messner and Rosenfeld’s institutional anomie theory, have expanded the scope conditions by emphasizing lethal criminal violence as an outcome to which anomie theory is highly relevant, and virtually all contemporary empirical studies have focused on applying the perspective to explaining spatial variation in homicide rates. In the present paper, we argue that current explications of Merton’s theory and IAT have not adequately conveyed the relevance of the core features of the anomie perspective to lethal violence. We propose an expanded anomie model in which an unbalanced pecuniary value system – the core causal variable in Merton’s theory and IAT – translates into higher levels of homicide primarily in indirect ways by increasing levels of firearm prevalence, drug market activity, and property crime, and by enhancing the degree to which these factors stimulate lethal outcomes. Using aggregate-level data collected during the mid-to-late 1970s for a sample of relatively large social aggregates within the U.S., we find a significant effect on homicide rates of an interaction term reflecting high levels of commitment to monetary success goals and low levels of commitment to legitimate means. Virtually all of this effect is accounted for by higher levels of property crime and drug market activity that occur in areas with an unbalanced pecuniary value system. Our analysis also reveals that property crime is more apt to lead to homicide under conditions of high levels of structural disadvantage. These and other findings underscore the potential value of elaborating the anomie perspective to explicitly account for lethal violence.