Sensitivity of the Optimum to Perturbations of the Profit or Weight of an Item in the Binary Knapsack Problem

In the binary single constraint Knapsack Problem, denoted KP, we are given a knapsack of fixed capacity c and a set of n items. Each item j, j = 1,...,n, has an associated size or weight w_j and a profit p_j. The goal is to determine whether or not item j, j = 1,...,n, should be included in the knapsack. The objective is to maximize the total profit without exceeding the capacity c of the knapsack. In this paper, we study the sensitivity of the optimum of the KP to perturbations of either the profit or the weight of an item. We give approximate and exact interval limits for both cases (profit and weight) and propose several polynomial time algorithms able to reach these interval limits. The performance of the proposed algorithms are evaluated on a large number of problem instances.     

Buchbesprechungen

Ohne Zusammenfassung     

Dual Career Couples als eine Variante von Work-Life-Integration

Dual Career Couples as a form of work-life-integrationThe author discusses the situation of dual career couples, when both are university graduates following an own career. Basing on a respective publication she delineates the current, mostly American research and reports on several German research projects, which endeavour to analyse the relation between gender and inequality in dual career couples.     

Von der Supervision zur Mediation und zurück

From supervision to mediation and vice versaMediation in organizations becomes more and more important because of increasing conflicts. The question is, which competencies of the counsellor are necessary, and above all, whether mediation is a particular method. The author explains the method of mediation and illustrates his concept of “patchwork-mediation”. This procedure allows to build a bridge between supervision and mediation.     

Ebert. Wolfgang (2001): Systemtheorien in der Supervision — Bestandsaufnahme und Perspektiven

Ohne Zusammenfassung     

Moving in or Breaking Up? The Role of Distance in the Development of Romantic Relationships

Most romantic relationships start with a living apart together (LAT) phase during which the partners live in two separate households. Over time, a couple might decide to move in together, to separate, or to remain together while maintaining their nonresidential status. This study investigates the competing risks that partners in a LAT relationship will experience the transition to coresidence or to separation. We consider the amount of time LAT partners have to travel to see each other to be a key determinant of relationship development. For our statistical analyses, we use seven waves of the German Family Panel Pairfam (2008/2009–2014/2015) and analyze couples in the age group 20–40 years. We distinguish between short-distance relationships (the partners have to travel less than one hour) and long-distance relationships (the partners have to travel one hour or more). Estimating a competing risks model, we find that couples in long-distance relationships are more likely to separate than those living in close proximity. By contrast, the probability of experiencing a transition to coresidence is lower for LAT couples in long-distance than for those in short-distance relationships. Interaction analyses reveal that distance seems to be irrelevant for the relationship development of couples with two nonemployed (unemployed, in education or other inactive) partners.