During the last two decades state funding of higher education in South Africa has decreased substantially (especially if public expenditure of HE as a percentage of GDP is used as a yardstick). HE institutions were forced to increase tuition fees and rely more on the third income stream to balance their books. In the process increases in instruction/research staff did not keep up with the increase in student numbers. During the period 1986-2003 qualifications awarded to students per full-time equivalent instruction/research staff member increased over time-indicating greater efficiency of the HE sector in delivering more teaching output. High-level research in the form of publication units in accredited journals, however, stagnated during this period. In recent years until 2007, however, publications in accredited journals increased substantially. This was mainly the result of broadening the number of accredited journals by the Department of Education. In this paper two indicators, linked to the current funding formula for higher education, to measure academic output of HEIs are defined and applied to the output of institutions for the period since 2002. It is concluded that there is large variability between HEIs as far as teaching and research output are concerned. A cause for concern is that the majority of the research is conducted by just a few HE institutions.
A subset X of the vertex set of a graph G is a secure dominating set of G if X is a dominating set of G and if, for each vertex u not in X, there is a neighbouring vertex v of u in X such that the swap set (X\{v}) ∪ {u} is again a dominating set of G, in which case v is called a defender. The secure domination number of G is the cardinality of a smallest secure dominating set of G. In this paper, we show that every graph of minimum degree at least 2 possesses a minimum secure dominating set in which all vertices are defenders. We also characterise the classes of graphs that have secure domination numbers 1, 2 and 3. (2010): 05C69, 05C99.
Mathematics Subject Classification
An order picking system that requires pickers to move in a clockwise direction around a picking line with fixed locations is considered. The problem is divided into three tiers. The tier in which orders must be sequenced is addressed. Eight tour construction heuristics are developed and implemented for an order picking system operating in unidirectional picking lines. Two classes of tour construction heuristics -the tour construction starting position (TCS) and the tour construction ending position (TCE) -are developed to sequence orders in a picking line. All algorithms are tested and compared using real life data sets. The best solution quality was obtained by a TCE heuristic with adaptations.
OPSOMMING'n Stelsel vir die opmaak van bestellings word ondersoek. Die stelsel vereis dat die werkers in 'n kloksgewyse rigting om 'n uitsoeklyn beweeg. Die probleem is verdeel in drie vlakke van besluite. Die besluit wat handel oor die volgorde waarin bestellings opgemaak word, word ondersoek. Agt toer-konstruksie-heuristieke is ontwikkel en geïmplementeer waarin die bestellings in 'n eenrigting uitsoeklyn opgemaak word. Twee klasse toer-konstruksieheuristieke -die toer-konstruksie-beginposisie (TCS) en die toer-konstruksie-eindposisie (TCE) -is ontwikkel om die volgorde van bestellings in 'n uitsoeklyn te bepaal. Al die algoritmes word getoets en vergelyk vir werklike datastelle. Die beste oplossingskwaliteit is verkry deur 'n TCE-heuristiek met aanpassings.
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