Scheduling batches with sequential job processing for two-machine flow and open shops

In this paper, we study a problem of scheduling and batching on two machines in a flow-shop and open-shop environment. Each machine processes operations in batches, and the processing time of a batch is the sum of the processing times of the operations in that batch. A setup time, which depends only on the machine, is required before a batch is processed on a machine, and all jobs in a batch remain at the machine until the entire batch is processed. The aim is to make batching and sequencing decisions, which specify a partition of the jobs into batches on each machine, and a processing order of the batches on each machine, respectively, so that the makespan is minimized. The flow-shop problem is shown to be strongly NP-hard. We demonstrate that there is an optimal solution with the same batches on the two machines; we refer to these as consistent batches. A heuristic is developed that selects the best schedule among several with one, two, or three consistent batches, and is shown to have a worst-case performance ratio of 4/3. For the open-shop, we show that the problem is NP-hard in the ordinary sense. By proving the existence of an optimal solution with one, two or three consistent batches, a close relationship is established with the problem of scheduling two or three identical parallel machines to minimize the makespan. This allows a pseudo-polynomial algorithm to be derived, and various heuristic methods to be suggested.

[Conference report] Magic and mathematics: The life and work of John Dee. National Maritime Museum, Greenwich, 13-14 June 2003

Tony Mann provides a report of a two-day meeting "Magic and mathematics: The life and work of John Dee" held from 13-14 June 2003 at the National Maritime Museum, Greenwich.

[Recording review] William Herschel, Symphonies Nos. 2, 8, 12, 13, 14, 17

Tony Mann provides a review of the recording: William Herschel, Symphonies Nos. 2, 8, 12, 13, 14, 17, soloists, London Mozart Players / Matthias Bamert, Chandos 10048, 2003, (68 mins). [CD]

The food multimix concept: potential of an innovative food based approach on nutritional status in pregnant women in resource-poor communities

RATIONALE & OBJECTIVES: The food multimix (FFM)concept states that limited food resources can be combined using scientific knowledge to meet nutrient needs of vulnerable groups at low cost utilizing the ‘nutrient strengths’ of individual or candidate foods in composite recipes within a cultural context. METHODS: The method employed the food-to-food approach for recipe development using traditional food ingredients. Recipes were subjected to proximate and micronutrient analysis and optimized to meet at tleast 40% of recommended daily intakes. End products including breads, porridge and soup were developed. RESULTS: FMM products were employed in a feeding trial among 120 healthy pregnant women in Gauteng, South Africa resulting in improvements in serum iron levels from baseline values of 14.59 (=/-7.67) umol/L and 14.02 (=/-8.13) umol/L for control and intervention groups (p=0.71), to 16.03 (=/-5.67) umol/L and 18.66 (=/-9.41) umol/L (p=0.19). The increases from baseline to post-intervention were however statistically significant within groups. Similarly Mean Cell Volume values improved from baseline as well as serum ferritin and transferritin levels. CONCLUSION: The FMM concept has potential value in feeding programs for vulnerable groups including pregnant and lactating mothers.

‘The trouble with Year 10’: 13 – 16 year old school students’ attitudes to higher education

This study looked at the impact of Widening Participation interventions on the attitudes of young people towards higher education. A total of 2731 adolescents aged 13–16 years completed a self-report measure of their attitudes to higher education, general and academic self concept and identification with school, family and peers. This was matched with data on the students’ academic attainment and social backgrounds. As expected, attainment scores were significantly positively correlated with take up of Widening Participation activities aimed at increasing participation in higher education, attitudes towards going to university and academic motivation. However, attainment was negatively correlated with perceptions of family attending university and identification with family. Regression analyses found that perceptions of family views about attending university were not a predictor of taking part in Widening Participation activities but were a predictor of attitudes towards higher education. Students in Year 10 aged 14–15 were significantly more negative on most factors than either older or younger students.