Scheduling to Minimize Total Weighted Completion Time via Time-Indexed Linear Programming Relaxations

We study approximation algorithms for scheduling problems with the objective of minimizing total weighted completion time, under identical and related machine models with job precedence constraints. We give algorithms that improve upon many previous 15 to 20-year-old state-of-art results. A major theme in these results is the use of time-indexed linear programming relaxations. These are natural relaxations for their respective problems, but surprisingly are not studied in the literature. We also consider the scheduling problem of minimizing total weighted completion time on unrelated machines. The recent breakthrough result of [Bansal-Srinivasan-Svensson, STOC 2016] gave a $(1.5-c)$-approximation for the problem, based on some lift-and-project SDP relaxation. Our main result is that a $(1.5 - c)$-approximation can also be achieved using a natural and considerably simpler time-indexed LP relaxation for the problem. We hope this relaxation can provide new insights into the problem

Framework for sustainable TVET-Teacher Education Program in Malaysia Public Universities

Studies had stated that less attention was given to the education aspect, such as teaching and learning in planning for improving the TVET system. Due to the 21st Century context, the current paradigm of teaching for the TVET educators also has been reported to be fatal and need to be shifted. All these disadvantages reported hindering the country from achieving the 5th strategy in the Strategic Plan for Vocational Education Transformation to transform TVET system as a whole. Therefore, this study aims to develop a framework for sustainable TVET Teacher Education program in Malaysia. This study had adopted an Exploratory Sequential Mix-Method design, which involves a semi-structured interview (phase one) and survey method (phase two). Nine experts had involved in phase one chosen by using Purposive Sampling Technique. As in phase two, 118 TVET-TE program lecturers were selected as the survey sample chosen through random sampling method. After data analysis in phase one (thematic analysis) and phase two (Principal Component Analysis), eight domains and 22 elements have been identified for the framework for sustainable TVET-TE program in Malaysia. This framework was identified to embed the elements of 21st Century Education, thus filling the gap in this research. The research findings also indicate that the developed framework was unidimensional and valid for the development and research regarding TVET-TE program in Malaysia. Lastly, it is in the hope that this research can be a guide for the nations in producing a quality TVET teacher in the future