Due to today's competitive automotive industrial challenges of providing a variety of products at a very low cost by smoothing productions on a flexible transfer line, one of the most fertile research topics in Industrial Mathematics is to penalize jobs both for being early and for being tardy. A problem is to determine a production sequence for producing different types of products on the line. Just-in-Time (JIT) mixed-model production system is used to address this problem, which involves producing only the right products of different models of a common base product in evenly balanced sequences in the exact quantities, at the right times, at the right place. For the bottleneck PRVP, a binary search technique is used to test the existence of a perfect matching and thereby to get optimal sequence. In this book, we study several algebraic structures, properties, existence of cyclic solutions, applications of bottleneck PRVP and some results of ORVP. An optimal sequence for an instance of max-absolute PRVP is obtained. A comparative study of different objectives is also summarized. Moreover, several directions for further research are explored including some emerged conjectures.