As applied to mixed-integer programming, Benders' original work made two primary contributions: (1) development of a "pure integer" problem (Problem P) that is equivalent to the original mixed-integer problem, and (2) a relaxation algorithm for solving Problem P that works iteratively on an LP problem and a "pure integer" problem. In this paper a modified algorithm for solving Problem P is proposed, in which the solution of a sequence of integer programs is replaced by the solution of a sequence of linear programs plus some (hopefully few) integer programs. The modified algorithm will still allow for taking advantage of any special structures (e.g., an LP subproblem that is a "network problem") just as in Benders' original algorithm. The modified Benders' algorithm is explained and limited computational results are given.
Continuous advancements in technology have paved the way for growth in distance education (DE). Nearly 90 percent of public institutions for higher education offer some DE courses. As these offerings continue to expand, more institutions are making the move to creating complete online programs, not just courses. This transition is especially viable for graduate education, where many participants are nontraditional students holding full-time employment. Many industrial personnel possess educational backgrounds in technical disciplines, but require management knowledge and skills to advance into management positions. As educational institutions partner with industrial organizations to fulfill this need the preferred delivery method of programs must be examined. This paper describes a study to determine the need for an online Master of Science in Technology Management in a regional service area. While this program will be available worldwide, our university requires that we demonstrate a regional need for all new programs. Human resource professionals were surveyed to determine their plans for hiring, or placing employees in graduate programs. This study also sought to determine if industrial partners have a preference for the delivery method of master's programs available to their employees. Survey results indicated that industrial partners were interested in hiring graduates of master's programs in addition to enrolling current employees in these programs. Additionally, industrial partners also showed preferences for online delivery of programs over traditional classroom delivery. As society continues to accept that distance education provides equal quality to that of a traditional delivery, specialized online graduate programs that meet the specific needs of fulltime industrial personnel should also continue to increase.
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