Lincoln College of New England

Blending religion, politics, and current events, it is no wonder that Christian Zionism has become a topic of intense interest in both popular and academic circles. This interest has only increased...

For many of us, modern-day linear programming (LP) started with the work of George Dantzig in 1947. However, it must be said that many other scientists have also made seminal contributions to the subject, and some would argue that the origins of LP predate Dantzig’s contribution. It is matter open to debate [36]. However, what is not open to debate is Dantzig’s key contribution to LP computation. In contrast to the economists of his time, Dantzig viewed LP not just as a qualitative tool in the analysis of economic phenomena, but as a method that could be used to compute actual answers to specific real-world problems. Consistent with that view, he proposed an algorithm for solving LPs, the simplex algorithm [12]. To this day the simplex algorithm remains a primary computational tool in linear and mixed-integer programming (MIP). In [11] it is reported that the first application of Dantzig’s simplex algorithm to the solution of a non-trivial LP was Laderman’s solution of a 21 constraint, 77 variable instance of the classical Stigler Diet Problem [41]. It is reported that the total computation time was 120 man-days! The first computer implementation of an at-least modestly general version of the simplex algorithm is reported to have been on the SEAC computer at the then National Bureau of Standards [25]. (There were apparently some slightly earlier implementations for dealing with models that were “triangular”, that is, where all the linear systems could be solved by simple addition and subtraction.) Orchard-Hays [35] reports that several small instances having as many as 10 constraints and 20 variables were solved with this implementation. The first systematic development of computer codes for the simplex algorithm began very shortly thereafter at the RAND Corporation in Santa Monica, California. Dantzig’s initial LP work occurred at the Air Force following

Modifying a high-occupancy vehicle (HOV) lane to a high-occupancy toll (HOT) lane generally involves allowing single-occupancy vehicles (SOVs) to travel on the free-flow HOV lane for a toll. This may entice some transit riders to pay the toll to obtain the benefits of traveling in their own vehicle on the HOV lane. Thus, the introduction of a HOT lane has the potential to affect transit ridership negatively; this situation would lower the average vehicle occupancy (AVO) of the lane. To investigate this potential problem, surveys were distributed to park-and-ride bus passengers on two Houston, Texas, freeway corridors. Passengers’ responses to questions regarding their trip characteristics, their socioeconomic characteristics, and their stated preference scenarios were used to develop a mode choice model. Scenarios with varying tolls and travel time savings were simulated using this model. For all scenarios, only a small percentage of transit passengers would choose to switch to driving alone on the HOT lane. Transit passengers shifting to SOVs on the HOT lane would reduce average vehicle occupancy on the lane by only about 1% to 2%. SOV drivers shifting from the general purpose lanes to the HOT lanes are likely to affect AVO much more. However, as long as free-flow conditions are maintained, this analysis shows that the HOV lane can be successfully adapted to a HOT lane and move more people, even if a few transit passengers choose to drive alone.