Efficient Algorithms for Unrelated Parallel Machine Scheduling Considering Time of Use Pricing and Demand Charges

There is an ever-increasing focus on sustainability and energy consumption worldwide. Manufacturing is one of the major areas where energy reduction is not only environmentally beneficial, but also incredibly financially beneficial. These industrial consumers pay for their electricity according to prices that fluctuate throughout the day. These price fluctuations are in place to shift consumption away from “peak” times, when electricity is in the highest demand. In addition to this consumption cost, industrial consumers are charged according to their highest level of demand in a given window of time in the form of demand charges. This paper presents multiple solution methods to solve a parallel machine shop scheduling problem to minimize the total energy cost of the production schedule under Time of Use (TOU) and demand charge pricing. The greedy heuristic and genetic algorithm developed are designed to provide efficient solutions to this problem. The results of these methods are compared to a previously developed integer program (IP) solved using CPLEX with respect to the quality of the solution and the computational time required to solve it. Findings of these tests show that the greedy heuristic handles the test problems with only a small optimality gap to the genetic algorithm and optimal IP solution. The largest test problems could not be solved by the genetic algorithm in the provided time period due to difficulty generating an initial solution population. However, when successful the genetic algorithm performed comparably to the CPLEX solver in terms solution quality yet provided faster solve times

2003 Clinic Yearbook

The Clinic is the yearbook of the Sidney Kimmel Medical College (formerly Jefferson Medical College) at Thomas Jefferson University

Introduction to Workshop on Physics Teaching and the Development of Reasoning

Are physics teachers in high schools, colleges, and universities knowledgeable concerning the reasoning patterns their students use? The personal experiences of many instructors and research carried out during the last few years indicate that a substantial fraction of physics students have difficulty applying functional relationships among variables, considering all necessary combinations of experimental and theoretical conditions of a problem, and examining their own reasoning critically to locate possible errors. The theory of intellectual development formulated by the Swiss psychologist and epistemologist Jean Piaget deals with these matters and can therefore be of help to physics teachers. We have prepared these individualized workshop materials to present the two principal concepts of Piaget’s theory, stages of development and self- regulation, with background and illustrations that will make clear their relevance for physics teaching

Introduction to Workshop on Physics Teaching and the Development of Reasoning

Are physics teachers in high schools, colleges, and universities knowledgeable concerning the reasoning patterns their students use? The personal experiences of many instructors and research carried out during the last few years indicate that a substantial fraction of physics students have difficulty applying functional relationships among variables, considering all necessary combinations of experimental and theoretical conditions of a problem, and examining their own reasoning critically to locate possible errors. The theory of intellectual development formulated by the Swiss psychologist and epistemologist Jean Piaget deals with these matters and can therefore be of help to physics teachers. We have prepared these individualized workshop materials to present the two principal concepts of Piaget’s theory, stages of development and self- regulation, with background and illustrations that will make clear their relevance for physics teaching