Predictive/reactive scheduling with controllable processing times and earliness-tardiness penalties

In this study, a machine scheduling problem with controllable processing times in a parallel-machine environment is considered. The objectives are the minimization of manufacturing cost, which is a convex function of processing time, and total weighted earliness and tardiness. It is assumed that parts have job-dependent earliness and tardiness penalties and distinct due dates, and idle time is allowed. The problem is formulated as a time-indexed integer programming model with discrete processing time alternatives for each part. A linear-relaxation-based algorithm is used to assign the parts to the machines and to find a sequence on each machine. A non-linear programming model is proposed to find the optimal starting and processing times of the parts for a given sequence. The proposed non-linear programming model is converted to a minimum-cost network flow model by piecewise linearization of the convex manufacturing cost in the objective function. The proposed method is used to find initial schedules in predictive scheduling. The proposed models are revised to incorporate a stability measure for reacting to unexpected disruptions such as machine breakdown, arrival of a new job, delay in the arrival or the shortage of materials in reactive scheduling

Due date and cost-based FMS loading, scheduling and tool management

In this study, we consider flexible manufacturing system loading, scheduling and tool management problems simultaneously. Our aim is to determine relevant tool management decisions, which are machining conditions selection and tool allocation, and to load and schedule parts on non-identical parallel CNC machines. The dual objectives are minimization of the manufacturing cost and total weighted tardiness. The manufacturing cost is comprised of machining and tooling costs (which are affected by machining conditions) and non-machining cost (which is affected by tool replacement decisions). We used both sequential and simultaneous approaches to solve our problem to show the superiority of the simultaneous approach. The proposed heuristics are used in a problem space genetic algorithm in order to generate a series of approximately efficient solutions

Non-identical parallel CNC machine scheduling

In this study, we solve the non-identical parallel CNC machine scheduling problem. We have two objectives: minimizing the manufacturing cost (comprising machining, non-machining and tooling costs) and minimizing the total weighted tardiness. The tooling constraints affect the non-machining times as well as the machining conditions, such as cutting speed and feed rate, which in turn specify the machining times and tool lives. We propose a two-stage algorithm to find optimal machining conditions and to determine machine allocation, tool allocation and part scheduling decisions. The proposed algorithm generates different schedules according to the relative importance of the objectives

Analysis of the Karmarkar-Karp Differencing Algorithm

The Karmarkar-Karp differencing algorithm is the best known polynomial time heuristic for the number partitioning problem, fundamental in both theoretical computer science and statistical physics. We analyze the performance of the differencing algorithm on random instances by mapping it to a nonlinear rate equation. Our analysis reveals strong finite size effects that explain why the precise asymptotics of the differencing solution is hard to establish by simulations. The asymptotic series emerging from the rate equation satisfies all known bounds on the Karmarkar-Karp algorithm and projects a scaling $n^{-c\ln n}$, where $c=1/(2\ln2)=0.7213...$. Our calculations reveal subtle relations between the algorithm and Fibonacci-like sequences, and we establish an explicit identity to that effect.Comment: 9 pages, 8 figures; minor change

A Classification of Hyper-heuristic Approaches

The current state of the art in hyper-heuristic research comprises a set of approaches that share the common goal of automating the design and adaptation of heuristic methods to solve hard computational search problems. The main goal is to produce more generally applicable search methodologies. In this chapter we present and overview of previous categorisations of hyper-heuristics and provide a unified classification and definition which captures the work that is being undertaken in this field. We distinguish between two main hyper-heuristic categories: heuristic selection and heuristic generation. Some representative examples of each category are discussed in detail. Our goal is to both clarify the main features of existing techniques and to suggest new directions for hyper-heuristic research

Is There Such a Thing as Christian Sex?

It is challenging for Christian pastors and counselors to discuss human sexuality in ways which do not alienate liberals on the left, conservatives on the right, or biologists in the middle. Feminists frequently see males as dominating or insensitive, and conservative Christians sometimes feed into this by emphasizing patriarchal models of marriage as if this were the biblical paradigm for all time. Evolutionary biologists view sexuality primarily as a means of propagating the species. Into this cacophony of strident voices the Christian seeks to inject a calm but clear message: Christian sexuality is primarily a search for intimacy. In a culture obsessed with sexuality as entertainment, the followers of Christ call others to view human sexuality not primarily in terms of eroticism, power, or procreation, but rather in terms of psychological intimacy. From a biblical perspective, becoming one flesh, with one\u27s mate also provides the occasion for becoming a co-creator with the eternal I AM. In addition to the procreational potential and orgasmic excitement provided by sexual intercourse, God intended for these encounters to be loaded with an abundance of psychological intimacy. Intimacy is the raison d\u27etre of sexual relationships. Intimacy provides sexuality with a quality that can mollify crises in the present life, and imbue sexuality with a splendor worthy of the next life as well. © 2002 Human Sciences Press, Inc