Avital Lann

Single machine scheduling to minimize the number of early and tardy jobs

We study single machine scheduling problems with the objective of minimizing the number of early and tardy jobs. Several cost structures are considered: job-independent, job-dependent and symmetric, and job-dependent and asymmetric. The first two problem-classes are shown to be polynomially solvable, whereas the latter is shown to be NP-hard, and heuristic solution methods are introduced. An extensive numerical study tests the performance of the proposed algorithms. Finally, separate treatment is given to the pre-emptive versions of the above models.

The allure of equality: Uniformity in probabilistic and statistical judgment ☆

Uniformity, that is, equiprobability of all available options is central as a theoretical presupposition and as a computational tool in probability theory. It is justified only when applied to an appropriate sample space. In five studies, we posed diversified problems that called for unequal probabilities or weights to be assigned to the given units. The predominant response was choice of equal probabilities and weights. Many participants failed the task of partitioning the possibilities into elements that justify uniformity. The uniformity fallacy proved compelling and robust across varied content areas, tasks, and cases in which the correct weights should either have been directly or inversely proportional to their respective values. Debiasing measures included presenting individualized and visual data and asking for extreme comparisons. The preference of uniformity obtains across several contexts. It seems to serve as an anchor also in mathematical and social judgments. Peoples pervasive partiality for uniformity is explained as a quest for fairness and symmetry, and possibly in terms of expediency.

A note on the maximum number of on-time jobs on parallel identical machines

Abstract This note addresses the scheduling problem of minimizing the number of on-time jobs. We introduce an efficient (O(N log N)) solution algorithm for the problem on parallel identical machines. Scope and purpose Many studies have been published on scheduling problems with due dates and earliness and tardiness costs (Just-In-Time scheduling). Most of these studies consider traditional (linear or monotonic) costs and several standard, commonly used objectives. However, the traditional scheduling literature has barely investigated problems with the objective of maximum number of on-time jobs, and has restricted itself to a single-machine environment. This note is the first to address and solve the problem in a multi-machine setting. Based on our results, future studies may focus on more complex scheduling settings and more general cost structures.

Tell Me the Method, I'll Give You the Mean

Different procedures underlying the determination of the mean of a set of values impart different weights to these values. Thus, different methods result in different weighted means. In particular, when the weights are directly proportional, or in fact equal, to the (weighted) values, the self-weighted mean is obtained, and when they are inversely proportional to the values, the harmonic mean results. Generally, the former is greater and the latter is smaller than the arithmetic (uniformly weighted) mean. We illustrate cases of sampling procedures and of geometric requirements that give rise to the self-weighted and harmonic means. We call attention to some psychological difficulties and to the didactic value of dealing with cases of differential weighting.

Average Speed Bumps: Four Perspectives on Averaging Speeds

highway, where each car travels at a constant speed. Assume that the distribution of the speeds is the same throughout the length of the highway. You adjust your speed so that during a given time unit you overtake the same number of cars as the number of cars that overtake you. Does this mean that your speed is the median of the speeds of the cars on the highway? Surprisingly, the answer is no! (Clevenson, Schilling, Watkins, & Watkins, 2001). Imagine further a radar device at the side of the highway, measuring and recording the speeds of all the cars that pass this point within a fixed time interval. Again, contrary to lay expectations, the arithmetic mean of these recordings would generally not reproduce the arithmetic mean of the speeds of all the cars on the highway (Stein & Dattero, 1985). The above examples illustrate that identifying the correct average may have its difficulties (the correct answers for both cases will be detailed later). Average speed, in general, is not all that self-evident a concept. The apparently simple question “what is the average speed of the cars that drive on the highway?” is equivocal. As students of introductory statistics know, the term average may be interpreted in various ways and hence may assume several different forms. One needs to know in what sense the average is supposed to represent a set of observations. Four Faces of the Average Speed