A new heuristic for three-machine flow shop scheduling

This paper considers the problem of sequencing n jobs in a three-machine flow shop with the objective of minimizing the makespan, which is the completion time of the last job. An O(n log n) time heuristic that is based on Johnson's algorithm is presented. It is shown to generate a schedule with length at most 5/3 times that of an optimal schedule, thereby reducing the previous best available worst-case performance ratio of 2. An application to the general flow shop is also discussed.

Scheduling for parallel dedicated machines with a single server

This paper examines scheduling problems in which the setup phase of each operation needs to be attended by a single server, common for all jobs and different from the processing machines. The objective in each situation is to minimize the makespan. For the processing system consisting of two parallel dedicated machines we prove that the problem of finding an optimal schedule is NP-hard in the strong sense even if all setup times are equal or if all processing times are equal. For the case of m parallel dedicated machines, a simple greedy algorithm is shown to create a schedule with the makespan that is at most twice the optimum value. For the two machine case, an improved heuristic guarantees a tight worst-case ratio of 3/2. We also describe several polynomially solvable cases of the later problem. The two-machine flow shop and the open shop problems with a single server are also shown to be NP-hard in the strong sense. However, we reduce the two-machine flow shop no-wait problem with a single server to the Gilmore-Gomory traveling salesman problem and solve it in polynomial time. (c) 2000 John Wiley & Sons, Inc.

A price worth paying?: Women and work – choice, constraint or satisficing

Purpose – Are women held back or holding back? Do women choose their jobs/careers or are they structurally or normatively constrained? The purpose of this paper is to shed fresh light on these questions and contribute to an on-going debate that has essentially focused on the extent to which part-time work is women’s choice, the role of structural and organisational constraints and the role of men in excluding women. Design/methodology/approach – The paper uses data from interviews with 80 working women – both full-time and part-time – performing diverse work roles in a range of organisations in the south east of England. Findings – It was found that many women do not make strategic job choices, rather they often ‘‘fall into’’ jobs that happen to be available to them. Some would not have aspired to their present jobs without male encouragement; many report incidents of male exclusion; and virtually all either know or suspect that they are paid less than comparable men. Those working reduced hours enjoy that facility, yet they are aware that reduced hours and senior roles are seen as incompatible. In short, they recognise both the positive and negative aspects of their jobs, whether they work full or part-time, whether they work in male-dominated or female-dominated occupations, and whatever their position in the organisational hierarchy. Accordingly, the paper argues that the concept of ‘‘satisficing’’, i.e. a decision which is good enough but not optimal, is a more appropriate way to view women’s working lives than are either choice or constraint theories. Originality/value – There is an ongoing, and often polarised, debate between those who maintain that women choose whether to give preference to work or home/family and others who maintain that women, far from being self-determining actors, are constrained structurally and normatively. Rather than supporting these choice or constraint theories, this paper argues that ‘‘satisficing’’ is a more appropriate and nuanced concept to explain women’s working lives.