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The two-machine open shop problem was proved to be solvable in linear time by Teofilo Gonzalez and Sartaj Sahni in 1976. Several algorithms for solving that problem have been proposed since that time. We introduce another optimal algorithm for that classical problem with an interesting property: it allows to process jobs in almost arbitrary order, unlike the Gohzalez–Sahni algorithm where jobs have to be partitioned into two specific subsets. This new algorithm in turn helps us to solve a much more general problem: the easy-TSP version of the routing open shop with a variable depot, in which unmovable jobs are located in the nodes of a transportation network (with optimal route known), and mobile machines have to travel between the nodes to process jobs in the open shop environment. The common initial location of the machines is not fixed but has to be chosen, and all machines have to return to that location—the depot—to minimize finish time. We also consider the generalization of this problem in which travel times are individual for each machine. This contributes to the discussion on the differences between different scheduling models with transportation delays: classic transportation delays (in our terms, with no depot at all), with a variable depot, and with a fixed depot. It turns out that the depot makes the difference and makes the problem harder to solve.

Historians have characterized the open-shop movement of the early twentieth century as a cynical attempt by business to undercut the labor movement by twisting the American ideals of independence and self-sufficiency to their own ends. The precursors to today's right-to-work movement, advocates of the open shop in the Progressive Era argued that honest workers should have the right to choose whether or not to join a union free from all pressure. At the same time, business owners systematically prevented unionization in their workplaces. While most scholars portray union opponents as knee-jerk conservatives, Chad Pearson demonstrates that many open-shop proponents identified themselves as progressive reformers and benevolent guardians of America's economic and political institutions. By exploring the ways in which employers and their allies in journalism, law, politics, and religion drew attention to the reformist, rather than repressive, character of the open-shop movement, Pearson's book forces us to consider the origins, character, and limitations of this movement in new ways. Throughout his study, Pearson describes class tensions, noting that open-shop campaigns primarily benefited management and the nation's most economically privileged members at the expense of ordinary people. Pearson's analysis of archives, trade journals, newspapers, speeches, and other primary sources elucidates the mentalities of his subjects and their times, rediscovering forgotten leaders and offering fresh perspectives on well-known figures such as Theodore Roosevelt, Louis Brandeis, Booker T. Washington and George Creel. Reform or Repression sheds light on businessmen who viewed strong urban-based employers' and citizens' associations, weak unions, and managerial benevolence as the key to their own, as well as the nation's, progress and prosperity.

At the opening of the twentieth century, labor strife repeatedly racked the nation. Union organization and collective bargaining briefly looked like a promising avenue to stability. But both employers and many middle-class observers remained wary of unions exercising independent power. Vilja Hulden reveals how this tension provided the opening for pro-business organizations to shift public attention from concerns about inequality and dangerous working conditions to a belief that unions trampled on an individual's right to work. Inventing the term closed shop , employers mounted what they called an open-shop campaign to undermine union demands that workers at unionized workplaces join the union. Employer organizations lobbied Congress to resist labor's proposals as tyrannical, brought court cases to taint labor's tactics as illegal, and influenced newspaper coverage of unions. While employers were not a monolith nor all-powerful, they generally agreed that unions were a nuisance. Employers successfully leveraged money and connections to create perceptions of organized labor that still echo in our discussions of worker rights.

Open-shop scheduling problem (OSSP) is a well-known topic with vast industrial applications which belongs to one of the most important issues in the field of engineering. OSSP is a kind of NP problems and has a wider solution space than other basic scheduling problems, i.e., Job-shop and flow-shop scheduling. Due to this fact, this problem has attracted many researchers over the past decades and numerous algorithms have been proposed for that. This paper investigates the effects of crossover and mutation operator selection in Genetic Algorithms (GA) for solving OSSP. The proposed algorithm, which is called EGA_OS , is evaluated and compared with other existing algorithms. Computational results show that selection of genetic operation type has a great influence on the quality of solutions, and the proposed algorithm could generate better solutions compared to other developed algorithms in terms of computational times and objective values.

We study the optimality of the very practical policy of equal allocation of jobs to batches in batch scheduling problems on an m-machine open shop. The objective is minimum makespan. We assume unit processing time jobs, machine-dependent setup times and batch availability. We show that equal allocation is optimal for a two-machine and a three-machine open shop. Although, this policy is not necessarily optimal for larger size open shops, it is shown numerically to produce very close-to-optimal schedules.

Purpose: The aims of this article are to develop a new mathematical formulation and a new heuristic for the problem of preemptive two-agent scheduling in open shops subject to machine maintenance and eligibility constraints. Design/methodology: Using the ideas of minimum cost flow network and constraint programming, a heuristic and a network based linear programming are proposed to solve the problem. Findings: Computational experiments show that the heuristic generates a good quality schedule with a deviation of 0.25% on average from the optimum and the network based linear programming model can solve problems up to 110 jobs combined with 10 machines without considering the constraint that each operation can be processed on at most one machine at a time. In order to satisfy this constraint, a time consuming Constraint Programming is proposed. For n = 80 and m = 10, the average execution time for the combined models (linear programming model combined with Constraint programming) exceeds two hours. Therefore, the heuristic algorithm we developed is very efficient and is in need. Practical implications: Its practical implication occurs in TFT-LCD and E-paper manufacturing wherein units go through a series of diagnostic tests that do not have to be performed in any specified order. Originality/value: The main contribution of the article is to split the time horizon into many time intervals and use the dispatching rule for each time interval in the heuristic algorithm, and also to combine the minimum cost flow network with the Constraint Programming to solve the problem optimally.

We study several two-machine shop scheduling problems, namely flow shop, job shop and open shop scheduling problems under linear constraints. In these problems, the processing times of two stages of jobs are also decision variables and satisfy a system of linear constraints. The goal of each problem is to determine the processing time of each job, and to schedule the jobs to the shop machine such that the makespan, i.e., the completion time of all jobs, is minimized. These problems can find application in various areas, such as industrial production, advertising and automotive maintenance. We study the computational complexity and propose polynomial-time optimal or approximation algorithms for them. In particular, we show that although a two-machine flow shop scheduling problem and a two-machine job shop scheduling problem without recirculation can be solved in polynomial time, the problems where processing times satisfy linear constraints are generally NP-hard in the strong sense. Then, we design algorithms for various settings of these problems. We design polynomial-time algorithms for them when there are a fixed number of constraints. For the general case, we first propose a simple 2-approximation algorithm, and then design a polynomial-time approximation schemes. In contrast to the previous two problems, we show that the two-machine open shop scheduling problem under linear constraints can be solved in polynomial time.

In this paper problems of time-dependent scheduling on dedicated machines are considered. The processing time of each job is described by a function which is dependent on the starting time of the job. The objective is to minimise the maximum completion time (makespan). We prove that under linear deterioration the two-machine flow shop problem is strongly NP-hard and the two-machine open shop problem is ordinarily NP-hard. We show that for the three-machine flow shop and simple linear deterioration there does not exist a polynomial-time approximation algorithm with the worst case ratio bounded by a constant, unless P=NP. We also prove that the three-machine open shop problem with simple linear deterioration is ordinarily NP-hard, even if the jobs have got equal deterioration rates on the third machine.

This paper considers several two-machine open shop problems with two agents. Each agent has an independent set of nonpreemptive jobs, and the objective is to find either a schedule minimizing a linear combination of the makespans of both agents, a schedule minimizing the makespan of one agent with the makespan of the other agent not exceeding a threshold, or all Pareto-optimal schedules with respect to the makespans of both agents. We present a number of results for the problems above, including a polynomial algorithm and a pseudo-polynomial algorithm for special cases, non-approximability, two approximation algorithms, and a fully polynomial-time approximation scheme. Finally, we run numerical experiments to show the effectiveness of the pseudo-polynomial algorithm and the approximation algorithms.

We address in this paper the two-machine open shop problem with a single server to prepare jobs before going through the processing so as to minimize the makespan. The server is only needed during the preparation phase before becoming available again, leaving the prepared job to complete its processing. We present three lower bounds with respect to the makespan. In addition, we show the NP-completeness of two restricted cases. Then, we present a well solvable case. Finally, we develop two mixed integer linear programming (MILP) models for the general problem along with an experimental study we conducted to analyze their performance.