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AbstractThe (mxn) sequencing problem may be characterized as follows: There are m machines which can produce a piece consisting of n parts. Each part has a determined order in which it is processed through the machines. It is assumed that each machine cannot deal with more than one part at a time and that the processing required for each part can be accomplished only on one machine. That is, the machines are all specialized so that alternate machines for the same processing on a part is not possible. The problem is to find the best production plan consisting in sequencing the different parts so as to make the whole amount of time from the beginning of work till the piece is completed the shortest possible. Such a plan is called an optimum one. In the first 4 sections of this paper, the problem (2xn) is solved for the (2xn) case in which the order in which parts come on the machine is not constrained by further assumptions. The remainder of the paper then takes up: 1) the (3xn) problem of Bellman‐Johnson (viz. the technological processing order through the machine is the same for all parts) for several new special cases; 2) the 2xn problem of sequencing when delay times must also be considered; and, 3) some properties of an approximating method for solving (mxn) problems, including a delineation of cases when the approximating method will yield optimal solutions.

ABSTRACTThis study examines the effects of sequencing flexibility on the performance of rules used to schedule operations in manufacturing systems. The findings show that taking advantage of even low levels of sequencing flexibility in the set of operations required to do a job results in substantial improvement in the performance of scheduling rules with respect to mean flowtime. Differences in the mean flowtime measure for various rules also diminish significantly with increasing sequencing flexibility. Performance improvements additionally result for such due‐date related performance measures as mean tardiness and the proportion of jobs tardy. At high levels of sequencing flexibility, some nonparametric scheduling rules outperform the shortest processing time rule in terms of the mean flowtime criterion. Rules based on job due dates also outperform rules based on operation milestones in terms of tardiness related criteria at high levels of sequencing flexibility. The implications of these findings for the design of manufacturing systems and product design are noted.

Abstract: Countries taking the initial steps from dictatorship toward electoral politics are especially prone to civil and international war. Yet states endowed with coherent institution's such as a functioning bureaucracy and the elements needed to construct a sound legal system, have often been able to democratize peacefully and successfully. Consequently, whenever possible, efforts to promote democracy should try to follow a sequence of building institutions before encouraging mass competitive elections. Democratizing in the wrong sequence not only risks bloodshed in the short term, but also the mobilization of durable illiberal forces with the capacity to block democratic consolidation over the long term.