Machine Sequencing Problem Research Articles

An Implicit Enumeration Algorithm for the Machine Sequencing Problem

An implicit enumeration algorithm is developed for the machine sequencing problem. The method is based on the graph-theoretical representation of the problem. The convergence of the algorithm is demonstrated, and its efficiency is evaluated by experiments carried out with a code written for the CDC 6400 computer.

A Simple Optimality Proof of Moore's Sequencing Algorithm

In a recent article J. M. Moore [Moore, J. M. 1968. An n job, one machine sequencing algorithm for minimizing the number of late jobs. Management Sci. 14(1, September) 102–109.] gave an algorithm for minimizing the number of late jobs in a one machine sequencing problem. As indicated by the author, T. J. Hodgson has proposed a simpler version of this algorithm, for which version the proof of optimality is similar to the proof given by the author for the original algorithm. In this note a simpler proof of optimality, based on the inductive principle, will be presented for Hodgson's algorithm. As Moore's algorithm only differs on minor points, this proof covers it as well.

A Heuristic Algorithm for the n Job, m Machine Sequencing Problem

This paper describes a simple algorithm for the solution of very large sequence problems without the use of a computer. It produces approximate solutions to the n job, m machine sequencing problem where no passing is considered and the criterion is minimum total elapsed time. Up to m − 1 sequences may be found.

Machine Sequencing Via Disjunctive Graphs: An Implicit Enumeration Algorithm

One formulation of the machine sequencing problem is that of finding a mini-maximal path in a disjunctive graph. This paper describes an implicit enumeration procedure that solves the problem by generating a sequence of circuit-free graphs and solving a slightly amended critical-path problem for each graph in the sequence. Each new term of the sequence is generated from an earlier one by complementing one disjunctive arc. The search tree is drastically cut down by the fact that the only disjunctive arcs that have to be considered for being complemented are those on a critical path. An evaluation of these candidates is used to direct the search at each stage. The procedure can start with any feasible schedule (like the one actually used in production, or generated by some heuristics), and gradually improve it. Thus one can possibly stop short of the optimum, with a reasonably “good” feasible schedule. Storage requirements are limited to the data pertinent to the current node of the search tree.

The machine sequencing problem – review and extensions

AbstractThe deterministic sequencing problem is reviewed from the points of view of variety, models, context, methodology, and current state of the art. The relationship between the theory of sequencing and other areas of control is illustrated with the relationship of sequencing to inventory. The “cyclical EMQ (Economical Manufacturing Quantities)” problem is discussed and new formulations are presented which promise a computationally feasible resolution of this outstanding problem.