The self-consistent parametric inference algorithm (SPI): optimisation in continuous search space

Article Abstract:

The self-consistent parametric inference algorithm represents a dynamical optimisation procedure in continuous search space based on a parametrised approach and supposed to solve procedural tasks in operations research. Continuous parametric descriptions and estimation by inference are extended to a functional self-consistency approach, which in the present work we discuss in the context of typical problems for flexible manufacturing systems. We focus on the question, once the problem is formally parametrised, whether the hypothesis yields a reasonable solution in a continuous search space. The constrained search space profile becomes visible through an analytical approximate solution and can be analysed in the spirit of meta-heuristics. Additionally, a quality measure for the solution is given, which extends the solving algorithm to a learning procedure yielding a guide for the progressive production of an adequate solution to the given optimisation problem. Keywords: Dynamical optimisation; Continuous parameter estimation; Self-consistent parametric inference

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Pattern generating procedure for the cutting stock problem

Article Abstract:

One of the factors that add to the complexity of the cutting stock problem is the large number of the cutting patterns that may be encountered. When the cutting stock problem is expressed as an integer-programming problem, the large number of cutting patterns involved generally makes computation infeasible. However, if the linear programming formulation of the cutting stock problem is free of integer variables, then the effect of the number of cutting patterns will be mitigated. An auxiliary problem arises from the formulation where the columns of the linear programming constraint matrix need to be determined. In this work, a simple pattern generating procedure is developed for solving the auxiliary problem. It is based on an ad hoc solution method described in literature for the knapsack problem. A search tree is used to develop the pattern generation method. Examples are given to illustrate the procedure and its applications. Keywords: Cutting stock problem; Pattern generation; Column generation

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Buffer allocation and required availability in a transfer line with unreliable machines

Article Abstract:

In this paper we study a system of n machines in series. Each pair of subsequent machines is separated by a finite buffer. The machines are unreliable and can break down. In such a production system, the allocation of buffer space between successive stages in the system is of capital importance since it has a significant influence on the availability of the system. We examine how the allocation of buffers can be expressed as a non-linear optimisation problem in which the total cost of installing and using the buffers is minimised. Some of the assumptions of this approximation model are also examined. Keywords: Buffer; Availability; Transfer line; Unreliable machines

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