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We sketch the integral transform method in a close connection with its historical development and survey newer applications to problems in production economics and finance. Keywords: Laplace transform; Fourier transform; Production planning

A study was conducted to analyze a framework for simultaneously obtaining the optimal run length and the production rate for a single item. In line with this, the item's output rate was characterized as a decision variable. It was then assumed that the production cost per unit was a quadratic function of the production rate. In addition, a numerical example and sensitivity analysis were carried out to characterize an iterative solution process.

A study was conducted to analyze a hybrid algorithm for the multi period multi product production planning problem. The algorithm supported mathematical programming and simulation frameworks of a manufacturing system. A production plan that is mathematically optimal and feasible was then developed. Results indicated that analytical models can be utilized with simulation frameworks to generate solutions for the problem.

The implementation of group technology as a way of factory organization is best carried out in conjunction with production flow analysis during the initial stage. Group technology involves the categorization of machine tools, human resources and other production resources. It is a newer organizational technique as compared to process organization, whose implementation is more widespread.

A simulated annealing algorithm is derived to deal with the problem of batching within the context of a flexible manufacturing system in production planning. The batching problem occurs because of the limited quantity of production resources. Computational results show that the derived algorithm performs quite well in terms of time and quality. Furthermore, the algorithm is considered applicable even for more difficult and bigger problems.

A study was conducted to extend the analysis of obtaining optimal safety stock levels in material requirements planning systems to a multi-level system supporting production that takes place based on a lot-for-lot policy. The production correlates with the application of the net present value as the objective criterion and a disregard of opportunities for joint set-up. Findings indicated the applicability of single-level results in multi-level cases during a lot-for-lot policy.