Determining the economic lot size has always represented one of the most important issues in production planning. This problem has long attracted the attention of researchers, and several models have been developed to meet requirements at minimum cost. In this paper we explore and discuss the evolution of these models during one hundred years of history, starting from the basic model developed by Harris in 1913, up to today. Following Harris's work, a number of researchers have devised extensions that incorporate additional considerations. The evolution of EOQ theory strongly reflects the development of industrial systems over the past century. Here we outline all the research areas faced in the past by conducting a holistic analysis of 219 selected journal papers and trying to give a comprehensive view of past work on the EOQ problem. Finally, a new research agenda is proposed and discussed.
Input-Output Analysis, together with the Laplace transform, have been applied to multi-level, multi-period production-inventory systems in a number of papers. This article gives a historical overview of the areas involved in these studies. It is shown that the input and output matrices as well as the Leontief inverse can be generalised to include timing properties for the inputs by means of the Laplace transform. The consequent advantages are exemplified in different production models, treating, for instance, capacity requirements and safety stock problems. The main literature in this field concerns assembly systems, but the approach is easily applicable to process industries with a divergent material flow or when feedback is essential.Laplace Transform, Multi-LEVEL Systems, Production-INVENTORY Systems,
During the last thirty years, the method of the Laplace transform has found an increasing number of applications in the fields of physics and technology. In this article the author points out the possibility of solving problems in the area of discounting with the aid of this method. Without any loss of general validity, it is shown that a discount factor can always be written in an exponential manner which implies that the present value of a cash-flow will obtain a very simple form in the Laplace terminology. This simplicity holds good for stochastic as well as for deterministic economic processes, and the results mentioned below should, therefore, be of immediate use when applied, e.g., to investment problems.
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