MRP theory is a theoretical body treating production-inventory systems, in which produced items are made up of sets of produced or purchased sub-items, required to be available a lead-time before each product is completed. The hierarchical dependence between items is captured using input matrices from input-output-analysis, the necessary advanced timing by employing Laplace transform methodology, and the economic consequences by applying the net present value. Little attention has hitherto been given to aspects of a non-empty initial state, e.g. an initial inventory position. Since such states are common in industry, there is a strong need for this theory to include such aspects, in order to gain further practical acceptance. In this paper, theoretical consequences from having a non-empty initial state are investigated. A method for finding the Lot-for-Lot solution is developed using the concept of a truncated monotonically non-decreasing time function, generalising the approach of the generalised Leontief inverse and instrumental for designing plans meeting the necessary inner-corner requirement for optimality. Also the definition of inventory-related costs needs a modification for this concept to be consistent with NPV. These findings are applied in an extensive numerical example. Immediate future research concerns investigating principles for the optimal removal of initial backlogs.

In this paper we compare the two basic risk preference measures suggested independently by John W. Pratt (1964) and Kenneth J. Arrow (1965) as to their impact on simple production decisions with uncertain economic outcomes. We develop a further related concept by introducing a risk aversion leverage measuring the dependence of absolute risk aversion on wealth. We also discover a remarkable approximate relation between risk aversion measures of different leverages making the corresponding risk preference functions similar and leading to a method for estimating different Certainty Monetary Equivalents using zero-leverage expressions. We concentrate on three simple cases of production decisions of the Newsboy type.

MRP theory concerns production-inventory systems, in which produced items are made up of sets of sub-items, either produced or purchased (imported into the system) and required to be available a lead-time before the product is completed. The hierarchical dependence of relations between items is captured by the use of input matrices from Input-Output Analysis, the necessary advanced timing by applying the methodology of Laplace transforms, and the production-economic consequences by the net present value (NPV). This theory has been developed for about 40 years, but little attention has been given to transient aspects, i.e. when there happens to be an initial available inventory of items usable in future production. In this paper, we attempt to highlight the theoretical consequences from having a positive initial available inventory.

n/a

In this paper we attempt to provide a partial answer to the question of why energy is a scarce resource. Scarcity is a fundamental concept in the science of economics. If resources, goods or services were not in scarce supply, we need not economise when utilising them. Indeed, free commodities we need not pay for, their prices are zero, we attach no economic value to them, and their supply is in abundance - at least beyond the point at which our needs and wants are satisfied. However, energy is regarded as a scarce resource, although energy - as such - is not scarce. To describe energy as a useful and therefore a valuable quantity, to which a price may be attached, energy will thus have to be characterised in further dimensions than energy content alone. Apart from quantity, there is a need for a uniform qualitative measure of energy. The obvious field to revert to for such considerations is thermodynamics, which offers a method for defining a uniform measure for the qualitative content of energy, namely exergy. Although exergy is defined from purely physical properties, it is shown to have an important role to play when comparing the economic value of energy in different forms. In particular, this paper will focus on the economic value of heat, especially heat delivered through a district heating system. The concept of exergy is defined from maximising a work output reversibly taking an infinite time. However, for processes to run within finite horizons, entropy must be generated. This leads us to add finite time considerations from examining consequences from the assumed availability of so-called endo-reversible processes. In a small case example we show that heat appears to be overpriced compared to electricity from an exergetic point of view and that this is even more pronounced adopting finite time considerations. (C) 2015 Elsevier B.V. All rights reserved.

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 Harriss 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.