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Grubbstrom R.W.,Linkoping Institute of Technology | Grubbstrom R.W.,Mediterranean Institute for Advanced Studies
International Journal of Production Economics | Year: 2015

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 rôle 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. © 2015 Elsevier B.V. Source


Grubbstrom R.W.,Linkoping Institute of Technology | Grubbstrom R.W.,Mediterranean Institute for Advanced Studies
International Journal of Production Economics | Year: 2014

The dynamic lotsizing problem concerns the determination of optimally produced/delivered batch quantities, when demand, which is to be satisfied, is distributed over time in different amounts at different times. The standard formulation assumes that these batches are provided instantaneously, i.e. that the production rate is infinite. Using a cumulative geometrical representation for demand and production, it has previously been demonstrated that the inner-corner condition for an optimal production plan reduces the number of possible optimal replenishment times to a finite set of given points, at which replenishments can be made. The problem is thereby turned into choosing from a set of zero/one decisions, whether or not to replenish each time there is a demand. If n is the number of demand events, this provides 2n-1 alternatives, of which at least one solution must be optimal. This condition applies, whether an Average Cost approach or the Net Present Value principle is applied, and the condition is valid in continuous time, and therefore in discrete time. In the current paper, the assumption of an infinite production rate is relaxed, and consequences for the inner-corner condition are investigated. It is then shown that the inner-corner condition needs to be modified to a tangency condition between cumulative requirements and cumulative production. Also, we have confirmed the additional restriction for feasibility in the finite production case (provided by Hill, 1997), namely the production rate restriction. Furthermore, in the NPV case, one further necessary condition for optimality, the distance restriction concerning the proximity between adjacent production intervals, has been derived. In an example this condition has shown to reduce the number of candidate solutions for optimality still further. An algorithm leading to the optimal solution is presented. © 2012 Elsevier B.V. Source


Grubbstrom R.W.,Linkoping Institute of Technology | Grubbstrom R.W.,Mediterranean Institute for Advanced Studies
International Journal of Production Economics | Year: 2014

The dynamic lotsizing problem concerns the determination of optimal batch quantities, when given required amounts appear at discrete points in time. The standard formulation assumes that no shortages are allowed and that replenishments are made instantaneously. For the case when no shortage is allowed, previously it has been demonstrated that the inner-corner condition for an optimal production plan in continuous time reduces the number of possible replenishment times to a finite set of given points at which either a replenishment is made, or not. The problem is thus turned into choosing from a set of zero/one decisions with 2n-1 alternatives, of which at least one solution must be optimal, where n is the number of requirement events. Recently, the instantaneous replenishment assumption has been replaced by allowing for a finite production rate, which turned the inner-corner condition into a condition of tangency between the cumulative demand staircase and cumulative production. In this paper we investigate relationships between optimal cumulative production and cumulative demand, when backlogging is permitted. The production rate is assumed constant and cumulative production will then be a set of consecutive ramps. Cumulative demand is a given staircase function. The net present value (NPV) principle is applied, assuming a fixed setup cost for each ramp, a unit production cost for each item produced and a unit revenue for each item sold at the time it is delivered. Among other results, it is shown that optimal cumulative production necessarily intersects the demand staircase. Instead of having 2n-1 production staircases as candidates for optimality, there are 2n-1 production structures as candidates. These are made up of sequences of batches, of which the set of batches may be optimised individually. Also is shown that the NPV of each batch has a unique timing maximum and behaves initially in a concave way and ends as convex. Results for the average cost approach are obtained from a zeroth/first order approximation of the objective function (NPV). © 2013 Published by Elsevier B.V. Source


Grubbstrom R.W.,Linkoping Institute of Technology | Grubbstrom R.W.,Mediterranean Institute for Advanced Studies | Tang O.,Linkoping Institute of Technology
International Journal of Production Economics | Year: 2012

MRP Theory combines the use of Input-Output Analysis and Laplace transforms, enabling the development of a theoretical background for multi-level, multi-stage production-inventory systems together with their economic evaluation, in particular applying the Net Present Value principle (NPV). In a recent paper (Grubbström et al., 2010), a general method for solving the dynamic lotsizing problem for a general assembly system was presented. It was shown there that the optimal production (completion) times had to be chosen from the set of times generated by the Lot-For-Lot (L4L) solution. Thereby, the problem could be stated in binary form by which the values of the binary decision variables represented either to make a production batch, or not, at each such time. Based on these potential times for production, the problem of maximising the Net Present Value or minimising the average cost could be solved, applying a single-item optimal dynamic lotsizing method, such as the Wagner-Whitin algorithm or the Triple Algorithm, combined with dynamic programming. This current paper follows up the former paper by investigating the complexity defined as the number of possible feasible solutions (production plans) to compare. We therefore investigate how properties of external demand timing and properties of requirements (Bill-of-Materials) have consequences on the size of this solution space. Explicit expressions are developed for how the total number of feasible production plans depends on numbers of external demand events on different levels for, in particular, the two extreme cases of a serial system and a full system (the latter, in which items have requirements of all existing types of subordinate items). A formula is also suggested for general systems falling in between these two extremes. For the most complex full system, it is shown that the number of feasible plans will be the product of elements taken from Sylvesters sequence (an instance of doubly exponential sequences) raised to powers depending on numbers of external demand events. © 2012 Elsevier B.V. All rights reserved. Source


Kovacic D.,Informacijsko Svetovanje | Hontoria E.,Technical University of Cartagena | Ros-McDonnell L.,Technical University of Cartagena | Bogataj M.,Mediterranean Institute for Advanced Studies
Central European Journal of Operations Research | Year: 2015

The current economic crisis is reflected in lower capacity expansion or even capacity contraction, closing of distant activities and reduction of lead time. However, the locations of suppliers are strongly connected with the quality of agricultural products. The transportation from distant locations can largely affect the food production business in all aspects. The article presents how the Extended Material Requirements Planning (EMRP) model enables to evaluate perturbations in lead time and temperature, and shows how distant growing areas of agricultural products, and, as a result, transportation lead times play a crucial role in the net present value calculation. In this paper, we show the impact of choosing a less distant site for growing of agricultural products, and overlapping the transportation and quarantine lead times on decreasing the perishability, hence increasing the added value in multi-level food assembly systems. Also, a case study of Spanish baby food industry is presented, using the principles of the well-developed EMRP Theory. © 2014, Springer-Verlag Berlin Heidelberg. Source

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