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Bogataj M.,University of Ljubljana | Bogataj M.,Mediterranean Institute for Advanced Studies | Grubbstrom R.W.,Linkoping Institute of Technology | Grubbstrom R.W.,Mediterranean Institute for Advanced Studies
International Journal of Production Economics | Year: 2012

MRP Theory has been developed during the last 25 years for capturing processes concerning multi-level, multi-stage production-inventory systems in a compact way. Input-output analysis has been used to describe structures, and Laplace transforms to describe the timing relations. This theory has mainly dealt with assembly systems, in which each item has only one successor. The lead times for the assembly of an item have usually been constants and equal for all items entering a given successor. For such systems, the equations describing the flows of components may be written to include the generalised input matrix as the product of an input matrix containing needed amounts, and a diagonal lead time matrix with lead time operators along its main diagonal. On occasion, there has been a need to deviate from this representation enabling lead times to vary depending on which input item that is considered. This paper deals with how to represent lead times and similar output delays (in diverging, arborescent systems), when the assumption of equal times is relaxed, in order to retain the basic structure of the fundamental balance equations involved. The intention of this paper is to create a general taxonomy for the representation of timing in algebraic form for a variety of systems covering both assembly systems and arborescent systems (such as extraction, distribution and remanufacturing), as well as systems with mixed properties. For instance, this method may be used directly for the evaluation of investments in capacity or in the location of activities in a production network, or even in a global supply chain. © 2012 Elsevier B.V. All rights reserved.

Bogataj M.,University of Ljubljana | Grubbstrom R.W.,Linkoping Institute of Technology
International Journal of Production Economics | Year: 2013

In this paper we extend and apply MRP theory towards reverse logistics including the considerations of transportation consequences. Our aim is to demonstrate the versatility obtained from using MRP theory when combining Input-Output Analysis and Laplace transforms. This enables an analysis of a supply chain including four sub-systems, namely manufacturing, distribution, consumption and reverse logistics, where the geographical distance between the activities play an important role. The main focus in this paper is on reverse logistics (recycling, remanufacturing). Especially we wish to model the evaluation of disposal and reverse activities far away from agglomerations, which often means an improved environment for nearby inhabitants. This is also illustrated in a numerical example. We use the Net Present Value as a measure of the economic performance. Our ambition is to show that supply chain sub-systems may accurately be described using input and output matrices collected together in corresponding matrices for the system as a whole. Activity levels in each sub-system govern the speed of the respective processes, and these activity levels, in general, will be considered as decision variables. We now analyse reverse logistics activities in which the flows of materials and goods are typically divergent (arborescent processes), similar to properties of the distribution sub-system, and recent results on the extensions of basic MRP theory introducing the concepts of output delays and the generalised output matrix are also introduced here, when modelling the reverse logistics sub-system. © 2012 Elsevier B.V. All rights reserved.

Capone A.,Polytechnic of Milan | Gualandi S.,Polytechnic of Milan | Yuan D.,Linkoping Institute of Technology
Ad Hoc Networks | Year: 2011

Cooperation schemes form a key aspect of infrastructure-less wireless networks that allow nodes that cannot directly communicate to exchange information through the help of intermediate nodes. The most widely adopted approach is based on hop-by-hop forwarding at the network layer along a path to destination. Cooperative relaying brings cooperation to the physical layer in order to fully exploit wireless resources. The concept exploits channel diversity by using multiple radio units to transmit the same message. The underlying fundamentals of cooperative relaying have been quite well-studied from a transmission efficiency point of view, in particular with a single pair of source and destination. Results of its performance gain in a multi-hop networking context with multiple sources and destinations are, however, less available. In this paper, we provide an optimization approach to assess the performance gain of cooperative relaying vis-a-vis conventional multi-hop forwarding under arbitrary network topology. The approach joint optimizes packet routing and transmission scheduling, and generalizes classical optimization schemes for non-cooperative networks. We provide numerical results demonstrating that the gain of cooperative relaying in networking scenarios is in general rather small and decreases when network connectivity and the number of traffic flows increase, due to interference and resource reuse limitations. In addition to quantifying the performance gain, our approach leads to a new framework for optimizing routing and scheduling in cooperative networks under a generalized Spacial Time Division Multiple Access (STDMA) scheme. © 2011 Elsevier B.V. All rights reserved.

Rohdin P.,Linköping University | Moshfegh B.,Linkoping Institute of Technology
Building and Environment | Year: 2011

Ventilation, heating and cooling systems in industrial premises are important issues as they are related to both energy cost and indoor climate management and the health of the premises' occupants. The present paper has two aims: (1) to evaluate the performance of Computational Fluid Dynamics (CFD) for planning new or renovating existing industrial ventilation systems, and (2) to evaluate the performance of two different supply principles in a contaminant-intensive process with temperature and density stratification. The comparisons between measurements and simulations show good agreement, with an average deviation of 1.1 °C for temperature and 0.11 m/s for velocity when using the most accurate model. Of the compared two-equation models (RNG, SKE and RKE), the RNG model produced the results most in agreement with the measurements. Good agreement was also found when measured and predicted values for contaminant removal efficiency were compared. When the mixing and displacement ventilation systems at the facility were compared, an increase in contaminant removal efficiency by a factor of 6 was found during winter for the displacement system, and the performance in terms of heat removal effectiveness increased by a factor of 3 for the same case. One drawback, however, was the slightly higher predicted discomfort and risk of draughts in the winter cases. In the summer cases, the difference in performance between the two systems was smaller. The overall performance of the displacement system decreased due to the diminishing stack effect as the temperature difference between supply air and the air in the room decreased. © 2011 Elsevier Ltd.

Andriolo A.,University of Padua | Battini D.,University of Padua | Grubbstrom R.W.,Linkoping Institute of Technology | Persona A.,University of Padua | Sgarbossa F.,University of Padua
International Journal of Production Economics | Year: 2014

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. © 2014 Elsevier B.V. All rights reserved.

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.

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.

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.

Holmberg K.,Linkoping Institute of Technology
Computers and Operations Research | Year: 2010

When addressing the problem of snow removal for secondary roads, a tool for solving the rural postman problem can be very useful. We present some ideas for heuristics for this problem. The heuristics are of the same type as the classical Frederickson heuristic. The ideas concern the order of the main steps in such a method, namely constructing a connected graph with all vertices having even degree, containing all the required edges. We also propose two postprocessing heuristics for improving the tours and removing unnecessary detours. The computational tests show that the ideas are interesting alternatives to the classical approach, and that running times are acceptable. We study problem characteristics that may indicate which method to choose. © 2009 Elsevier Ltd. All rights reserved.

Fahlen E.,Chalmers University of Technology | Trygg L.,Linkoping Institute of Technology | Ahlgren E.O.,Chalmers University of Technology
Energy Conversion and Management | Year: 2012

Heat load variations, daily as well as seasonal, are constraining co-generation of high-value energy products as well as excess heat utilisation. Integration of heat-driven absorption cooling (AC) technology in a district heating and cooling (DHC) system raises the district heat (DH) demand during low-demand periods and may thus contribute to a more efficient resource utilisation. In Sweden, AC expansion is a potentially interesting option since the cooling demand is rapidly increasing, albeit from low levels, and DH systems cover most of the areas with potential cooling demand. This study aims to assess the potential for cost and CO 2 emission reduction due to expansion of DH-driven AC instead of electricity-driven compression cooling in the DHC system of Göteborg, characterised by a high share of low-cost excess heat sources. The DHC production is simulated on an hourly basis using the least-cost model MARTES. Despite recent advances of compression chillers, the results show potential for cost-effective CO 2 emission reduction by AC expansion, which is robust with regards to the different scenarios applied of energy market prices and policies. While the effects on annual DHC system results are minor, the study illustrates that an increased cooling demand may be met by generation associated with low or even negative net CO 2 emissions - as long as there is high availability of industrial excess heat in the DHC system, or if e.g. new biomass-based combined heat and power capacity is installed, due to the avoided and replaced marginal power generation. © 2012 Elsevier Ltd. All rights reserved.

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