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  • 1.
    Andriolo, Alessandro
    et al.
    University of Padova, Italy.
    Battini, Dania
    University of Padova, Italy.
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Persona, Alessandro
    University of Padova, Italy.
    Sgarbossa, Fabio
    University of Padova, Italy.
    A century of evolution from Harriss basic lot size model: Survey and research agenda2014In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 155, p. 16-38Article in journal (Refereed)
    Abstract [en]

    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.

  • 2.
    Bogataj, Marija
    et al.
    University of Ljubljana, Slovenia Mediterranean Institute Adv Studies, Slovenia .
    Grubbström, Robert W
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    On the representation of timing for different structures within MRP theory2012In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 140, no 2, p. 749-755Article in journal (Refereed)
    Abstract [en]

    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. less thanbrgreater than less thanbrgreater thanOn 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.

  • 3.
    Bogataj, Marija
    et al.
    University of Ljubljana, Slovenia MEDIFAS, Slovenia .
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Transportation delays in reverse logistics2013In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 143, no 2, p. 395-402Article in journal (Refereed)
    Abstract [en]

    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.

  • 4.
    Bogataj, Marija
    et al.
    University of Ljubljana, Slovenia.
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology. Mediterranean Institute for Advanced Studies, Sempeter pri Gorici, Slovenia.
    Bogataj, Ludvik
    University of Ljubljana, Slovenia.
    Efficient location of industrial activity cells in a global supply chain2011In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 133, no 1, p. 243-250Article in journal (Refereed)
    Abstract [en]

    Inefficient locations for production, distribution and reverse logistics plants will result in excess costs no matter how well material requirements planning (MRP), inventory control, distribution and information sharing decisions are optimized. In this paper we study ways in which aspect of activity cell location decisions can be analyzed within an extended MRP model. This model has previously been extended by including distribution and reverse logistics components in a compact form, presented in Grubbstrom et al. (2007). Our aim is to demonstrate the basic differences between an approach to location problems with MRP "under the same roof" as the global supply chain, in which transportation time delays and direct transportation costs have substantial influence. We discuss possibilities of how to present location aspects in the supply chain model obtained from combining input-output analysis and Laplace transforms in four sub-systems, namely manufacturing, distribution, consumption and reverse logistics, and show how the transportation costs and lead time influenced by the location of all these activities affect the resulting net present value (NPV). Our aim is to build a model supporting decisions concerning the structure of a supply chain as an alternative to a mixed integer programming formulation. The model developed is based on the use of continuous functions describing spatial distributions of cost and customer demand. Continuous functions are embedded in the MRP extension previously introduced in Grubbstrom et al. (2007). Location decisions influence (i) production costs, because timing influences the cost of activities involved in creating a product, cf. (Grubbstrom and Bogataj, submitted for publication), and (ii) logistics costs, which refer to the procurement and physical transmission of materials through the supply chain. In this current paper we wish to combine both of these aspects into a comprehensive model, where we show the interaction between the "space of flows" and the "space of places" as Giovanni Arrighi distinguishes one from the other in his book The Long Twentieth Century.

  • 5.
    Disney, S. M.
    et al.
    Cardiff University.
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Economic consequences of a production and inventory control policy2004In: International Journal of Production Research, ISSN 0020-7543, E-ISSN 1366-588X, Vol. 42, no 17, p. 3419-3431Article in journal (Refereed)
    Abstract [en]

    The economic performance of a generalized Order-Up-To policy is investigated in response to an Auto Regressive stochastic demand process. Focus is on the case where the physical production/distribution lead time is one period and where demand is forecasted with simple exponential smoothing. Two sets of convex piece-wise linear costs are considered. The first set is the traditional inventory holding and backlog costs. The second set of costs is piece-wise linear and increasing convex costs associated with the production order rate within and above a capacity constraint. Numerical investigations reveal that the classical Order-Up-To policy is no longer optimal when a broader range of costs is considered in the objective function.

  • 6.
    Disney, Stephen M.
    et al.
    Cardiff University, Wales.
    Naim, Mohamed M.
    Cardiff University, Wales.
    Williams, Sharon J.
    Swansea University, Wales.
    Nussey, Ian
    IBM United Kingdom Ltd, England.
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, Faculty of Science & Engineering.
    Biographical-Item: In Memoriam: Professor Denis R. Towill 1933-2015 in INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS, vol 170, issue , pp III-V2015 (ed. 170)Book (Other academic)
    Abstract [en]

    n/a

  • 7.
    Grubbström, Robert
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Cumulative staircase considerations for dynamic lotsizing when backlogging is allowed2014In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 157, p. 201-211Article in journal (Refereed)
    Abstract [en]

    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).

  • 8.
    Grubbström, Robert
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Dynamic lotsizing with a finite production rate2014In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 149, p. 68-79Article in journal (Refereed)
    Abstract [en]

    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.

  • 9.
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    An Attempt to Introduce Dynamics Into Generalised Exergy Considerations2004Conference paper (Refereed)
  • 10.
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    An attempt to introduce dynamics into generalised exergy considerations2007In: Applied Energy, ISSN 0306-2619, E-ISSN 1872-9118, Vol. 84, no 7-8, p. 701-718Article in journal (Refereed)
    Abstract [en]

    In previous research, the author developed a general abstract framework for the exergy content of a system of finite objects [Grubbström RW. Towards a generalized exergy concept. In: van Gool W, Bruggink JJC, editors. Energy and time in the economic and physical sciences. Amsterdam: North-Holland, 1985. p. 41-56]. Each such object is characterised by its initial extensive properties and has an inner energy written as a function of these properties. It was shown that if these objects were allowed to interact, there is a maximum amount of work that can be extracted from the system as a whole, and a general formula for this potential was provided. It was also shown that if one of the objects was allowed to be of infinite magnitude initially, taking on the role as an environment having constant intensive properties, then the formula provided took on the same form as the classical expression for exergy. As a side result, the theoretical considerations demonstrated that the second law of thermodynamics could be interpreted as the inner energy function being a (weakly) convex function of its arguments, when these are chosen as the extensive properties. Since exergy considerations are based on the principle that total entropy is conserved when extracting work, these processes would take an infinite time to complete. In the current paper, instead, a differential-equation approach is introduced to describe the interaction in finite time between given finite objects of a system. Differences in intensive properties between the objects provide a force enabling an exchange of energy and matter. An example of such an interaction is heat conduction. The resulting considerations explain how the power extracted from the system will be limited by the processes being required to perform within finite-time constraints. Applying finite-time processes, in which entropy necessarily is generated, leads to formulating a theory for a maximal power output from the system. It is shown that such a theory is possible to develop, and the resulting equilibrium conditions are compared with to those of the exergetic equilibrium. © 2007 Elsevier Ltd. All rights reserved.

  • 11.
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Balancing Queuing Costs and Capacity Costs along the Assembly Line- A Queuing-Theoretic Approach with Accounting Implications2007In: Produktions- ond Logistikmanagement / [ed] Haasis, Hans-Dietrich, München: Verlag Franz Vahlen , 2007, p. 395-417Chapter in book (Other academic)
    Abstract [de]

    Die nachhaltige Gestaltung von Produktion und Logistik ist wesentlich für eine wettbewerblich starke Positionierung von Unternehmen in internationalen Wertschöpfungsprozessen. Aktuelle Herausforderungen betreffen unter anderem Lösungen im Zusammenhang mit regionalen Produktionsnetzwerken, einem nachhaltigen Supply Chain Management, Produktdienstleistungen, E-Business, Mass Customization und Kreislaufwirtschaft.Dieses Buch bietet nach einer Einordnung in die Betriebswirtschaftslehre und den Bereich des nachhaltigen Wirtschaftens einen fundierten Überblick über Möglichkeiten der Gestaltung und Planung unternehmensbezogener Strukturen und Prozesse in den betriebswirtschaftlichen Bereichen Produktion und Logistik. Neben theoretischen Grundlagen werden darauf aufbauend anhand von Case Studies innovative strategische und operative Ansätze aufgezeigt. Übungsaufgaben verdeutlichen die Begriffe und Zusammenhänge auch zum Selbststudium. Das Buch richtet sich an Studierende und Dozenten der Wirtschaftswissenschaften, des Wirtschaftsingenieurwesens und verwandter Studienrichtungen an Universitäten, Fachhochschulen, Akademien und Weiterbildungsinstitutionen sowie an Praktiker aus den Bereichen Produktion und Logistik.

  • 12.
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    International Logistics Management Game, Game Control Centre Manual, Version Date: December 20042004Other (Other (popular science, discussion, etc.))
  • 13.
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    On the Dynamics of La Bille2004In: Tanulmányok Chikán Attila tiszteletére: Vállalati versenyképesség, logisztika, készletek (Papers in Honour of Attila Chikán - Enterprise Competitiveness, Logistics, Inventories) / [ed] Erzsébet Czakó,Attila Chikán, Budapest: ISIR , 2004, p. 222-230Chapter in book (Other academic)
  • 14.
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology. Mediterranean Institute for Advanced Studies,SI- 5290 Š empeter pri Gorici, Slovenia.
    On the Exergy Content of an Isolated Body in Thermodynamic Disequilibrium2012In: International Journal of Energy Optimization and Engineering, ISSN 2160-9500, Vol. 1, no 1, p. 1-18Article in journal (Other academic)
    Abstract [en]

    Exergy is a concept that is gaining an increasingly wider recognition as a proper measure for the actual energy resources consumed, when energy is used. Energy as such is indestructible, but exergy is not. As entropy is generated while energy is used, exergy is consumed. Exergy can be interpreted as the qualitative content of energy, or as energy in its highest quality. Therefore, there is an interest in investigating this concept from as many theoretical aspects as possible.

    In earlier papers the author has developed formulae for the exergy potential of a system of finitely extended objects, not necessarily having any environment. It was there shown that the classical formula for exergy obtains as one of the objects grows beyond all bounds thereby taking on the rôle as an environment.

    In this current paper formulae are derived for the exergy content of an isolated body in thermodynamic disequilibrium, viewed as a system of infinitely many objects each with infinitesimal extension and in microscopic equilibrium.

  • 15.
    Grubbström, Robert W
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, Faculty of Science & Engineering. Mediterranean Institute Adv Studies, Slovenia.
    On the true value of resource consumption when using energy in industrial and other processes2015In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 170, p. 377-384Article in journal (Refereed)
    Abstract [en]

    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.

  • 16.
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Recent Developments in MRP Theory - and Future Opportunities2009In: PROCEEDINGS OF THE 10TH INTERNATIONAL SYMPOSIUM ON OPERATIONAL RESEARCH SOR 09 / [ed] Stirn, LZ; Zerovnik, J; Drobne, S; Lisec, A, Ljubljana, Slovenia: Slovenian Society Informatika, Section for Operational Research , 2009, p. 23-24Conference paper (Refereed)
    Abstract [en]

    Material Requirements Theory (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 (NPV) principle. The time scale may be continuous ("bucketless" in MRP terminology) or discrete. Since the average cost measure may be viewed as an approximation of NPV, the theory may be applied to cases, when average costs are preferred as the objective function.

  • 17.
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Some aspects on modelling as a base for scientific recommendations2001In: Kybernetes, ISSN 0368-492X, E-ISSN 1758-7883, Vol. 30, no 9-10, p. 1126-1138Article in journal (Refereed)
    Abstract [en]

    Argues that the Hempel-Oppenheimian logical scheme for explanations and predictions also applies to prescriptive statements (recommendations) derived from theoretical models in the normative sciences. Presents ideas concerning the allocation of effort in developing normative models for such purposes. Three characteristics of the model and the model-building process, together with a suggested qualitative relationship between these properties, are discussed, namely the "applicability" of the model, the "simplicity" of the principle derived from the model, and the "level of technique " applied, a discussion similar to that of Bronfenbrenner. It is proposed that the subjective value to the model-builder may be envisaged as a function of these three main characteristics and that the model-design process then may be interpreted as a constrained optimisation problem.

  • 18.
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    The Newsboy problem when customer demand is a compound renewal process2010In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 203, no 1, p. 134-142Article in journal (Refereed)
    Abstract [en]

    The Newsboy (Newsvendor) problem is probably the simplest of all stochastic inventory problems, involving a one-time purchase decision and a stochastic sales outcome. As an investment, it can be interpreted as the simplest stochastic version of the point-in, point-out investment problem of Jevons [Jevons, W.S., Theory of Political Economy, Macmillan, London 1871].

    This paper provides a compound variation of the Newsboy problem. Instead of demand simply being known as to its distribution, here demand is generated by customers arriving at different points in time requiring amounts of varying size. Arrivals follow a renewal process, and amounts required are each taken from a second independent distribution.

    It is shown how the optimal purchase quantity in explicit form depends on properties of the two distributions, maximising the expected net present value (NPV) of the payments involved. The solution to the compound problem will be the solution to the classical problem, if designing a special distribution for the demand process.

    The developments make use of the relation between the NPV and the Laplace transform, simultaneously using the Laplace transform as a moment-generating function.

  • 19.
    Grubbström, Robert W
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    The time-averaged L4L solution - a condition for long-run stability applying MRP theory2012In: International Journal of Production Research, ISSN 0020-7543, E-ISSN 1366-588X, Vol. 50, no 21, p. 6099-6110Article in journal (Refereed)
    Abstract [en]

    MRP theory provides a theoretical background for multi-level, multi-stage production-inventory systems (material requirements planning in a general sense) together with their economic evaluation, in particular applying the net present value principle. The theory combines the use of input-output analysis and Laplace transforms, the former for capturing product structures, and the latter for incorporating timing, including time lags, lead times, and output delays. In this paper, we consider any production policy, when given any external demand as a vector-valued function of time. It is shown that in order for available inventory to be kept at finite levels at any time, the lot-for-lot (L4L) solution must be valid for the time averages of production and deliveries, irrespective of the policy followed. This analysis is carried out using properties the Laurent expansions of the transforms involved.

  • 20.
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Transform Methodology Applied to Some Inventory Problems2007In: Zeitschrift für Betriebswirtschaft, ISSN 0044-2372, Vol. 77, no 3, p. 297-324Article in journal (Refereed)
  • 21.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Bikovska, Jana
    Riga Technical University.
    The International Logistics Management Game Internet Version 3.0, Participants' Manual, Version Date: December 20042004Other (Other (popular science, discussion, etc.))
  • 22.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology. Mediterranean Institute for Advanced Studies, Šempeter pri Gorici, Slovenia.
    Bogataj, Marija
    University of Ljubljana, Ljubljana, Slovenia.
    Bogataj, Ludvik
    University of Ljubljana, Ljubljana, Slovenia.
    Optimal lotsizing within MRP Theory2010In: Annual Reviews in Control, ISSN 1367-5788, E-ISSN 1872-9088, Vol. 34, no 1, p. 89-100Article in journal (Refereed)
    Abstract [en]

    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 this paper we concentrate our attention on the question of optimal lotsizing decisions within the MRP Theory framework. MRP Theory has mainly dealt with assembly structures by which items produced downstream (on a higher level in the product structure) contain one or more sub-items on lower levels, but at each stage, the assembly activity produces only one type of output. This enables the input matrix, after enumerating all items suitably, to be organised as a triangular matrix, with non-zero elements only appearing below its main diagonal. The introduction of a diagonal lead time matrix capturing the advanced timing when required Inputs are needed, enables compact expressions to be obtained, explaining the development of key variables such as available inventory and backlogs in the frequency domain. Central in this theory is the generalised input matrix showing when and how much the internal (dependent) demand amounts to for any production plan. Previously has been demonstrated that in a one-product case, inner-corner conditions for an optimum production plan in continuous time reduce the number of possible replenishment times to a finite set of given points at which either a replenishment is made, or not. The dynamic lotsizing problem is thus turned into choosing from a set of zero-one decisions with 2(m-1) alternatives, of which one (or possibly several equivalent) solution(s) must be optimal, where m is the number of requirement (demand) events. Given these points in time and the corresponding staircase function describing cumulative demand, the optimal plan may be obtained, for instance by employing the Triple Algorithm of dynamic lotsizing. This applies either an Average Cost approach, or the Net Present Value principle is applied In this paper, we extend this analysis to a general multi-item system of the assembly type. Among other issues, it is shown how the number of internal demand events depends on product structure and number of external demand events. Also the inner-corner condition is proven still to be valid in this somewhat more complex situation, when demand for lower-level items no longer is given from the outset, but instead depends on decisions concerning production of items on higher levels in the product structure. A simple dynamic program procedure is provided offering a solution to maximising the NPV for any general assembly system. To solve for the optimal production plan, the Triple Algorithm may be applied to each stage.

  • 23.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Hammond, G.P.
    University of Bath, UK.
    Probert, S.D.
    Cranfield University, Bedford, UK.
    Reis, A.J.P.S.
    Lusíada University, Famalicao, Portugal.
    Industrial energy-analysis and management: A European perspective2007In: Applied Energy, ISSN 0306-2619, E-ISSN 1872-9118, Vol. 84, no 7-8, p. 671-674Article in journal (Other academic)
  • 24.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering. Linköping University, The Institute of Technology.
    Hinterhuber, Hans H
    Department of Management, University of Innsbruck, Innsbruck, Austria.
    Developments in Production Economics2009In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 121, no 2, p. 299-300Article in journal (Other academic)
    Abstract [en]

    n/a

  • 25.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Hinterhuber, Hans H.
    Innsbruck University School of Management, Austria.
    Editorial2006In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 104, no 1, p. 1-2Article in journal (Other academic)
  • 26.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Hinterhuber, Hans H.
    University of Innsbruck.
    Editorial2004In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 89Article in journal (Refereed)
  • 27.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Hinterhuber, Hans H.
    University of Innsbruck.
    Igls 20002002In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 77, no 3, p. 189-190Article in journal (Other academic)
    Abstract [en]

    [No abstract available]

  • 28.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, Faculty of Science & Engineering.
    Hinterhuber, Hans H.Universität Innsbruck, Austria.
    Nineteenth International Working Seminar on Production Economics, Pre-prints, Volume 1: Papers scheduled for Tuesday, February 23 2016 8.00 am to 21.15 pm2016Conference proceedings (editor) (Other academic)
  • 29.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, Faculty of Science & Engineering.
    Hinterhuber, Hans H.Universität Innsbruck, Austria.
    Nineteenth International Working Seminar on Production Economics, Pre-prints, Volume 2: Papers scheduled for Tuesday, February 24, 2016, 8.00 am to 21.15 pm2016Conference proceedings (editor) (Other academic)
  • 30.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, Faculty of Science & Engineering.
    Hinterhuber, Hans H.Universität Innsbruck, Austria.
    Nineteenth International Working Seminar on Production Economics, Pre-prints, Volume 3: Papers scheduled for Tuesday, February 25, 2016, 8.00 am to 20.30 pm2016Conference proceedings (editor) (Other academic)
  • 31.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, Faculty of Science & Engineering.
    Hinterhuber, Hans H.Universität Innsbruck, Austria.
    Nineteenth International Working Seminar on Production Economics, Pre-prints, Volume 4: Papers scheduled for Tuesday, February 26, 2016, 8.00 am to 10.45 am2016Conference proceedings (editor) (Other academic)
  • 32.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Hinterhuber, Hans H.
    University of Innsbruck.
    Preface - Igls 20002002Other (Other academic)
  • 33.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Hinterhuber, Hans H.
    Universität Innsbruck.
    Strategic Issues And Innovation In Production Economics - Editorial2006In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 104, no 1, p. 1-2Article in journal (Other academic)
  • 34.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Hinterhuber, Hans H.
    University of Innsbruck.
    Suppy Chain Management - Editorial2004In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 89, no 2, p. 5-6Article in journal (Other academic)
  • 35.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering. Linköping University, The Institute of Technology.
    Hinterhuber, Hans H.
    University of Innsbruck, Innsbruck, Austria.
    Tang, Ou
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Innsbruck 20082011In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 131, no 1, p. 1-3Article in journal (Other academic)
  • 36.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Huynh, Thuy
    Linköping University, Department of Production Economics. Linköping University, The Institute of Technology.
    Analysis of standard ordering policies within the framework of MRP theory2006In: International Journal of Production Research, ISSN 0020-7543, E-ISSN 1366-588X, Vol. 44, no 18-19, p. 3759-3773Article in journal (Refereed)
    Abstract [en]

    A number of different standard ordering policies are presented within the methodology of Material Requirements Planning (MRP), such as Lot-For-Lot (L4L), Fixed Order Quantity (FOQ), Fixed Period Requirements (FPR), etc. In MRP theory the time development of the production-inventory system is determined by a set of fundamental equations for available inventory, total inventory and backlogs using Input-Output Analysis for capturing the Bill of Materials and Laplace transforms for describing the advanced timing requirements. This paper aims at formally introducing standard ordering policies into the fundamental equations of MRP Theory in order to analyse the possibility to obtain closed-form expressions for the time development of the system, when such rules are applied.

  • 37.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Huynh, Thuy
    Linköping University, The Institute of Technology. Linköping University, Department of Production Economics.
    Multi-level, multi-stage capacity-constrained production-inventory systems in discrete time with non-zero lead times using MRP theory2006In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 101, no 1 SPEC. ISS., p. 53-62Article in journal (Refereed)
    Abstract [en]

    A substantial amount of research has been carried out on capacity-constrained production-inventory systems. This has mostly dealt with models assuming deterministic demand and single-item systems. In previous work, one of the authors together with a co-researcher designed a basic theoretical model for systems with multiple items and stochastic external demand. These developments were presented within a discrete time framework. Lead times were assumed to be given constants and the net present value principle was applied. Although the theory developed concerned situations in which the lead times could be any non-zero constants, in order to design an analytical solution procedure, the assumption was made that lead times were zero, in order to be able to apply dynamic programming. Cumulative production and cumulative demand were taken as state variables. In this paper, we remain in the discrete time framework and develop a methodology for the case that lead times are non-zero, whereas demand is deterministic. Our emphasis is on the design of the state space, the properties of which depend on the product structures (the input matrix), the distribution of lead times among the production processes (the lead time matrix), and on the historical sequences of the production vectors. Once an efficient state space is designed, dynamic programming may be applied as a solution method. The net present value principle is again applied. © 2005 Elsevier B.V. All rights reserved.

  • 38.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Kingsman, Brian G.
    Ordering and inventory policies for step changes in the unit item cost: A discounted cash flow approach2004In: Management science, ISSN 0025-1909, E-ISSN 1526-5501, Vol. 50, no 2, p. 253-267Article in journal (Refereed)
    Abstract [en]

    This paper considers the problem of determining the optimal ordering quantities of a purchased item where there are step changes in price, either up or down. Other costs incurred include ordering costs associated with each replenishment and holding costs related to capital tied up in inventory and physical stock holding. The net present value (NPV) principle is applied. Explicit expressions for the development of the optimal order quantities over time are presented. It is shown that three cases may be distinguished: (i) when the price change is very small, (ii) when an essential price increase occurs, and (iii) when there is an essential price decrease. Although the optimal last-order quantity before a price increase is similar in magnitude to what has been presented in other articles applying average cost approaches, in certain respects, this paper offers novel results contradictory to those suggested by other authors. Analysis shows that the average-cost model solutions are first-order approximations in the discount rate. Numerical evaluations of a range of price increases and times to the price increase suggest that, with certain important caveats, the average-cost formulae are likely to be acceptable for most practical situations for the infinite horizon situation.

  • 39.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Tang, Ou
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    An Overview of Input-Output Analysis Applied to Production-Inventory Systems2000In: Economic Systems Research, ISSN 0953-5314, E-ISSN 1469-5758, Vol. 12, no 1, p. 3-25Article in journal (Refereed)
    Abstract [en]

    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.

  • 40.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Tang, Ou
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Further Developments on Safety Stocks in an MRP System Applying Laplace Transforms and Input-Output Analysis1999In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 60-61, p. 381-387Article in journal (Refereed)
    Abstract [en]

    In a sequence of previous papers, the Laplace transform and Input–Output Analysis have been applied to formulate a theoretical basis for material requirements planning (MRP) under different levels of generalisation. Searching for the optimal safety stock is one of the extensions of this theory. This paper investigates the safety stock properties in the case that the time interval of demand is Gamma-distributed. The Generalised Leontief inverse plays an effective role in describing the multi-level production–inventory system when the subordinate products are produced according to a lot-for-lot (L4L) policy.

  • 41.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Tang, Ou
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Modelling Rescheduling Activities in a Multi-Period Production-Inventory System2000In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 68, no 2, p. 123-135Article in journal (Refereed)
    Abstract [en]

    Decisions for planning production activities for multi-period production–inventory systems have been studied in a number of papers applying input–output analysis and the Laplace transform. The decisions have concerned activities spread out over time without having the opportunity to adjust future decisions when the external and/or internal circumstances change. In this paper, we extend the analysis to situations when rescheduling is possible. Firstly, different classes of causes justifying rescheduling activities are presented including periodic rescheduling and “net change”. Secondly, in terms of previously developed theory, we model the behaviour of a simple single-level production–inventory system for which its production plan may be modified at one point in the future.

  • 42.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Tang, Ou
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Optimal production opportunities in a remanufacturing system2006In: International Journal of Production Research, ISSN 0020-7543, E-ISSN 1366-588X, Vol. 44, no 18-19, p. 3953-3966Article in journal (Refereed)
    Abstract [en]

    In recent years, remanufacturing has emerged in various industrial sectors, and it adds an additional production alternative apart from the conventional manufacturing process. With remanufacturing, a used return product is often disassembled, reprocessed, and then reassembled into a new product. The remanufactured product is often of the same quality as those from regular manufacturing. Even though remanufacturing saves a substantial cost of materials, it often requires more labour and other inputs. Thus, it becomes important to examine the expanded production opportunity of the system. In this paper, we therefore make a first attempt to model such a system with respect to its optimal production. This model is based on the Cobb-Douglas (Wicksell) production function. More specifically, we focus on how labour costs, material costs, and the budget influence optimal production decisions. Explicit properties of the optimal plan are derived and presented as theorems. Results of this study are intended to provide a guideline for managers to make sound decisions, when dealing with the increasingly important remanufacturing systems.

  • 43.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Tang, Ou
    Linköping University, Department of Production Economics. Linköping University, The Institute of Technology.
    The moments and central moments of a compound distribution2005In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 170, no 1, p. 106-119Article in journal (Refereed)
    Abstract [en]

    The compound distribution is of interest for the study of production/inventory problems, since it provides a flexible description of the stochastic properties of the system. However, due to the difficulties involved in obtaining analytical results for the compound distribution, studies are usually limited to searching for a good approximation by replacing a more complex model with a simpler one applying only the first few moments as parameters. This paper presents general closed form formulae for the moments and central moments of any order of a compound distribution made up of non-negative stochastic variables. The Laplace and z-transform methods play an important role in this study. The importance of taking into consideration higher-order moments, when computing a safety factor for inventory control, is illustrated in a numerical example. © 2004 Elsevier B.V. All rights reserved.

  • 44.
    Grubbström, Robert W
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Tang, Ou
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    The space of solution alternatives in the optimal lotsizing problem for general assembly systems applying MRP theory2012In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 140, no 2, p. 765-777Article in journal (Refereed)
    Abstract [en]

    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). less thanbrgreater than less thanbrgreater thanIn a recent paper (Grubbstrom 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. less thanbrgreater than less thanbrgreater thanThis 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.

  • 45.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Production Economics. Linköping University, The Institute of Technology.
    Wang, Zhiping
    Linköping University, Department of Production Economics. Linköping University, The Institute of Technology.
    A stochastic model of multi-level/multi-stage capacity-constrained production–inventory systems2003In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 81-82, p. 483-494Article in journal (Refereed)
    Abstract [en]

    A great deal of research has been done on capacity-constrained production–inventory systems, most of which concerns deterministic demand situations and single-product systems. In this paper we present a model of a multi-level capacity-constrained system when external demand is stochastic. Unlike the traditional total cost objective, adopted in the vast majority of capacity-constrained production–inventory models, the (expected) Net Present Value is here used as the objective function. Dynamic programming is chosen as the solution procedure. Numerical examples are given to explain the model and to illustrate features when changing available capacity.

    The Laplace transform together with input–output analysis are employed as tools to construct the model. This approach has been used in previous research to formulate a theoretical base for Material Requirements Planning (MRP) systems.

    The paper provides a further argument for the use of transforms in combination with matrix representations of product structures and capacity requirements, and it extends previous theory in the direction of capacity considerations combined with uncertainty in external demand. Dynamic programming is also shown to be a practical method for the multi-stage optimisation involved.

    The numerical examples further illustrate, for instance, the natural propensity for subordinate items to be lot sized in a more lumpy way than their parents, and also how the marginal benefit of capacity increments follows the law of diminishing returns. Also comparisons are made with solutions from the deterministic equivalence model, using average demand as a proxy.

  • 46.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Production Economics. Linköping University, The Institute of Technology.
    Wang, Zhiping
    Linköping University, Department of Production Economics. Linköping University, The Institute of Technology.
    Ideas for introducing capacity planning into MRP applying input-output analysis and Laplace transforms2001In: Promet - Traffic - Traffico, ISSN 0353-5320, Vol. 13, no 6, p. 371-377Article in journal (Refereed)
    Abstract [en]

    Laplace transform and input-output analysis have been used to formulate a theoretical basis for Material Requirements Planning (MRP) system. In this paper, we will formulate a model for capacity-constrained production-inventory system applying Laplace transform and input-output analysis, which is different from the classical method of handling the capacity problem.

  • 47.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Production Economics. Linköping University, The Institute of Technology.
    Wang, Zhiping
    Linköping University, Department of Production Economics. Linköping University, The Institute of Technology.
    Introducing capacity limitations into multi-level, multi-stage production-inventory systems applying the input-output/Laplace transform approach2000In: International Journal of Production Research, ISSN 0020-7543, E-ISSN 1366-588X, Vol. 38, no 17, p. 4227-4234Article in journal (Refereed)
    Abstract [en]

    The Laplace transform and Input-Output Analysis have been used to formulate a theoretical basis for Material Requirements Planning (MRP). In this paper, as a first step to incorporating capacity limitations into this theory, we introduce alternative formulations of a model for capacity-constrained production-inventory systems in a deterministic environment applying the same approach. We focus our attention on the way in which the balance equations constraining the system need to be modified. A numerical example is given to explain the model.

  • 48.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Production Economics. Linköping University, The Institute of Technology.
    Wang, Zhiping
    Linköping University, Department of Production Economics. Linköping University, The Institute of Technology.
    Modelling capacity-constrained production-inventory systems: a review2000In: Proceedings of the 11th International Working Seminar on Production Economics, Vol. 1, 2000, p. 99-105Conference paper (Refereed)
    Abstract [en]

    This paper presents a survey of the current literature on capacity-constrained production-inventory problems in the MRP context. Research work within both the deterministic and stochastic environments are summarised. Certain aspects related to model formulation are also discussed. Our aim is to give a generalunderstanding of the capacitated lot-sizing problem rather than a comprehensive literature study. The literature covered is mostly since 1980. A basic aim is also to create a background to generalisations of theoretical developments on material requirements planning applying input-output analysis and Laplace transforms.

  • 49.
    Hvalica, Dusan
    et al.
    University of Ljubljana, Slovenia .
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Biographical-Item: In memoriam: Professor DDr Ludvik Bogataj 1949-2009 in INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS, vol 122, issue 2, pp 517-5182009Other (Other academic)
    Abstract [en]

    n/a

  • 50.
    Mercer, Alan
    et al.
    Lancaster University.
    Grubbström, Robert W.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    In memoriam: Professor Brian G. Kingsman 1939-2003 - Obituary2003Other (Other academic)
12 1 - 50 of 60
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