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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: 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 Recently, the instantaneous replenishment assumption has been replaced by allowing for a finite production rate, which turned the inner-corner condition into a condition of tangency between the cumulative demand staircase and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
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


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. Source


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. Source


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. Source

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