W. van den Heuvel (Wilco)
http://repub.eur.nl/ppl/1510/
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http://repub.eur.nl/
RePub, Erasmus University RepositoryEconomic lot-sizing with remanufacturing: Complexity and efficient formulations
http://repub.eur.nl/pub/76484/
Thu, 02 Jan 2014 00:00:01 GMT<div>M.R. Helmrich</div><div>R.F. Jans</div><div>W. van den Heuvel</div><div>A.P.M. Wagelmans</div>
Within the framework of reverse logistics, the classic economic lot-sizing problem has been extended with a remanufacturing option. In this extended problem, known quantities of used products are returned from customers in each period. These returned products can be remanufactured so that they are as good as new. Customer demand can then be fulfilled from both newly produced and remanufactured items. In each period, one can choose to set up a process to remanufacture returned products or produce new items. These processes can have separate or joint setup costs. In this article, it is shown that both variants are NP-hard. Furthermore, several alternative mixed-integer programming (MIP) formulations of both problems are proposed and compared. Because "natural" lot-sizing formulations provide weak lower bounds, tighter formulations are proposed, namely, shortest path formulations, a partial shortest path formulation, and an adaptation of the (l, S,WW) inequalities used in the classic problem with Wagner-Whitin costs. Their efficiency is tested on a large number of test data sets and it is found that, for both problem variants, a (partial) shortest path-type formulation performs better than the natural formulation, in terms of both the linear programming relaxation and MIP computation times. Moreover, this improvement can be substantial. CopyrightThe economic lot-sizing problem with lost sales and bounded inventory
http://repub.eur.nl/pub/40216/
Thu, 01 Aug 2013 00:00:01 GMT<div>H.C. Hwang</div><div>W. van den Heuvel</div><div>A.P.M. Wagelmans</div>
This article considers an economic lot-sizing problem with lost sales and bounded inventory. The structural properties of optimal solutions under different assumptions on the cost functions are proved. Using these properties, new and improved algorithms for the problem are presented. Specifically, the first polynomial algorithm for the general lot-sizing problem with lost sales and bounded inventory is presented, and it is shown that the complexity can be reduced considerably in the special case of non-increasing lost sales costs. Moreover, with the additional assumption that there is no speculative motive for holding inventory, an existing result is improved by providing a linear time algorithm. A note on "the economic lot sizing problem with inventory bounds"
http://repub.eur.nl/pub/76586/
Fri, 16 Nov 2012 00:00:01 GMT<div>M. Önal</div><div>W. van den Heuvel</div><div>T. Liu</div>
In a recent paper, Liu [3] considers the lot-sizing problem with lower and upper bounds on the inventory levels. He proposes an O( n2) algorithm for the general problem, and an O(n) algorithm for the special case with non-speculative motives. We show that neither of the algorithms provides an optimal solution in general. Furthermore, we propose a fix for the former algorithm that maintains the O( n2) complexity.Integrated market selection and production planning: Complexity and solution approaches
http://repub.eur.nl/pub/23233/
Sat, 01 Sep 2012 00:00:01 GMT<div>W. van den Heuvel</div><div>O.E. Kundakcioglu</div><div>J. Geunes</div><div>H.E. Romeijn</div><div>T.C. Sharkey</div><div>A.P.M. Wagelmans</div>
Emphasis on effective demand management is becoming increasingly recognized as an important factor in operations performance. Operations models that account for supply costs and constraints as well as a supplier's ability to influence demand characteristics can lead to an improved match between supply and demand. This paper presents a class of optimization models that allow a supplier to select, from a set of potential markets, those markets that provide maximum profit when production/procurement economies of scale exist in the supply process. The resulting optimization problem we study possesses an interesting structure and we show that although the general problem is NP -complete, a number of relevant and practical special cases can be solved in polynomial time. We also provide a computationally very efficient and intuitively attractive heuristic solution procedure that performs extremely well on a large number of test instances. The Economic Lot-Sizing Problem with an Emission Constraint
http://repub.eur.nl/pub/37650/
Thu, 03 May 2012 00:00:01 GMT<div>M. Retel Helmrich</div><div>R.F. Jans</div><div>W. van den Heuvel</div><div>A.P.M. Wagelmans</div>
We consider a generalisation of the lot-sizing problem that includes an emission constraint. Besides the usual financial costs, there are emissions associated with production, keeping inventory and setting up the production process. Because the constraint on the emissions can be seen as a constraint on an alternative cost function, there is also a clear link with bi-objective optimisation. We show that lot-sizing with an emission constraint is NP-hard and propose several solution methods. First, we present a Lagrangian heuristic to provide a feasible solution and lower bound for the problem. For costs and emissions for which the zero inventory property is satisfied, we give a pseudo-polynomial algorithm, which can also be used to identify the complete Pareto frontier of the bi-objective lot-sizing problem. Furthermore, we present a fully polynomial time approximation scheme (FPTAS) for such costs and emissions and extend it to deal with general costs and emissions. Special attention is paid to an efficient implementation with an improved rounding technique to reduce the a posteriori gap, and a combination of the FPTASes and a heuristic lower bound. Extensive computational tests show that the Lagrangian heuristic gives solutions that are very close to the optimum. Moreover, the FPTASes have a much better performance in terms of their gap than the a priori imposed performance, and, especially if the heuristic’s lower bound is used, they are very fast.Improved algorithms for a lot-sizing problem with inventory bounds and backlogging
http://repub.eur.nl/pub/72034/
Sun, 01 Apr 2012 00:00:01 GMT<div>H.C. Hwang</div><div>W. van den Heuvel</div>
This article considers a dynamic lot-sizing problem with storage capacity limitation in which backlogging is allowed. For general concave procurement and inventory costs, we present an O(T 2) dynamic programming algorithm where T is the length of the planning horizon. Furthermore, in case of a fixed-charge cost structure without speculative motives, we show that the problem can be solved in O(T) time. By carefully choosing decompositions of the problems, we can use classical results like an efficient matrix searching algorithm and geometric techniques to achieve the results.Note on "An efficient approach for solving the lot-sizing problem with time-varying storage capacities"
http://repub.eur.nl/pub/30665/
Sat, 01 Oct 2011 00:00:01 GMT<div>W. van den Heuvel</div><div>J.M. Gutierrez</div><div>H.C. Hwang</div>
In a recent paper Gutierrez et al. (2008) show that the lot-sizing problem with inventory bounds can be solved in O(T log T) time. In this note we show that their algorithm does not lead to an optimal solution in general.Improved Algorithms for a Lot-Sizing Problem with Inventory Bounds and Backlogging
http://repub.eur.nl/pub/18591/
Mon, 29 Mar 2010 00:00:01 GMT<div>H.C. Hwang</div><div>W. van den Heuvel</div>
This paper considers a dynamic lot-sizing problem with storage capacity limitation in which backlogging
is allowed. For general concave production and inventory costs, we present an O(T2) dynamic
programming algorithm where is the length of the planning horizon. Furthermore, for
fixed-charge and nonspeculative costs, we provide O(Tlog T) and O(T) algorithms, respectively.
This paper therefore concludes that the time complexity to solve the bounded inventory lot-sizing
problem with backlogging is the same as the complexity to solve the uncapacitated lot-sizing
problem for the commonly used cost structuresWorst-case analysis for a general class of online lot-sizing heuristics
http://repub.eur.nl/pub/19322/
Fri, 01 Jan 2010 00:00:01 GMT<div>W. van den Heuvel</div><div>A.P.M. Wagelmans</div>
In this paper, we analyze the worst-case performance of heuristics for the classical economic lot-sizing problem with time-invariant cost parameters. We consider a general class of online heuristics that is often applied in a rolling-horizon environment. We develop a procedure to systematically construct worst-case instances for a fixed time horizon and use it to derive worst-case problem instances for an infinite time horizon. Our analysis shows that any online heuristic has a worst-case ratio of at least 2.A holding cost bound for the economic lot-sizing problem with time-invariant cost parameters
http://repub.eur.nl/pub/18357/
Sun, 01 Mar 2009 00:00:01 GMT<div>W. van den Heuvel</div><div>A.P.M. Wagelmans</div>
We show that in an optimal solution of the economic lot-sizing problem the total holding cost in an order interval is bounded from above by a quantity proportional to the setup cost and the logarithm of the number of periods in the interval. We present two applications of this result.Four equivalent lot-sizing models
http://repub.eur.nl/pub/14361/
Tue, 01 Jul 2008 00:00:01 GMT<div>W. van den Heuvel</div><div>A.P.M. Wagelmans</div>
We study the following lot-sizing models that recently appeared in the literature: a lot-sizing model with a remanufacturing option, a lot-sizing model with production time windows, and a lot-sizing model with cumulative capacities. We show the equivalence of these models with a classical model: the lot-sizing model with inventory bounds.Worst case analysis for a general class of on-line lot-sizing heuristics.
http://repub.eur.nl/pub/10859/
Wed, 31 Oct 2007 00:00:01 GMT<div>W. van den Heuvel</div><div>A.P.M. Wagelmans</div>
In this paper we analyze the worst case performance of heuristics for the classical economic lot-sizing problem with time-invariant cost parameters. We consider a general class of on-line heuristics that is often applied in a rolling horizon environment. We develop a procedure to systematically construct worst case instances for a fixed time horizon and use it to derive worst case problem instances for an infinite time horizon. Our analysis shows that any on-line heuristic has a worst case ratio of at least 2. Furthermore, we show how the results can be used to construct heuristics with optimal worst case performance for small model horizons.Integrated market selection and production planning: complexity and solution approaches
http://repub.eur.nl/pub/10776/
Mon, 01 Oct 2007 00:00:01 GMT<div>W. van den Heuvel</div><div>H.E. Romeijn</div><div>A.P.M. Wagelmans</div><div>O.E. Kundakcioglu</div>
Emphasis on effective demand management is becoming increasingly recognized as an important factor in operations performance. Operations models that account for supply costs and constraints as well as a supplier's ability to in°uence demand characteristics can lead to an improved match between supply and demand. This paper presents a new class of optimization models that allow a supplier to select, from a set of potential markets, those markets that provide maximum profit when production/procurement economies of scale exist in the supply process. The resulting optimization problem we study possesses an interesting structure and we show that although the general problem is NP-complete, a number of relevant and practical special cases can be solved in polynomial time. We also provide a computationally very effcient and intuitively attractive heuristic solution procedure that performs extremely well on a large number of test instances.Economic lot-sizing games
http://repub.eur.nl/pub/19265/
Tue, 16 Jan 2007 00:00:01 GMT<div>W. van den Heuvel</div><div>P. Blom</div><div>H.J.M. Hamers</div>
In this paper we introduce a new class of OR games: economic lot-sizing (ELS) games. There are a number of retailers that have a known demand for a fixed number of periods. To satisfy demand the retailers order products at the same manufacturer. By placing joint orders instead of individual orders, costs can be reduced and a cooperative game arises. In this paper we show that ELS games are balanced. Furthermore, we show that two special classes of ELS games are concave.Four equivalent lot-sizing models
http://repub.eur.nl/pub/10452/
Mon, 01 Jan 2007 00:00:01 GMT<div>W. van den Heuvel</div><div>A.P.M. Wagelmans</div>
We study the following lot-sizing models that recently appeared in the literature: a lot-sizing model with a
remanufacturing option, a lot-sizing model with production time windows, and a lot-sizing model with cumulative
capacities. We show the equivalence of these models with a classical model: the lot-sizing model with inventory bounds.The Economic Lot-Sizing Problem: New Results and Extensions
http://repub.eur.nl/pub/8193/
Thu, 07 Dec 2006 00:00:01 GMT<div>W. van den Heuvel</div>
Een manier waarop bedrijven kosten kunnen reduceren is efficiënte productieplanning. Het centrale thema in dit proefschrift is een klassiek productieplanningsprobleem: het economische lot-sizing (ELS) probleem. Het doel in dit probleem is om aan de gegeven vraag voor een eindige, discrete planningshorizon te voldoen en de totale setup-, productie- en voorraadkosten te minimaliseren. We bekijken zowel aspecten rondom het klassieke probleem als uitbreidingen van het probleem. Ten eerste onderzoeken we de verhouding tussen de voorraadkosten en de setupkosten in een optimale oplossing. Vervolgens voeren we een worst-case analyse uit op een brede klasse van on-line heuristieken.
Omdat het klassieke probleem relatief eenvoudig is, bekijken we ook een aantal uitbreidingen. We zijn geïnteresseerd of er efficiënte algoritmen bestaan voor deze uitbreidingen. Eerst bekijken we een integraal model waarin de vaststelling van de verkoopprijs en het maken van het productieschema simultaan plaatsvindt. We beschouwen zowel een model met een constante prijs als een model met verschillende prijzen over de tijd.
Verder breiden we het ELS model uit met een mogelijkheid tot herproductie. We veronderstellen dat er een gegeven hoeveelheid producten terugkomt van de klant in elke periode. Deze producten kunnen geherproduceerd worden om aan de vraag te voldoen (naast reguliere productie). We ontwikkelen algoritmen en leiden complexiteitsresultaten af voor twee varianten van het probleem. In de ene variant zijn er gezamenlijke setupkosten voor productie en herproductie (in het geval van een gezamenlijke productielijn) en in de andere variant zijn er aparte setupkosten (in het geval van afzonderlijke productielijnen).One way for firms to reduce cost is efficient production planning. The main theme in this thesis is a classical production planning problem: the economic lot-sizing (ELS) problem. The objective of this problem is to find a production plan that satisfies the given demand for a finite, discrete planning horizon, and minimizes the total setup, production and holding costs. We study aspects of the classical problem as well as extensions of this problem.
In the first part of the thesis we consider the ELS model with time-invariant cost parameters. We analyze properties of an optimal solution and, in particular, we are interested in the proportion of holding cost and setup cost in an optimal solution. Furthermore, we perform a worst case analysis on a broad class of on-line heuristics for the problem.
Because the classical model is relatively simple, we also consider extensions of the model. We are interested whether there exist algorithms to solve the extensions efficiently. In the first extension we incorporate pricing decisions in the ELS model. The problem is now to find optimal price(s) and an optimal production plan simultaneously. We consider models with variable prices and a constant price over time.
Furthermore, we extend the ELS model with a remanufacturing option. It is assumed that a known quantity of products returns from the customer in each period and those returned products can be remanufactured to satisfy demand (besides regular manufacturing). We derive algorithms and complexity results for models with a joint setup cost for manufacturing and remanufacturing (in case of a single production line) and a separate setup cost (in case of separate production lines).Wilco van den Heuvel (1979) obtained his master’s degree in
Econometrics and Operations Research with honors from Erasmus
University Rotterdam in 2002. In the same year he started
with his PhD research. His main interests are in Operations
Research and in particular in (extensions of) the classical economic
lot-sizing problem. His research resulted in five papers
published in Computers & Operations Research, European Jour-
nal of Operational Research, International Journal of Production
Research and Operations Research Letters. Finally, in 2005 he
was awarded the Chorafas Prize, a prize to stimulate young researchers.An efficient dynamic programming algorithm for a special case of the capacitated lot-sizing problem
http://repub.eur.nl/pub/14390/
Fri, 01 Dec 2006 00:00:01 GMT<div>W. van den Heuvel</div><div>A.P.M. Wagelmans</div>
In this paper we consider the capacitated lot-sizing problem (CLSP) with linear costs. It is known that this problem is NP-hard, but there exist special cases that can be solved in polynomial time. We derive a new O(T2) algorithm for the CLSP with non-increasing setup costs, general holding costs, non-increasing production costs and non-decreasing capacities over time, where T is the length of the model horizon. We show that in every iteration we do not consider more candidate solutions than the O(T2) algorithm proposed by [Chung and Lin, 1988. Management Science 34, 420–6]. We also develop a variant of our algorithm that is more efficient in the case of relatively large capacities. Numerical tests show the superior performance of our algorithms compared to the algorithm of [Chung and Lin, 1988. Management Science 34, 420–6].Dynamic lot sizing with product returns and remanufacturing
http://repub.eur.nl/pub/65260/
Sun, 15 Oct 2006 00:00:01 GMT<div>R.H. Teunter</div><div>Z.P. Bayindir</div><div>W. van den Heuvel</div>
A polynomial time algorithm for a deterministic joint pricing and inventory model
http://repub.eur.nl/pub/14388/
Sun, 16 Apr 2006 00:00:01 GMT<div>W. van den Heuvel</div><div>A.P.M. Wagelmans</div>
In this paper we consider the uncapacitated economic lot-size model, where demand is a deterministic function of price. In the model a single price need to be set for all periods. The objective is to find an optimal price and ordering decisions simultaneously. In 1973 Kunreuther and Schrage proposed an heuristic algorithm to solve this problem. The contribution of our paper is twofold. First, we derive an exact algorithm to determine the optimal price and lot-sizing decisions. Moreover, we show that our algorithm boils down to solving a number of lot-sizing problems that is quadratic in the number of periods, i.e., the problem can be solved in polynomial time.A comparison of methods for lot-sizing in a rolling horizon environment
http://repub.eur.nl/pub/14395/
Thu, 01 Sep 2005 00:00:01 GMT<div>W. van den Heuvel</div><div>A.P.M. Wagelmans</div>
We argue that the superior performance of a recent method for lot-sizing in a rolling horizon scheme is to a large extent due to the assumption that quite accurate future demand estimates are available. We show that other methods, including a straightforward one, can use this information just as effectively.