On the complexity of the economic lot-sizing problem with remanufacturing options

In this paper we investigate the complexity of the economic lot-sizing problem with remanufacturing (ELSR) options. Whereas in the classical economic lot-sizing problem demand can only be satisfied by production, in the ELSR problem demand can also be satisfied by remanufacturing returned items. Although the ELSR problem can be solved efficiently for some special cases, we show that the problem is NP-hard in general, even under stationary cost parameters

The Economic Lot-Sizing Problem: New Results and Extensions

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 costWilco 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

Four equivalent lot-sizing models

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

A note on a multi-period profit maximizing model for retail supply chain management

In this note we present an efficient exact algorithm to solve the joint pricing and inventory problem for which Bhattacharjee and Ramesh (2000) proposed two heuristics. Our algorithm appears to be superior also in terms of computation time. Furthermore, we point out several mistakes in the paper by Bhattacharjee and Ramesh

A Polynomial Time Algorithm for a Deterministic Joint Pricing and Inventory Model

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 Polynomial Time Algorithm for a Deterministic Joint Pricing and Inventory Model

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 Geometric Algorithm to solve the NI/G/NI/ND Capacitated Lot-Sizing Problem in O(T^2) Time

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 backward algorithm, based on the forward algorithm by Chen et al. (1994), to solve the general CLSP. By adapting this backward algorithm, we arrive at a new O(T^2) algorithm for the CLSP with non-increasing setup cost, general holding cost, non-increasing production cost and non-decreasing capacities over time. Numerical tests show the superior performance of our algorithm compared to the algorithm proposed by Chung and Lin (1988). We also analyze why this is the case

Worst case analysis for a general class of on-line lot-sizing heuristics.

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

A Note on Ending Inventory Valuation in Multiperiod Production Scheduling

In a recent paper, Fisher et al. (2001) present a method to mitigate end-effects in lot sizing byincluding a valuation term for end-of-horizon inventory in the objective function of the short-horizon model. Computational tests show that the proposed method outperforms the Wagner-Whitin algorithm and the Silver-Meal heuristic, under several demand patterns, within arolling horizon framework. We replicate the computational tests also including a straightforward method that assumes the same knowledge about future demand as the ending inventory valuation method. Our results indicate that the superior performance reported by Fisher et al. is to a large extent due to the fact that their method assumes that quite accurate knowledge about future demand is available, whereas the traditional methods do not use any information about demand beyond the short model horizon. Moreover

Aggregate statistics on trafficker-sestination relations in the Atlantic slave trade

The available aggregated data on the Atlantic slave trade in between 1519 and 1875 concern the numbers of slaves transported by a country and the numbers of slaves who arrived at various destinations (where one of the destinations is ‘deceased’). It is however unknown how many slaves, at an aggregate level, were transported to where and by whom; that is, we know the row and column totals, but we do not known the numbers in the cells of the matrix. In this research note, we use a simple mathematical technique to fill in the void. It allows us to estimate trends in the deaths per transporting country, and also to estimate the fraction of slaves who went to the colonies of the transporting country, or to other colonies. For example, we estimate that of all the slaves who were transported by the Dutch only about 7 per cent went to Dutch colonies, whereas for the Portuguese this number is about 37 per cent