Erwin van der Laan

Quantitative models for reverse logistics: A review

Abstract This article surveys the recently emerged field of reverse logistics. The management of return flows induced by the various forms of reuse of products and materials in industrial production processes has received growing attention throughout this decade. Many authors have proposed quantitative models taking those changes in the logistics environment into account. However, no general framework has been suggested yet. Therefore the time seems right for a systematic overview of the issues arising in the context of reverse logistics. In this paper we subdivide the field into three main areas, namely distribution planning, inventory control, and production planning. For each of these we discuss the implications of the emerging reuse efforts, review the mathematical models proposed in the literature, and point out the areas in need of further research. Special attention is paid to differences and/or similarities with classical ‘forward’ logistics methods.

Production planning and inventory control with remanufacturing and disposal

textabstractIn this paper we consider a stochastic inventory system with production, remanufacturing, and disposal operations. Customer demands must either be fulfilled from the production of new products or by the remanufacturing of used products. Used products are either remanufactured or disposed of. To coordinate production, remanufacturing and disposal operations efficiently, we extend the PUSH and PULL strategies that Van der Laan et al. developed to control a system in which all returned products are remanufactured and no planned disposals occur. The other contributions of this paper are to indicate when and why planned disposals are economically beneficial, and to compare the PUSH-disposal strategy to the PULL-disposal strategy. In addition, we investigate the robustness of the control parameters of the PUSH- and PULL-disposal strategy over the different stages of a product life-cycle.

An (s, Q) inventory model with remanufacturing and disposal

textabstractIn this paper we analyse an (s, Q) inventory model in which used products can be remanufactured to new ones. We develop two approximations for the average costs and compare their performance with that of an approximation suggested by Muckstadt and Isaac. Next we extend the model with the option to dispose returned products and present a heuristic optimisation procedure which is checked with full enumeration.

An investigation of lead-time effects in manufacturing/remanufacturing systems under simple PUSH and PULL control strategies

In this paper we extend the PUSH and PULL control strategies defined by van der Laan et al. (E.A. van der Laan, M. Salomon, R. Dekker, Production planning and inventory control for remanufacturable durable products, Working paper 9531/A, Econometric Institute, Erasmus University Rotterdam, The Netherlands, 1995) to evaluate numerically the effects of lead-time duration and lead-time variability on total expected costs in production/inventory systems with remanufacturing. Although both strategies are non-optimal, they are relatively easy to analyse numerically and, more importantly, they are actually used in practice. The most important outcomes of the study are, that for both control strategies: (i) manufacturing lead-times have a larger influence on system costs than remanufacturing lead-times; (ii) a larger remanufacturing lead-time may sometimes result in a cost decrease; and (iii) a larger variability in the manufacturing lead-time may sometimes result in a cost decrease.

Leadtime effects and policy improvement for stochastic inventory control with remanufacturing

When returns of goods and remanufacturing options have to be taken into consideration in inventory control situations, two additional sources of complexity appear in the traditional approaches of optimizing stochastic inventory control. Firstly, due to uncertainty of returns, an additional stochastic impact has to be regarded. Secondly, with remanufacturing a second mode of supply of serviceable goods is given, so that coordination with the regular mode of procurement becomes necessary. It can be shown that under these conditions we face extremely complicated optimal control rules if the leadtimes for remanufacturing and regular procurement differ. This holds for both the structure of the control policy and the inventory information necessary for optimal stock adjustment. In this context, the meaning of the inventory position, which is well-defined in traditional inventory control, is no longer evident. In practice, in these situations usually simple (suboptimal) decision rules are applied that only use a few control parameters and additionally do not take into consideration the complexity of defining the inventory position appropriately. For such a simple (4-parameter) control rule it is shown that by determining the inventory position in a proper way the performance of the policy can be improved considerably. This effect is equivalent to using the remanufacturing leadtime as a decision variable which has to be fixed in an optimal way.

Product remanufacturing and disposal: A numerical comparison of alternative control strategies

In this paper we consider a single-product, single-echelon production and inventory system with product returns, product remanufacturing, and product disposal. For this system we consider three different procurement and inventory control strategies i.e., the (sp, Qp, sd,N) strategy, the (sp, Qp, sd) strategy, and the (sp, Qp, N) strategy. The control parameters in these strategies relate to the inventory position at which an outside procurement order is placed (sp), the inventory position at which returned products are disposed of (sd), the outside procurement order quantity (Qp), and the capacity of the remanufacturing facility (N). For each of the strategies we derive exact expressions of the total expected costs as functions of the control parameters. Main objective of this paper is to compare the performance of each of the alternative strategies with respect to costs, under different system conditions.

How to set the holding cost rates in average cost inventory models with reverse logistics

Among both inventory theorists and practitioners, it is common use to include an opportunity cost rate in the holding cost rate. In that way, the cost of capital can be roughly incorporated in an average cost (AC) inventory model. The traditional way for calculating the opportunity cost rate is to multiply the interest rate (or discount rate) by the marginal cost for producing/ordering an item. For single source inventory systems with only forward logistics, this method is easy to use, and leads to near-optimal policies from a discounted cash flow (DCF) point of view. For inventory systems with reverse logistics, however, the method is no longer straightforward. In this paper we compare different methods for calculating the opportunity cost rates of returned non-serviceable, remanufactured, and manufactured items. We discuss which method gives the best results for a specific reverse logistics model with setup costs, non-zero lead times, and disposal.

On the non-optimality of the average cost approach for inventory models with remanufacturing

When analyzing average cost (AC) inventory models, it is common use to add the discount rate times the capital tied up in a product, to the out-of-pocket holding cost rate. This way, capital costs are (roughly) included. In this paper we show that such a method may not always be appropriate for reverse logistics inventory models with both remanufacturing and disposal of returned products.

Inventory control with product returns: the impact of imperfect information

Product returns are characterized by considerable uncertainty on time and quantity. In the literature on inventory management for product return environments best forecasts of future returns are associated with methods that use the most information regarding product return history. In practice, however, data is often scarce and unreliable, while forecasts based on historical data, reliable or not, are never perfect. In this paper we therefore investigate the impact of imperfect information with respect to the return process on inventory management performance. We show that in the case of imperfect information the most informed method does not necessarily lead to best performance. The results have relevant implications regarding investments in product return information systems.

Managing Product Returns: The Role of Forecasting

In this article, we discuss ways of actively influencing product returns and we review data-driven methods for forecasting return flows that exploit the fact that future returns are a function of past sales. In particular we assess the value of return forecasting at an operational level, specifically inventory control. We conclude with implications for supply chain management.