http://repub.eur.nl/res/aut/968/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/15482/ 2008-07-01T00:00:00Z We analyze the classical inventory model with backordering, where the inventory position is controlled by an order level, order quantity policy. The cost for a backorder contains a fixed and a time-proportional component. Demand can be driven by any discrete process. Order lead times may be stochastic and orders are allowed to cross. The optimality condition for the order-level, given some predetermined order quantity, is derived using an easy and insightful marginal cost analysis. It is further shown how this condition can easily be (approximately) rewritten in well-known forms for special cases. http://repub.eur.nl/res/pub/14822/ 2006-12-01T00:00:00Z Inventory policies for joint remanufacturing and manufacturing have recently received much attention. Most efforts, though, were related to (optimal) policy structures and numerical optimization, rather than closed form expressions for calculating near optimal policy parameters. The focus of this paper is on the latter. We analyze an inventory system with unit product returns and demands where remanufacturing is the cheaper alternative for manufacturing. Manufacturing is also needed, however, since there are less returns than demands. The cost structure consists of setup costs, holding costs, and backorder costs. Manufacturing and remanufacturing orders have non-zero lead times. To control the system we use certain extensions of the familiar (s, Q) policy, called push and pull remanufacturing policies. For all policies we present simple, closed form formulae for approximating the optimal policy parameters under a cost minimization objective. In an extensive numerical study we show that the proposed formulae lead to near-optimal policy parameters. http://repub.eur.nl/res/pub/14821/ 2006-01-01T00:00:00Z We explore the value of information (VOI) in the context of a firm that faces uncertainty with respect to demand, product return, and product recovery (yield). The operational decision of interest in matching supply with demand is the quantity of new product to order. Our objective is to evaluate the VOI from reducing one or more types of uncertainties, where value is measured by the reduction in total expected holding and shortage costs. We start with a single period model with normally distributed demands and returns, and restrict the analysis to the value of full information (VOFI) on one or more types of uncertainty. We develop estimators that are predictive of the value and sensitivity of (combinations of) different information types. We find that there is no dominance in value amongst the different types of information, and that there is an additional pay-off from investing in more than one type. We then extend our analysis to the multi-period case, where returns in a period are correlated with demands in the previous period, and study the value of partial information (VOPI) as well as full information. We demonstrate that our results from the single period model (adapted for VOPI) carry-over exactly. Furthermore, a comparison with uniformly distributed demand and return show that these results are robust with respect to distributional assumptions. http://repub.eur.nl/res/pub/11888/ 2005-09-18T00:00:00Z We study the case of a catalogue/internet mail order retailer selling style goods and receiving large numbers of commercial returns. Returned products arriving before the end of the selling season can be resold if there is sufficient demand. A single order is placed before the season starts. Excess inventory at the end of the season is salvaged and all demands not met directly are lost. Since little historical information is available, it is impossible to determine the shape of the distribution of demand. Therefore, we analyze the distribution-free newsboy problem with returns, in which only the mean and variance of demand are assumed to be known. We derive a simple closed-form expression for the distribution-free order quantity, which we compare to the optimal order quantities when gross demand is assumed to be normal, lognormal or uniform. We find that the distribution-free order rule performs well when the coefficient of variation (CV) is at most 0.5, but is far from optimal when the CV is large. http://repub.eur.nl/res/pub/6557/ 2005-04-18T00:00:00Z We address the dynamic lot sizing problem for systems with product returns. The demand and return amounts are deterministic over the finite planning horizon. Demands can be satisfied by manufactured/procured new items, but also by remanufactured returned items. The objective is to determine those lot sizes for manufacturing and remanufacturing that minimize the total cost composed of holding cost for returns and serviceable products and set-ups costs. Two different set-up cost schemes are considered; there is either a joint set-up cost for manufacturing and remanufacturing (single production line) or separate set-up costs (dedicated production lines). For the joint set-up cost case, we present an exact, polynomial time dynamic programming algorithm. For both cases, we propose a number of heuristics and test them in an extensive numerical study. http://repub.eur.nl/res/pub/2006/ 2005-03-31T00:00:00Z We consider a joint manufacturing / remanufacturing environment with remanufacturing yield loss. Demand and return follow independent stationary Poisson processes. Returns can be disposed off upon arrival to the system. Manufacturing and remanufacturing operations performed in the same facility at exponential rates. Yield information becomes available after remanufacturing. Demands that are not directly satisfied are lost. We investigate what inventories to consider when making production and disposal decisions, with the objective of maximizing the long-run average expected profit. Four different policies are compared that base disposal decisions on either the local (returns) inventory or the global inventory, and production decisions on either the local (serviceable) inventory or the global inventory. By modelling the system as a Markov process, expressions for the profit associated with each policy are derived. An extensive numerical study shows that it is always optimal to base disposal decisions on the local inventory and production decisions on the global inventory within the parameter sets considered. A sensitivity analysis reveals further insights. http://repub.eur.nl/res/pub/1830/ 2004-12-20T00:00:00Z Control of spare parts is very difficult as demands can be very low (once in a few years is no exception), while the consequences of a stockout can be severe. While in the past many companies choose to have very large spares inventories, one now observe trends in areas with good transportation connections to keep spare parts at the suppliers. Hence it is very important to make a good selection of which spare parts to stock at the start-up of new plants. To this end Shell Global Solutions has developed an electronic decision tool, called E-SPIR. In this report we analyse the decision rules used in it. We consider stockout penalties and advise to use criticality classifications instead. Furthermore, we investigate minimum stock levels, demand distributions and order quantities. http://repub.eur.nl/res/pub/1786/ 2004-10-29T00:00:00Z Inventory policies for joint remanufacturing and manufacturing have recently received much attention. Most efforts, though, were related to (optimal) policy structures and numerical optimization, rather than closed form expressions for calculating near optimal policy parameters. The focus of this paper is on the latter. We analyze an inventory system with unit product returns and demands where remanufacturing is the cheaper alternative for manufacturing. Manufacturing is also needed, however, since there are less returns than demands. The cost structure consists of setup costs, holding costs, and backorder costs. Manufacturing and remanufacturing orders have non-zero lead times. To control the system we use certain extensions of the familiar (s,Q) policy, called push and pull remanufacturing policies. For all policies we present simple, closed form formulae for approximating the optimal policy parameters under a cost minimization objective. In an extensive numerical study we show that the proposed formulae lead to near-optimal policy parameters. http://repub.eur.nl/res/pub/1513/ 2004-08-19T00:00:00Z Inventory policies for joint remanufacturing and manufacturing have recently received much attention. Most efforts, though, were related to (optimal) policy structures and numerical optimization, rather than closed form expressions for calculating near optimal policy parameters. The focus of this paper is on the latter. We analyze an inventory system with unit product returns and demands where remanufacturing is the cheaper alternative for manufacturing. Manufacturing is also needed, however, since there are less returns than demands. The cost structure consists of setup costs, holding costs, and backorder costs. Manufacturing and remanufacturing orders have non-zero lead times. To control the system we use certain extensions of the familiar (s,Q) policy, called push and pull remanufacturing policies. For all policies we present simple, closed form formulae for approximating the optimal policy parameters under a cost minimization objective. In an extensive numerical study we show that the proposed formulae lead to near-optimal policy parameters. http://repub.eur.nl/res/pub/1447/ 2004-08-06T00:00:00Z We explore the value of information in the context of a remanufacturer that faces uncertainty with respect to demand, product return, and product recovery (yield loss). We assume a single period model in which the operational decision of interest is the quantity of new product to order. Our objective is to evaluate the absolute and relative value of the different types of information that such a firm may choose to invest in order to reduce the uncertainty it experiences in matching supply with demand. The different types of information include demand, return, and yield loss. Our results are extensive and reveal that the value for any specific type of information depends both on the overall level of uncertainty and the level of uncertainty that is attributed to the information for which it explains. We develop and test a theoretical model that is predictive of 1) the value of each type of information, 2) the conditions that give rise to the value for each type of information, and 3) the relative value for each type of information. http://repub.eur.nl/res/pub/14836/ 2004-05-01T00:00:00Z We describe hybrid manufacturing/remanufacturing systems with a long lead time for manufacturing and a short lead time for remanufacturing. We review the classes of inventory strategies for hybrid systems in the literature. These are all based on equal lead times. For systems with slow manufacturing and fast remanufacturing, we propose a new class. An extensive numerical experiment shows that the optimal strategy in the new class almost always performs better and often much better than the optimal strategies in all other classes. http://repub.eur.nl/res/pub/1198/ 2004-03-19T00:00:00Z Price promotions induce consumers to purchase higher-than-usual quantities, resulting in higher stocks that lead to increased consumption. We show for a stylized model with a single shop and a single loyal customer that because of this stockpiling effect, promotions can be profitable even if they do not attract extra customers. http://repub.eur.nl/res/pub/1195/ 2004-03-18T00:00:00Z We present a stochastic dynamic programming algorithm for determining the optimal disassembly and recovery strategy, given the disassembly tree, the process dependent quality distributions of assemblies, and the quality dependent recovery options and associated profits for assemblies. This algorithm generalizes the one proposed by Krikke et al. \\cite{Krikke98} in two ways. First, there can be multiple disassembly processes. Second, partial disassembly is allowed. Both generalizations are important for practise. http://repub.eur.nl/res/pub/1184/ 2004-03-09T00:00:00Z Khouja and Park (Omega 31, 539-545, 2003) analyze the problem of optimizing the lot size under continuous price decrease. They show that the classic EOQ formula can lead to far from optimal solutions and develop an alternative lot size formula using the software package Mathematica. This formula is more exact, but also more complicated. In this note, we study the net present value formulation of the model, and thereby gain an insight that leads to the proposal of a modified EOQ formula. In an extensive numerical experiment, we show that it leads to nearly optimal solutions. It is therefore a good alternative to the formula developed by Khouja and Park, especially if mathematical complexity may hamper implementation. http://repub.eur.nl/res/pub/975/ 2003-10-17T00:00:00Z We study the case of a catalogue/internet mail order retailer selling seasonal products and receiving large numbers of commercial returns. Returned products arriving before the end of the selling season can be resold if there is sufficient demand. A single order is placed before the season starts. Excess inventory at the end of the season is salvaged and all demands not met directly are lost. Since little historical information is available, it is impossible to determine the shape of the distribution of demand. Therefore, we analyze the distribution-free newsboy problem with returns, in which only the mean and variance of demand are assumed to be known. We derive a simple closed-form expression for the distribution-free order quantity, which we compare to the optimal order quantities when gross demand is assumed to be normal, lognormal or uniform. We find that the distribution-free order rule performs well in most realistic cases. http://repub.eur.nl/res/pub/903/ 2003-08-07T00:00:00Z This paper presents the results of a case study in a batch production facility for biological vaccines. The problem considered is that of finding the best bottling strategy for produced batches. A batch can be bottled directly after production, after positive intermediate test results, or after positive final test results. Strategies that start the bottling process quickly after production, have the advantages of a low capacity requirement for production tanks and of a small throughput time if all test results are positive. However, a production batch can only be reworked as long as it has not been bottled. So fast bottling reduces the possibilities for rework and therefore reduces the production yield. We present performance measures for comparing the different strategies and derive closed-form expressions for them. We illustrate the results obtained for the considered case. http://repub.eur.nl/res/pub/905/ 2003-08-07T00:00:00Z The repair kit problem is that of finding the optimal set of parts in the kit of a repairman. An important aspect of this problem, in many real-life situations, is that several job-sites are visited before a kit is restocked. In this paper, we present two heuristics for solving the multiple-job repair kit problem. Both heuristics can be used to determine a solution under the service-objective (minimal holding cost for a required job-fill rate) as well as the cost-objective (minimal expected total cost, including a penalty cost for each `broken' job). The `Job Heuristic (JH)' almost always determines the exact optimal solution, as is shown in an extensive numerical experiment. However, it can not (easily) be used in cases where several parts of the same type may be needed on a job, or part failures are dependent, or the number of jobs in a tour varies. The `Part Heuristic (PH)' is simpler and easy to use in these cases also. In fact, it can be applied in a spreadsheet software package, as we illustrate. The numerical experiments show that it s leads to near-optimal solutions (average `cost error' of less than 0.1 per cent). Therefore, the PH is an excellent method for solving repair kit problems in practise. http://repub.eur.nl/res/pub/906/ 2003-08-07T00:00:00Z We analyze a newsboy problem with resalable returns. A single order is placed before the selling season starts. Purchased products may be returned by the customer for a full refund within a certain time interval. Returned products are resalable, provided they arrive back before the end of the season and are undamaged. Products remaining at the end of the season are salvaged. All demands not met directly are lost. We derive a simple closed-form equation that determines the optimal order quantity given the demand distribution, the probability that a sold product is returned, and all relevant revenues and costs. We illustrate its use with real data from a large catalogue/internet mail order retailer. http://repub.eur.nl/res/pub/907/ 2003-08-07T00:00:00Z We study inventory systems with product recovery. Recovered items are as-good-as-new and satisfy the same demands as new items. The demand rate and return fraction are deterministic. The relevant costs are those for ordering recovery lots, for ordering production lots, for holding recoverable items in stock, and for holding new/recovered items in stock. We derive simple formulae that determine the optimal lot-sizes for the production/procurement of new items and for the recovery of returned items. These formulae are valid for finite and infinite production rates as well as finite and infinite recovery rates, and therefore more general than those in the literature. Moreover, the method of derivation is easy and insightful. http://repub.eur.nl/res/pub/908/ 2003-08-07T00:00:00Z Valuation of inventories has different purposes, in particular accounting and decision making, and it is not necessary for a firm to use the same valuation method for both purposes. In fact, it is not uncommon to use accounting books as well as management books. In this chapter, we will only consider inventory values from the perspective of decision making. More specifically, we will analyze the effect of inventory valuation on inventory control decisions (and not the corresponding financial results) for systems with product recovery. http://repub.eur.nl/res/pub/909/ 2003-08-07T00:00:00Z Schering spends considerable effort to undertake product recovery activities in pharmaceutical production. The two main recovery activities are by-product recycling and solvent reuse. The main driver for engaging in these activities is economical. Recovery leads to annual savings of approximately DM 25 million, which is about 8.5 % of the total production cost. This figure does not include additional savings due to reduced disposal quantities and additional costs due to investments in recovery equipment, of which we do not have reliable estimates. Furthermore, being engaged in recovery activities has additional benefits for Schering that are related to the reduced waste stream: production is in accordance with environmental legislation, the company builds an environmentally friendly image, and there is less strain on the environment. The downside of the recovery activities is that they complicate production and inventory planning. Especially the added complexity of production planning, resulting from cycles in the production structure, is a disadvantage.A simple MRP approach, as commonly used in practice, is no longer applicable but has to be replaced by a more sophisticated planning procedure. Schering has developed an advanced decision support system which integrates a MIP procedure. Thus it turns out that reverse logistics also is a field which creates challenges for developing advanced planning systems in order to support practical decision making. http://repub.eur.nl/res/pub/11588/ 2003-01-01T00:00:00Z The profitability of remanufacturing depends on the quantity and quality of product returns and on the demand for remanufactured products. The quantity and quality of product returns can be influenced by varying quality-dependent acquisition prices, i.e., by using product acquisition management. Demand can be influenced by varying the selling price. We develop a simple framework for determining the optimal prices and the corresponding profitability. We motivate and illustrate our framework using an application from the cellular telephone industry. http://repub.eur.nl/res/pub/231/ 2002-09-30T00:00:00Z We describe hybrid manufacturing/remanufacturing systems with a long lead time for manufacturing and a short lead time for remanufacturing. We review the classes of inventory strategies for hybrid systems in the literature. These are all based on equal lead times. For systems with slow manufacturing and fast remanufacturing, we propose a new class. An extensive numerical experiment shows that the optimal strategy in the new class almost always performs better and often much better than the optimal strategies in all other classes. http://repub.eur.nl/res/pub/14859/ 2002-09-01T00:00:00Z 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. http://repub.eur.nl/res/pub/268/ 2002-02-07T00:00:00Z We analyze a newsboy problem with resalable returns. A single order is placed before the selling season starts. Purchased products may be returned by the customer for a full refund within a certain time interval. Returned products are resalable, provided they arrive back before the end of the season and are undamaged. Products remaining at the end of the season are salvaged. All demands not met directly are lost. We derive a simple closed-form equation that determines the optimal order quantity given the demand distribution, the probability that a sold product is returned, and all relevant revenues and costs. We illustrate its use with real data from a large catalogue/internet mail order retailer. http://repub.eur.nl/res/pub/14858/ 2002-01-01T00:00:00Z While the net present value (NPV) approach is widely accepted as the right framework for studying production and inventory control systems, average cost (AC) models are more widely used. For the well known EOQ model it can be verified that (under certain conditions) the AC approach gives near optimal results, but does this also hold for more complex systems? In this paper it is argued that for more complex systems, like multi-source systems, one has to be extremely careful in applying the AC approach on intuition alone, even when these systems are deterministic. Special attention is given to a two-source inventory system with manufacturing, remanufacturing, and disposal, and it is shown that for this type of models there is a considerable gap between the AC approach and the NPV approach. http://repub.eur.nl/res/pub/1704/ 2001-11-28T00:00:00Z We consider a production line that is dedicated to a single product. Produced lots may be non-defective, reworkable defective, or non-reworkable defective. The production line switches between production and rework. After producing a fixed number (N) of lots, all reworkable defective lots are reworked. Reworkable defectives are perishable, i.e., worsen while held in stock. We assume that the rework time and the rework cost increase linear with the time that a lot is held in stock. Therefore, N should not be too large. On the other hand, N should not be too small either, since there are set-up times and costs associated with switching between production and rework. For a given N, we derive an explicit expression for the average profit (sales revenue minus costs). Using that expression, the optimal value for N can be determined numerically. http://repub.eur.nl/res/pub/1706/ 2001-11-28T00:00:00Z The profitability of remanufacturing depends on the quantity and quality of product returns and on the demand for remanufactured products. The quantity and quality of product returns can be influenced by varying quality dependent acquisition prices, i.e., by using product acquisition management. Demand can be influenced by varying the selling price. We develop a framework for determining the optimal prices and the corresponding profitability. http://repub.eur.nl/res/pub/1710/ 2001-11-28T00:00:00Z More and more supply chains emerge that include a return flow of materials. Many original equipment manufacturers are nowadays engaged in the remanufacturing business. In many process industries, production defectives and by-products are reworked. These closed-loop supply chains deserve special attention. Production planning and control in such hybrid systems is a real challenge, especially due to increased uncertainties. Even companies that are engaged in remanufacturing operations only, face more complicated planning situations than traditional manufacturing companies. We point out the main complicating characteristics in closed-loop systems with both remanufacturing and rework, and indicated the need for new or modified/extended production planning and control approaches. An overview of the existing scientific contributions is given. It appears that we only stand at the beginning of this line of research, and that many more contributions are needed and expected in the future. http://repub.eur.nl/res/pub/1712/ 2001-11-28T00:00:00Z We analyze the classical inventory model with backordering, where the inventory position is controlled by an order level, order quantity policy. The cost for a backorder contains a fixed and a time-proportional component. Demand can be driven by any discrete process. Order lead times may be stochastic and orders are allowed to cross. The optimality condition for the order-level, given some predetermined order quantity, is derived using an easy and insightful marginal cost analysis. It is further shown how this condition can easily be (approximately) rewritten in well-known forms for special cases. http://repub.eur.nl/res/pub/53/ 2000-11-06T00:00:00Z While the net present value (NPV) approach is widely accepted as the right framework for studying production and inventory control systems, average cost (AC) models are more widely used. For the well known EOQ model it can be verified that (under certain conditions) the AC approach gives near optimal results, but does this also hold for more complex systems? In this paper it is argued that for more complex systems, like multi-source systems, one has to be extremely careful in applying the AC approach on intuition alone, even when these systems are deterministic. Special attention is given to a two-source inventory system with manufacturing, remanufacturing, and disposal, and it is shown that for this type of models there is a considerable gap between the AC approach and the NPV approach. http://repub.eur.nl/res/pub/14931/ 2000-08-01T00:00:00Z 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.