http://repub.eur.nl/res/aut/711/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/2286/ 2002-09-01T00:00:00Z In this paper an inventory model with several demand classes, prioritised according to importance, is analysed. We consider a lot-for-lot or (S - 1, S) inventory model with lost sales. For each demand class there is a critical stock level at and below which demand from that class is not satisfied from stock on hand. In this way stock is retained to meet demand from higher priority demand classes. A set of such critical levels determines the stocking policy. For Poisson demand and a generally distributed lead time, we derive expressions for the service levels for each demand class and the average total cost per unit time. Efficient solution methods for obtaining optimal policies, with and without service level constraints, are presented. Numerical experiments in which the solution methods are tested demonstrate that significant cost reductions can be achieved by distinguishing between demand classes. http://repub.eur.nl/res/pub/15417/ 2000-01-01T00:00:00Z Whenever demand for a single item can be categorised into classes of different priority, an inventory rationing policy should be considered. In this paper we analyse a continuous review (s, Q) model with lost sales and two demand classes. A so-called critical level policy is applied to ration the inventory among the two demand classes. With this policy, low-priority demand is rejected in anticipation of future high-priority demand whenever the inventory level is at or below a prespecified critical level. For Poisson demand and deterministic lead times, we present an exact formulation of the average inventory cost. A simple optimisation procedure is presented, and in a numerical study we compare the optimal rationing policy with a policy where no distinction between the demand classes is made. The benefit of the rationing policy is investigated for various cases and the results show that significant cost reductions can be obtained. http://repub.eur.nl/res/pub/15346/ 1999-10-16T00:00:00Z In most multi-item inventory systems, the ordering costs consist of a major cost and a minor cost for each item included. Applying for every individual item a cyclic inventory policy, where the cycle length is a multiple of some basic cycle time, reduces the major ordering costs. An efficient algorithm to determine the optimal policy of this type is discussed in this paper. It is shown that this algorithm can be used for deterministic multi-item inventory problems, with general cost rate functions and possibly service level constraints, of which the well-known joint replenishment problem is a special case. Some useful results in determining the optimal control parameters are derived, and worked out for piecewise linear cost rate functions. Numerical results for this case show that the algorithm significantly outperforms other solution methods, both in the quality of the solution and in the running time. http://repub.eur.nl/res/pub/1538/ 1998-12-03T00:00:00Z Whenever demand for a single item can be categorized into classes of different priority, an inventory rationing policy should be considered. In this paper we analyse a continuous review (s,Q) model with lost sales and two demand classes. A so-called critical level policy is applied to ration the inventory among the two demand classes. With this policy, low--priority demand is rejected in anticipation of future high--priority demand whenever the inventory level is at or below a prespecified critical level. For Poisson demand and deterministic lead times, we present an exact formulation of the average inventory cost. A simple optimization procedure is presented, and in a numerical study we compare the optimal rationing policy with a policy where no distinction between the demand classes is made. The benefit of the rationing policy is investigated for various cases and the results show that significant cost reductions can be obtained. http://repub.eur.nl/res/pub/1534/ 1998-11-26T00:00:00Z In this chapter we discuss inventory systems where several demand classes may be distinguished. In particular, we focus on single-location inventory systems and we analyse the use of a so-called critical level policy. With this policy some inventory is reserved for high-priority demand. A number of practical examples where several demand classes naturally arise are presented, and the implications and modelling of the critical level policy in distribution systems are discussed. Finally, an overview of the literature on inventory systems with several demand classes is given. http://repub.eur.nl/res/pub/1546/ 1998-08-13T00:00:00Z In this paper we consider a 1-warehouse, N-retailer inventory system where demand occurs at all locations. We introduce an inventory model which allows us to set different service levels for retailers and direct customer demand at the warehouse. For each retailer a critical level is defined, such that a retailer replenishment order is delivered from warehouse stock if and only if the stock level exceeds this critical level. It is assumed that retailer replenishment orders which are not satisfied from warehouse stock are delivered directly from the outside supplier, instead of being backlogged. We present an analytical upper bound on the total cost of the system, and develop a heuristic method to optimise the policy parameters. Numerical experiments indicate that our technique provides a very close approximation of the exact cost. Also, we show that differentiating among the retailers and direct customer demand can yield significant cost reductions. http://repub.eur.nl/res/pub/7788/ 1997-10-31T00:00:00Z In this paper an inventory model with several demand classes, prioritised according to importance, is analysed. We consider a lot-for-lot or (S-1,S) inventory model with lost sales. For each demand class there is a critical stock level at and below which demand from that class is not satisfied from stock on hand. In this way stock is retained to meet demand from higher priority demand classes. A set of such critical levels determines the stocking policy. For Poisson demand and a generally distributed lead time we derive expressions for the service levels for each demand class and the average total cost per unit time. Efficient solution methods for obtaining optimal policies, with and without service level constraints, are presented. Numerical experiments in which the solution methods are tested demonstrate that significant cost reductions can be achieved by distinguishing between demand classes. http://repub.eur.nl/res/pub/15259/ 1997-10-01T00:00:00Z In this paper we discuss a general framework for single component replacement models. This framework is based on the regenerative structure of these models and by using results from renewal theory a unified presentation of the discounted and average finite and infinite horizon cost models is given. Finally, some well-known replacement models are discussed, and making use of the previous results an easy derivation of their cost functions is presented. http://repub.eur.nl/res/pub/15258/ 1997-09-01T00:00:00Z In this paper we investigate the conditions under which the marginal cost approach of Refs. 1–3 holds. As observed in Ref. 4, the validity of the marginal cost approach gives rise to a useful framework of single-component maintenance optimization models, which covers almost all models used in practice. For the class of unimodal finite-valued marginal cost functions, we show that these optimization models are easy to solve. http://repub.eur.nl/res/pub/1402/ 1997-01-01T00:00:00Z In this paper we discuss a general framework for single item inventory control models. This framework is based on the regenerative structure of these models. Using results from the theory of regenerative processes a unified presentation of those models is presented. Although most of the results are already known for special cost structures this unified presentation yields us the possibility to show that the same techniques can be applied to each instance. http://repub.eur.nl/res/pub/1404/ 1997-01-01T00:00:00Z In this chapter we discuss a tactical optimisation problem that arises in a multistage distribution system where customer orders can be delivered from any stockpoint. A simple rule to allocate orders to locations is a break quantity rule, which routes large orders to higher-stage stockpoints and small orders to end-stockpoints. A so-called break quantity determines whether an order is small or large. We present a qualitative discussion on the implications of this rule for the marketing process, and a qualitative and quantitative analysis on the implications for the transportation and inventory costs. Furthermore, we present a case study for a company that implemented a break quantity rule. Finally, in the last section the main results are summarised. http://repub.eur.nl/res/pub/1405/ 1997-01-01T00:00:00Z In this paper we analyse the effect of satisfying in a different way customers with an order larger than a prespecified cutoff transaction size, in a simple newsboy setting. For compound Poisson demand with discrete order sizes, we show how to determine the expected costs and the optimal cutoff transaction size. Moreover, by approximating the distribution of the total demand during a period by the normal distribution one can determine an expression for the average cost function that depends on the cutoff transaction size only. A main advantage of this approximation is that the computational effort is much less. The quality of using the normal approximation is evaluated through a number of numerical experiments, which show that the approximative results are satisfactory. http://repub.eur.nl/res/pub/1423/ 1997-01-01T00:00:00Z In most multi-item inventory systems, the ordering costs consist of a major cost and a minor cost for each item included. Applying for every individual item a cyclic inventory policy, where the cycle length is a multiple of some basic cycle time, reduces the major ordering costs. An efficient algorithm to determine the optimal policy of this type is discussed in this paper. It is shown that this algorithm can be used for deterministic multi-item inventory problems, with general cost rate functions and possibly service level constraints, of which the well-known joint replenishment problem is a special case. Some useful results in determining the optimal control parameters are derived, and worked out for piecewise linear cost rate functions. Numerical results for this case show that the algorithm significantly outperforms other solution methods, both in the quality of the solution as in the running time. http://repub.eur.nl/res/pub/1370/ 1996-01-01T00:00:00Z In this paper we discuss a general framework for single component replacement models. This framework is based on the regenerative structure of these models and by using results from renewal theory a unified presentation of the discounted and average finite and infinite horizon cost models is given. Moreover, we present sufficient conditions for the numerator of the cost function to have a vanishing singular part. Finally, some well-known replacement models are discussed, and making use of the previous results an easy derivation of their cost functions is presented. http://repub.eur.nl/res/pub/1371/ 1996-01-01T00:00:00Z In this paper we verify the conditions under which the marginal cost approach of Berg (1980, 1995) holds. As observed by Aven and Dekker (1996) the validity of the marginal cost approach gives rise to a useful framework of single component maintenance optimization models which covers almost all models used in practice. For the class of unimodal finite-valued marginal cost functions we show that these optimization models are easy to solve. http://repub.eur.nl/res/pub/1383/ 1996-01-01T00:00:00Z In this paper the effect of the break quantity rule on the inventory costs in a 1-warehouse, N-retailers distribution system is analyzed. The break quantity rule is to deliver large orders from the warehouse, and small orders from the nearest retailer, where a so--called break quantity determines whether an order is small or large. Under the assumptions that the stock at the warehouse can only be used to satisfy large orders, and that demand during the leadtimes is normally distributed, an expression for the inventory costs is derived. The objective of this paper is to provide insight into the effect of the break quantity rule on the inventory holding costs, and therefore we present extensive computational results, showing that in many cases the rule leads to a significant cost reduction. http://repub.eur.nl/res/pub/1384/ 1996-01-01T00:00:00Z Demand for spare parts can sometimes be classified into critical and non-critical demand, depending on the criticality of the equipment in which it is installed. To effectively handle this situation in spare parts inventory control, we propose a stocking policy where some of the stock is reserved for critical demand. For Poisson demand and a lot-for-lot stocking policy with positive replenishment leadtime, approximations of the service levels for both classes of demand are derived, and verified by simulation. Finally, a numerical example is presented to illustrate the advantages of using the proposed policy. http://repub.eur.nl/res/pub/1361/ 1995-01-01T00:00:00Z In multi-echelon distribution systems it is usually assumed that demand is only satisfied from the lowest echelon. In this paper we will consider the case where demand can be satisfied from any level in the system. However, then the problem arises of how to allocate orders from customers to the different locations. A possible way of dealing with this problem consists of using a so-called break quantity rule. This easy implementable rule is to deliver every order with a size exceeding the break quantity from a higher echelon. The use of the break quantity rule now results in a reduction of the demand variability at the retailer and hence less safety stocks need to be held. The concept is studied for a two-echelon distribution system, consisting of one warehouse and one retailer, where the inventory at the retailer is controlled by an order up to level policy, and where at the warehouse there is enough inventory to satisfy all orders from the retailer and the customers. For this system an approximation for the long run average costs as a function of the break quantity is derived, and an algorithm is presented to determine the cost-optimal break quantity. Computational results indicate that the break quantity rule can lead to significant cost reductions.