http://repub.eur.nl/res/aut/31/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/533/ 2003-07-04T00:00:00Z The most recent optimization algorithm for (s,S) order policies with continuous demand was developed by Federgruen and Zipkin (1985). This was also the first efficient algorithm, which uses policy iteration instead of discretization. Zheng and Federgruen (1991) developed an even more efficient algorithm for computing discrete order quantity (s,S) inventory policies. Since the continuous case prohibits enumeration, this algorithm does not apply to continuous order quantity systems. In this paper an efficient algorithm for continuous order quantity (s,S) policies is developed. A marginal cost approach is used for determining the optimal s. Furthermore, we construct two aid functions (generated by the optimality conditions for s and S), and exploiting their special properties a simple and efficient algorithm is obtained. The algorithm converges monotonically, such that at every iteration a policy improvement is obtained. Since every iteration finds a local minimum of the expected average cost, the number of iterations is at most N, where N<infinity represents the number of local minimums. The algorithm also applies to discrete order quantity systems, in which case it basically reduces to the algorithm of Zheng and Federgruen (with the difference that in general our algorithm will take larger than unit steps, since we are not using enumeration. http://repub.eur.nl/res/pub/534/ 2003-07-04T00:00:00Z This paper extends a fundamental result about single-item inventory systems. This approach allows more general performance measures, demand processes and order policies, and leads to easier analysis and implementation, than prior research. We obtain closed form expressions for the Laplace transforms of the expressions of the performance measures, and with the help of an efficient inversion algorithm, the approximations of these cost and service measures are almost up to machine precision. http://repub.eur.nl/res/pub/535/ 2003-07-04T00:00:00Z In this paper we consider a two level decentralized distribution system, consisting of one warehouse and N retailers. The warehouse and each retailer follows each his own (s,nQ) order policy. We extended the models as known in the literature to compound renewal demand. http://repub.eur.nl/res/pub/536/ 2003-07-04T00:00:00Z In this paper we consider stochastic processes with an embedded Harris chain. The embedded Harris chain describes the dependence structure of the stochastic process. That is, all the relevant information of the past is contained in the state of the embedded Harris chain. For these processes we proved a powerful reward theorem. Futher, we show how we can control these type of processes and give a formulation similar to semi-Markov decision processes. Finally we discuss a number of applications in inventory management. http://repub.eur.nl/res/pub/1725/ 2002-12-19T00:00:00Z This paper extends a fundamental result about single-item inventory systems. This approach allows more general performance measures, demand processes and order policies, and leads to easier analysis and implementation, than prior research. We obtain closed form expressions for the Laplace transforms of the expressions of the performance measures, and with the help of an efficient inversion algorithm, the approximations of these cost and service measures are almost up to machine precision. http://repub.eur.nl/res/pub/1726/ 2002-12-19T00:00:00Z The most recent optimization algorithm for (s,S) order policies with continuous demand was developed by Federgruen and Zipkin (1985). This was also the first efficient algorithm, which uses policy iteration instead of discretization. Zheng and Federgruen (1991) developed an even more efficient algorithm for computing discrete order quantity (s,S) inventory policies. Since the continuous case prohibits enumeration, this algorithm does not apply to continuous order quantity systems. In this paper an efficient algorithm for continuous order quantity (s,S) policies is developed. A marginal cost approach is used for determining the optimal s. Furthermore, we construct two aid functions (generated by the optimality conditions for s and S), and exploiting their special properties a simple and efficient algorithm is obtained. The algorithm converges monotonically, such that at every iteration a policy improvement is obtained. Since every iteration finds a local minimum of the expected average cost, the number of iterations is at most N, where N < infinity represents the number of local minimums. The algorithm also applies to discrete order quantity systems, in which case it basically reduces to the algorithm of Zheng and Federgruen (with the difference that in general our algorithm will take larger than unit steps, since we are not using enumeration). http://repub.eur.nl/res/pub/1724/ 2002-12-17T00:00:00Z In this paper we consider a two level decentralized distribution system, consisting of one warehouse and N retailers. The warehouse and each retailer follows each his own (s,nQ) order policy. We extended the models as known in the literature to compound renewal demand. http://repub.eur.nl/res/pub/6837/ 2001-10-16T00:00:00Z The most recent optimization algorithm for (s, S) order policies with continuous demand was developed by Federgruen and Zipkin (1985). This was also the first efficient algorithm, which uses policy iteration instead of discretization. Zheng and Federgruen (1991) developed an even more efficient algorithm for computing discrete order quantity (s, S) inventory policies. Since the continuous case prohibits enumeration, this algorithm does not apply to continuous order quantity systems. In this paper an efficient algorithm for continuous order quantity (s, S) policies is developed. A marginal cost approach is used for determining the optimal s. Furthermore, we construct two aid functions (generated by the optimality conditions for s and S) , and exploiting their special properties a simple and efficient algorithm is obtained. The algorithm converges monotonically, such that at every iteration a policy improvement is obtained. Since every iteration finds a local minimum of the expected average cost, the number of iterations is at most N, where N < ? represents the number of local minimums. The algorithm also applies to discrete order quantity systems, in which case it basically reduces to the algorithm of Zheng and Federgruen (with the difference that in general our algorithm will take larger than unit steps, since we are not using enumeration). http://repub.eur.nl/res/pub/6838/ 2001-10-16T00:00:00Z This paper extends a fundamental result about single-item inventory systems. This approach allows more general performance measures, demand processes and order policies, and leads to easier analysis and implementation, than prior research. We obtain closed form expressions for the Laplace transforms of the expressions of the performance measures, and with the help of an efficient inversion algorithm, the approximations of these cost and service measures are almost up to machine precision. http://repub.eur.nl/res/pub/1646/ 2000-04-12T00:00:00Z In this article a single item inventory model with backlogging is analyzed, which is a generalization of the most well-known simple models. This formulation enables us to separate the analysis of the system to the analysis of the control rule (reduced to the analysis of a Markov chain) and of the time stationary distribution for the arrival process of customers. This facilitates a much better understanding of such systems. A simple sample path argument enables a straightforward derivation of average holding costs, ordering costs, services measures. A recently developed algorithm of Laplace transform inversion technique provides us with an efficient tool for the computation of these cost expressions. http://repub.eur.nl/res/pub/1600/ 1999-09-15T00:00:00Z In this paper we will discuss a general framework for single item inventory models based on the theory of regenerative processes. After presenting without proof the main theorems for regenerative processes we analyze in detail how the different single item models can be embedded within this general theory. This facilitates to write down the expressions for the average cost associated with an arbitrary costrate function ƒ, and some of the service measures, which appear most frequently in the literature. http://repub.eur.nl/res/pub/1601/ 1999-09-15T00:00:00Z This article is a continuation of the paper "Inventory Control and Regenerative processes: Theory" (Bazsa et al.; 1998) and presents closed form expressions for Laplace transforms associated with the cost functions of the classical single item inventory models with indivisible items, a fixed lead time and backlogging. For given instances of these inventory control models these Laplace transforms will be used as input functions in a newly developed Laplace transform inversion algorithm (Iseger; A new method for inverting Laplace transforms; 1998) which yields highly accurate computational results of the associated cost functions. http://repub.eur.nl/res/pub/1527/ 1998-12-31T00:00:00Z In this paper we will discuss a general framework for single item inventory models based on the theory of regenerative processes. After resenting without proof the main theorems for regenerative processes we analyze in detail how the different single item models can be embedded within this general theory. This facilitates to write down the expressions for the average cost associated with an arbitrary costrate function f. Since these expressions are still complicated, involving convolutions, we use a recently developed numerically stable Laplace inversion algorithm to compute these objective functions in MATLAB. This enables us to compute the exact costs instead of using approximations.