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2 2014

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Stochastic demand in inventory location

Bieniek M.

Logistyka

2014

nr 4

In this paper we consider the location inventory model which centralizes or decentralizes the stock. In this model we have to choose between the location of inventory in the regional warehouses or the location in the central warehouse. The choice is done due to minimum the holding costs of the safety stock and also the minimum of supply costs. The important aspect is that the customers can represent the stochastic demands on the inventory items. Additionally, the complex analysis of possible probabilistic demands' distributions is conducted. Some special cases of the model for normally, Poisson and exponentially distributed demands are also studied.

W pracy rozważany jest model lokalizacji zapasu, który centralizuje albo decentralizuje zapas. W tym modelu wybierana jest lokalizacja zapasu jako jedna z dwóch możliwych: w magazynach regionalnych lub w magazynie centralnym. Wybór jest dokonany na podstawie kryterium minimalizacji kosztów utrzymania zapasu zabezpieczającego. Ważnym aspektem tego modelu jest uwzględnienie stochastyczności popytu klientów. Dodatkowo przeprowadzona jest kompleksowa analiza możliwych rozkładów popytu. Ponadto przedstawiona jest postać modelu dla kilku szczególnych przypadków gdy popyt ma rozkład normalny, Poissona lub wykładniczy.

Service level in model of inventory location with stochastic demand

Bieniek M.

Archives of Transport

2014

Vol. 31, iss. 3

7--21

In this paper we consider the influence of the safety factor on the decision of the inventory location. This decision is done based on the model which centralizes or decentralizes the safety stock. In this model we have to choose between the location of the inventory in the regional warehouses or the location in the central warehouse. The decision is made due to the minimizing the holding costs and the supply costs of the safety stock from the central warehouse to the customer. The main assumption is that the customers have the stochastic demands on the inventory items. Moreover, the customers’ demands have the known distribution with the known parameters. The complex analysis of the influences of possible probabilistic demands' distributions on the safety factors is conducted. The numerical computations for the safety factors used in the facility location model are also presented. In numerical examples we take into considerations the demands’ distributions the most often used in practice like the normal, the Poisson, the Gamma and the exponential distribution. Some graphs for the safety factors of these distributions are also drawn. Moreover for the mentioned demands’ distributions the model of the safety stock location depends on the specific factors. Among other things these factors are the mean and the variance of the demand, the number of the regional warehouses, the assumed service level, and some cost factors like the holding costs and the transportation costs. Some graphs which illustrated the dependence of the model elements on some listed before parameters are presented and their influence on the location decision is studied also.