Abstract
In this paper the appropriate size of an intermediate storage is investigated. The input process is described by a stochastic process and the output process is deterministic. Both filling time points and filled amounts of material are described by discrete random variables. We focus on the necessary volume of the intermediate storage for the material in order to avoid the overfilling. To solve the sizing problem for a given reliability, an auxiliary function is defined and a difference equation is set up for it. In special cases it is solved analytically. Overflow probabilities and expected time of overflow are compared in continuous and discrete models. Analytic results are compared to the results arising from Monte-Carlo simulations as well. In general cases approximate solutions are presented and used for determining the necessary volume of storage for the change of material.
Highlights
Intermediate storages are frequently applied in many fields of industry, e.g. food industry, pharmaceutical industry, chemical industry [1, 2], in environmental systems, logistic, supply chain [3], information technology, in data storage systems, etc, the investigation of their operation is important in practice
We focus on the necessary volume of the intermediate storage for the material in order to avoid the overfilling
1 Introduction Intermediate storages are frequently applied in many fields of industry, e.g. food industry, pharmaceutical industry, chemical industry [1, 2], in environmental systems, logistic, supply chain [3], information technology, in data storage systems, etc, the investigation of their operation is important in practice
Summary
Intermediate storages are frequently applied in many fields of industry, e.g. food industry, pharmaceutical industry, chemical industry [1, 2], in environmental systems, logistic, supply chain [3], information technology, in data storage systems, etc, the investigation of their operation is important in practice Their applications serve to compensate the differences in the operations of different kinds of producing systems. The time interval between the kth and (k+1)th filling is given by the random variables tk , k = 1,2,... Are independent, identically distributed nonnegative discrete random variables with nonnegative integer values. Are independent random variables with nonnegative integer values and the distribution of tk is given by P(tk = j) = f(j), j = 0,1,2,. As the filling process is stochastic, the required size can be determined to a given reliability.
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