Approximations for a lost-Sales Production-Inventory Control Model with Service Level Constraints

Article Abstract:

This paper deals with a one-product production-inventory model, where the production rate can be dynamically adjusted in order to cope with random fluctuations in demand. The inventory level is controlled by using one of two possible production rates where under each production rate the production is continually added to the inventory. The demand process for the product is described by a compound Poisson process. Also, excess demand is lost. In accordance with common practice we consider service measures as the average number of lost-sales occurences per unit time and the fraction of demand that is lost. For a two-critical-number control rule we derive practically useful approximations for the switch-over level in order to achieve a prespecified service level. Numerical experiments reveal that the approximations are quite accurate. (Reprinted by Permission of Publisher.)

Manufacturing, Inventory control, Poisson distribution, Demand, Production, Management Science

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Discrete Approximations of Probability Distributions

Article Abstract:

Probability distributions are approximated by a few representative values and their associated probabilities when the models get too large. These discrete approximations tend to underestimate the moments of the original distribution. A new procedure, based on gaussian quadrature, can decrease the approximation error to any level. Tables and graphs are used to present results.

Statistics (Data), Error analysis (Mathematics), Estimation, Statistics, Error Analysis, Operations Research, Probability, Discrete Mathematics, Gaussian Error Integral

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Sharp bounds and simple approximations for the Erlang delay and loss formulas

Article Abstract:

Approximations and bounds for the Erlang loss and delay formulas are obtained. A simple analytical solution to the server allocation problem is derived from one of the approximation results.

Research, Queuing theory, Inequalities (Mathematics)

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