Title: Approximated closed-form minimum-cost solutions to the (S − 1, S) policy with complete backordering

Authors: Marcello Braglia; Davide Castellano; Marco Frosolini

Addresses: Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Largo Lucio Lazzarino – 56126 Pisa, Italy ' Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Largo Lucio Lazzarino – 56126 Pisa, Italy ' Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Largo Lucio Lazzarino – 56126 Pisa, Italy

Abstract: In this paper, we consider the continuous review (S − 1, S) policy with complete backordering, deterministic and constant lead-time, and with a Poissonian lead-time demand. Moreover, we take into account two different expressions of the total expected cost depending on the customer-service criterion adopted. First, we approximate the Poissonian lead-time demand with a well-suited Gaussian random variable. Although this system can be easily solved with a simple algorithmic approach, it is interesting to be aware of the direct analytical functional relationship between the optimal value of the decision variable and the parameters of the model. Hence, the second step consists in providing some approximated closed-form minimum-cost solutions for both cost models considered under a Gaussian lead-time demand. An extensive numerical study is finally shown to characterise the precision achieved by the approximations developed.

Keywords: inventory policy; base-stock policy; nonlinear programming; logistic function; approximation; Gaussian lead-time demand; closed-form solutions; minimum-cost solutions; complete backordering; inventory management; continuous review policy; lead times.

DOI: 10.1504/IJMOR.2016.073276

International Journal of Mathematics in Operational Research, 2016 Vol.8 No.1, pp.1 - 27

Available online: 28 Oct 2015 *

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