Title: A periodic review inventory system under stochastic demand with controllable safety stock, lead time, and price discount under partially backlogged shortages

Authors: Nughthoh Arfawi Kurdhi; Rumi Iqbal Doewes; Yuliana

Addresses: Department of Mathematics, Faculty of Mathematics and Natural Science, Sebelas Maret University, Surakarta, 57126, Indonesia ' Faculty of Teacher Training and Education, Sebelas Maret University, Surakarta, 57126, Indonesia ' Department of Mathematics Education, Widya Dharma University, Klaten, Indonesia

Abstract: The stochastic inventory system analysed in this paper explores the problem of the backorder price discount, safety stock, lead time, and review period as control variables to widen applications for a periodic review inventory model. In many practical situations, the variable lead time can be divided into some components which have a crashing cost for the reduced lead time. Moreover, the firm may offer a price discount to the obliged and loyal customers to pay off the uncomfortableness of backordering. Furthermore, the protection interval demand (i.e., review period plus lead time) is assumed to follows a normal distribution. The aim is to develop an algorithm to determine the optimal solutions, so that the total expected annual cost reaches at a minimum value. A numerical example is given to illustrate the application of the system.

Keywords: periodic review; safety stock; backorder discount; protection interval; lead time.

DOI: 10.1504/IJVCM.2020.111079

International Journal of Value Chain Management, 2020 Vol.11 No.4, pp.328 - 345

Received: 03 Oct 2019
Accepted: 02 Mar 2020

Published online: 20 Oct 2020 *

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