Title: Optimising replenishment policy in an integrated supply chain with controllable lead time and backorders-lost sales mixture

Authors: Marcello Braglia; Davide Castellano; Dongping Song

Addresses: Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Largo Lucio Lazzarino, 56122 Pisa, Italy ' Dipartimento di IngegneriaChimica, dei Materiali e della Produzione Industriale, Università degli Studi di Napoli 'Federico II', Piazzale V. Tecchio 80, 80125 Napoli, Italy ' School of Management, University of Liverpool, Chatham Street, Liverpool, L69 7ZH, UK

Abstract: This paper aims to optimise the inventory replenishment policy in an integrated supply chain consisting of a single supplier and a single buyer. The system under consideration has the features such as backorders-lost sales mixture, controllable lead time, stochastic demand, and stockout costs. The underlying problem has not been studied in the literature. We present a novel approach to formulate the optimisation problem, which is able to satisfy the constraint on the number of admissible stockouts per time unit. To solve the optimisation problem, we propose two algorithms: an exact algorithm and a heuristic algorithm. These two algorithms are developed based on some analytical properties that we established by analysing the cost function in relation to the decision variables. The heuristic algorithm employs an approximation technique based on an ad-hoc Taylor series expansion. Extensive numerical experiments are provided to demonstrate the effectiveness of the proposed algorithms.

Keywords: integrated supply chain; replenishment policy; stochastic demand; controllable lead time; backorders; lost sales; joint economic lot size; JELS.

DOI: 10.1504/IJLSM.2018.090474

International Journal of Logistics Systems and Management, 2018 Vol.29 No.4, pp.476 - 501

Received: 27 Jul 2016
Accepted: 28 Oct 2016

Published online: 01 Mar 2018 *

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