Title: Lead time uncertainty and supply chain coordination in lost sales inventory models

Authors: Barry R. Cobb

Addresses: Department of Marketing, Missouri State University, Springfield, MO, USA

Abstract: The effects of lead time uncertainty on optimal inventory policies in a two-echelon supply chain operating under continuous review inventory assumptions are examined. In this system, the buyer selects an inventory order quantity and reorder point to maximise its profits, while the seller selects an order quantity from its external supplier that is an integer multiple of the buyer's order quantity; unsatisfied demand is accounted for as lost sales and may also incur a penalty cost representing lost customer goodwill. Normally distributed demand per unit time is assumed and lead time can follow any discrete probability distribution, resulting in a mixture of Gaussians distribution for lead time demand. Examples where lead time is discrete and not well-approximated by a continuous distribution are examined, and use of the mixture of Gaussians approach versus a single normal distribution for lead time demand in these cases reduces supply chain costs by between 12% and 13%.

Keywords: continuous review; supply chain coordination; discounting; inventory management; lead time uncertainty; supply chain management; SCM; lost sales; inventory modelling; mixture of Gaussians; order quantity; reorder point; lead times; optimal inventory policies; two-echelon supply chains.

DOI: 10.1504/IJIR.2016.077453

International Journal of Inventory Research, 2016 Vol.3 No.1, pp.5 - 30

Received: 20 Feb 2016
Accepted: 23 Mar 2016

Published online: 30 Jun 2016 *

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