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

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%.