A stochastic inventory model of dual sourced supply chain with lead-time reduction

Recently, the amount of literature on analyzing the effects of investment strategies to control lead times has been increasing. Issues on investment to reduce lead times are important because variability in lead time between successive stages often has a great effect on the coordination of supply chain. This paper considers dual-sourcing models with stochastic lead times and constant unit demand in which lead times are reduced at a cost that can be viewed as an investment. In order to obtain an analytically tractable model, the distributions of lead times for two suppliers are assumed to be exponential. In our two-supplier model, we will concentrate on lead times as random variables, which are made endogenous in the stochastic lead-time model through ‘expediting factors’, the constants of proportionality between the expedited lead times and ordinary lead times, as was done by Bookbinder and Çakanyildirim. Firstly, we determine the order quantity (Q), reorder point level (r), and order splitting proportion (k1) in the case of no lead-time reduction. Using the (Q,r) found, we decide the expediting factors and new k1 in the case of lead-time reduction. We compare the expected total cost per unit time for the two models and investigate savings. Additionally, sensitivity analyses are conducted with respect to the various cost parameter ranges, and remarks are made for further research.