Investing in lead-time variability reduction in a collaborative vendor-buyer supply chain model with stochastic lead time

This study deals with investing in lead-time variability reduction problems for the integrated vendor-buyer supply chain system with partial backlogging under stochastic lead time. We consider that lead time variability can be reduced through further investment; more specifically, a logarithmic investment function is used that allows investment to be made to reduce lead-time variability. By using the proposed supply chain model, considerable savings can be achieved to increase the competitive edge. The objective is to derive the optimal production/ordering strategy, and the best investment policy to minimize joint total cost. A computer code using the software, Mathematica, is developed to derive the optimal solution. Furthermore, we discuss the sensitivity of the optimal solution together with the changes of the values of the parameters associated with the model for decision-making. Various numerical examples are given to illustrate the results.