Integrated inventory model with stochastic lead time and controllable variability for milk runs

The current study deals with the lead-time variability reduction problem in a multi-supplier and single-buyer system with a milk-run delivery network. Under the assumption of finite-range stochastic lead time, we consider that the lead-time variance can be shortened at an extra crashing cost. Aiming to minimize the joint system costs, an integrated inventory model is formulated with a capacity constraint, and a solution procedure is developed to simultaneously optimize lead-time variance, replenishment cycle time, reorder point, and the integer numbers of shipment per production cycle for multiple suppliers. We also show that the buyer does a tradeoff between the crashing cost and the sum of holding and shortage costs for the decision making of the optimal lead-time variability. Numerical examples and sensitivity analysis are presented to validate the proposed model.