# American Institute of Mathematical Sciences

July  2012, 8(3): 657-672. doi: 10.3934/jimo.2012.8.657

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

 1 Department of Customs Management, Shanghai Customs College, Shanghai, 201204, China, China, China

Received  May 2011 Revised  January 2012 Published  June 2012

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.
Citation: Xin Zhou, Liangping Shi, Bingzhi Huang. Integrated inventory model with stochastic lead time and controllable variability for milk runs. Journal of Industrial & Management Optimization, 2012, 8 (3) : 657-672. doi: 10.3934/jimo.2012.8.657
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##### References:
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