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

Xin Zhou; Liangping Shi; Bingzhi Huang

doi:10.3934/jimo.2012.8.657

Article Contents

2012, Volume 8, Issue 3: 657-672. Doi: 10.3934/jimo.2012.8.657

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

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

Received: April 30, 2011

Revised: December 31, 2011

Published: June 2012

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Abstract

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.

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Mathematics Subject Classification: Primary: 90B05, 90B15; Secondary: 90C90.

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