Halkos, George and Kevork, Ilias and Tziourtzioumis, Chris (2014): On the convexity of the cost function for the (Q,R) inventory model.

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Abstract
In this paper we investigate the convexity of the annual total cost function for the Hadley & Whitin (1963) continuous review (Q,R) inventory model with backorders and fixed leadtime, when the reorder point is nonnegative and the cost per unit backordered is used to calculate the expected annual shortage cost. Efficient procedures for finding the order quantity and reorder point which ensure a global minimum are provided when the demand in the lead time follows the Normal and LogNormal distributions. Convexity conditions are obtained for each distribution and numerical examples are given to explain how the values of the model cost parameters affect the optimal solution. The results indicate strong interaction between convexity and cost parameters as their values determine when the minimum cost obtained from solving the first order conditions is global and when the global minimum is attained setting the reorder point to zero.
Item Type:  MPRA Paper 

Original Title:  On the convexity of the cost function for the (Q,R) inventory model 
Language:  English 
Keywords:  Logistics; Continuous review inventory model; Expected total cost function; Convexity conditions; Cost parameters. 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61  Optimization Techniques ; Programming Models ; Dynamic Analysis M  Business Administration and Business Economics ; Marketing ; Accounting ; Personnel Economics > M1  Business Administration > M11  Production Management M  Business Administration and Business Economics ; Marketing ; Accounting ; Personnel Economics > M2  Business Economics > M21  Business Economics 
Item ID:  55675 
Depositing User:  G.E. Halkos 
Date Deposited:  05. May 2014 14:13 
Last Modified:  05. May 2014 14:48 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/55675 