A new newsvendor policy model for dual-sourcing supply chains by considering disruption risk and special order

Abstract

Newsvendor model is one of the most important issues in inventory models. In this paper, we investigate a newsvendor model without lead time, which have difference between distributer and wholesale/retailer. At the end of day, the residual products of newsvendor sold to a secondary market at a unit salvage value. Also, the amount of orders that cannot be met, should be paid the penalty for each unit. In addition, in each one of channels, the percent of these orders cannot be met by the distributer. Then, the newsvendor provides the difference between the amount that ordered to distributor and the amount that met in the occurrence of interruptions risk as a special order from the manufacturer, more expensive than the price of distributor. The limitations of the study are the procurement budget that used for special order. Finally, the model is applied in a real case as a numerical example to determine order amount that maximize profit and is solved by Maple 15. The Kuhn–Tucker method was used to illustrate the optimal points that have necessary condition. Also, the hessian matrix was used to illustrate the optimal points that have sufficient condition for optimization. Consequently, the considered points are global optimum. The main factor in the disruption risk that effect on the ordering amount and profit, are including the probability of appearing of disruption $(p_i)$ and a percent of ordering amount which are met in the case of appearing of disruption $(y_i)$. Therefore, the analysis of sensitivity has been done on two parameters of $p_i$ and $y_i$ by using contour curves. According to result of solved problem, the change of disruption appearance reduced. Finally, the proposed method besides being simple is so exact which is sensible in the solved problems.