On a single item single stage mixture inventory models with independent stochastic lead times
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On a single item single stage mixture inventory models with independent stochastic lead times Achin Srivastav1 · Sunil Agrawal1
Received: 6 August 2016 / Revised: 18 May 2018 / Accepted: 19 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract In this paper, the optimal (r, Q) replenishment policies are developed for stochastic mixture inventory models for both the without order crossover and the order crossover cases. The shortage costs are considered on a per stockout basis. Expressions of total cost are developed for both cases, and their convexities are proved. A normal approximation method is used to determine the distribution of the lead-time demand. The effect of the changing proportions of the mixture of backorders and lost sales (q) on various inventory performance measures, such as total inventory cost, service levels and turnover ratio, is studied. Further, a simulation study is performed to validate the order crossover model. The results obtained are compared with the factorial experiments, which are conducted for the expressions developed. Regression equations are developed for determining the optimal order quantity, inventory cost and safety stock factor. It is determined that there is a remarkable reduction in inventory cost by considering ordering crossover in inventory models. Finally, a sensitivity analysis is done to study the effect of the reorder point (r) on the total inventory cost. The results of a robustness study show that the order crossover model is robust and applicable to many real-world inventory problems. Keywords Stochastic · Inventory · Order crossover · Robustness · Sensitivity · Simulation
* Achin Srivastav [email protected] 1
Mechanical Engineering, PDPM IIITDM Jabalpur, Jabalpur, Madhya Pradesh, India
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A. Srivastav, S. Agrawal
1 Introduction In inventory systems having stochastic/variable lead times, the replenishment orders may not be received in the same sequence in which they were placed; thus, the orders cross. This phenomenon of crossing the orders is known as order crossover (Riezebos 2006). There can be several possible causes for orders crossing and not arriving in the same sequence in which they were placed. Some of the causes reported in the various literature are the presence of different transportation modes, the location of the facility of global suppliers, the frequency of ordering, and the large distances between suppliers and retailers. As per the study and per discussions held by Srinivasan et al. (2011) with managers in various industries, such as those of consumer goods, food processing, petroleum products and computer systems integrators, the reasons for the occurrence of order crossover can be due to the variable lead times of global suppliers, which can result in out of stock and excess inventory problems. According to Riezebos (2006), the firms situated upstream in the supply chain or that use natural resources are more likely to experience order crossovers. Managers, especially in the retail supply chain,
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