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<p>We consider a continuous time inventory system with two types of inventories, namely main inventory (MI) and defective inventory (DI). The arrival times of customers in the system follow a Poisson process. We adopt the (<i>s</i>,&#xa0;<i>S</i>) ordering policy. When the order is received, the received items are fully inspected and segregated into perfect and defective items. These items are stored separately in MI and DI respectively. The defective items are then repaired individually and delivered to MI after repair. If there is no item in MI, even if DI has either a positive inventory or no inventory, the incoming customer joins the orbit of retrial customers and tries to meet his demand again after a random time. The lead time, repair time, and retrial time follow independent exponential distributions. We derived the joint probability distribution of the number of customers in orbit, the level of MI, and the level of DI. Some key system performance measures are derived and these measures are used to calculate the expected total cost. The results are illustrated numerically using Julia software.</p>

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A continuous-review retrial inventory system with repair options for defective items

  • 期刊论文

  • 发表日期：

    2026年1月22日

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  • Saranyadas Sivadasan,
  • Shophia Lawrence Arputham

摘要

We consider a continuous time inventory system with two types of inventories, namely main inventory (MI) and defective inventory (DI). The arrival times of customers in the system follow a Poisson process. We adopt the (s, S) ordering policy. When the order is received, the received items are fully inspected and segregated into perfect and defective items. These items are stored separately in MI and DI respectively. The defective items are then repaired individually and delivered to MI after repair. If there is no item in MI, even if DI has either a positive inventory or no inventory, the incoming customer joins the orbit of retrial customers and tries to meet his demand again after a random time. The lead time, repair time, and retrial time follow independent exponential distributions. We derived the joint probability distribution of the number of customers in orbit, the level of MI, and the level of DI. Some key system performance measures are derived and these measures are used to calculate the expected total cost. The results are illustrated numerically using Julia software.