Inventory management of reusable surgical supplies

Abstract

We investigate the inventory management practices for reusable surgical instruments that must be sterilized between uses. We study a hospital that outsources their sterilization services and model the inventory process as a discrete-time Markov chain. We present two base-stock inventory models, one that considers stockout-based substitution and one that does not. We derive the optimal base-stock level for the number of reusable instruments to hold in inventory, the expected service level, and investigate the implied cost of a stockout. We apply our theoretical results to a dataset collected from a surgical unit at a large tertiary care hospital specializing in colorectal operations. We demonstrate how to implement our model when determining base-stock levels for future capacity expansion and when considering alternative stockout protocols. Our analysis suggests that the hospital can reduce the number of reusable instrument sets held in inventory if on-site sterilization techniques (e.g., flash sterilization) are employed. Our results will guide future procurement decisions for surgical units based on costs and desired service levels.

A Markovian approach to modeling a periodic order‐up‐to‐level policy under stochastic discrete demand and lead time with lost sales

“…(2015), Diamant et al. (2018), and Saha and Ray (2019). The inventory problems in the research of Kapalka et al.…”

“…In the literature of inventory research, especially the policy, various assumptions regarding the distributions of demand, lead time, and demand during the protection interval are made to simplify the problems. For the demand, most studies assumed that the demand is subject to a constant rate (Rashid et al., 2015), follows a theoretical distribution (Mak et al., 2005; Isotupa, 2006; Bijvank and Vis, 2012; Guerero et al., 2013; Bijvank et al., 2014; Haijema, 2014; Seyedhoseini et al., 2015; Saedi et al., 2016; Xu et al., 2017; Diamant et al., 2018; Nguyen and Chen, 2020; Braglia et al., 2021; Meneses et al., 2021), or a theoretical distribution with a fuzzy means (Sarkar and Mahapatra, 2017). For the lead time, common assumptions include negligible lead time (Kang and Kim, 2010; Diaz et al., 2016; Nguyen and Chen, 2020), constant fractional lead time (Chiang and Gutierrez, 1998; Kapalka et al., 1999), or constant integer lead time (Veinott, 1966; Teunter et al., 2010; Silver and Bischak, 2011; Bijvank et al., 2014; Cunha et al., 2017; Xu et al., 2017; Meneses et al., 2021).…”

“…(2013), and Diamant et al. (2018) for healthcare inventory systems, in which demand is assumed to be either independent and identically distributed (Bijvank and Vis, 2012; Diamant et al., 2018) or Poisson (Guerrero et al., 2013). Different from Kapalka et al.…”

“…An effective and wellknown approach to capturing the behaviors of the inventory system with stochastic elements is the Markov chain (Bijvank and Vis, 2011). Indeed, Markov inventory models are developed in several studies, including that of Kapalka et al (1999), Mak et al (2005), Isotupa (2006), Archibald (2007), Xu et al (2011, Bijvank and Vis (2012), Guerrero et al (2013), Nasr and Maddah (2015), Rashid et al (2015), Diamant et al (2018), andSaha andRay (2019). The inventory problems in the research of Kapalka et al (1999), Mak et al (2005), Isotupa (2006), Xu et al (2011, Guerrero et al (2013), Nasr and Maddah (2015), Rashid et al (2015), Diamant et al (2018), Xu et al (2019), and Zhang et al (2019 are developed as mathematical models, in which the dynamics of their inventory systems are modeled by using Markov chain, while that in the studies of Archibald (2007) and Saha and Ray (2019) are formulated as Markov decision process models, in which system behaviors are captured in the state space and inventory policies are included in the action space.…”

“…Specifically, Kapalka et al (1999) model the levels of stock between two consecutive review periods in an inventory system experiencing a discrete stochastic demand as a stationary discrete-time Markov chain. This model also is adopted in the studies of Bijvank and Vis (2012), Guerrero et al (2013), andDiamant et al (2018) for healthcare inventory systems, in which demand is assumed to be either independent and identically distributed (Bijvank and Vis, 2012;Diamant et al, 2018) or Poisson (Guerrero et al, 2013). Different from Kapalka et al (1999), Mak et al (2005) construct an imbedded Markov chain, which represents the transitions of inventory positions in a system with a compound Poisson demand.…”