TY - JOUR
T1 - Stockout risk of production-inventory systems with compound Poisson demands
AU - (Ai-Chih) Chang, Jasmine
AU - Lu, Haibing
AU - (Junmin) Shi, Jim
N1 - Funding Information:
The authors are indebted to Prof. Benjamin Melamed and Prof. Michael N. Katehakis at Rutgers University for their meticulous review and detailed comments through the very early stage of the study. The corresponding author is partially supported by the USDA grant (16-TMTSD-NJ-0008). The second author is partially supported by GEIRI North America, San Jose, California, under SGCC Science and Technology Project Fund SGRIJSKJ[2015]1029.
Funding Information:
The authors are indebted to Prof. Benjamin Melamed and Prof. Michael N. Katehakis at Rutgers University for their meticulous review and detailed comments through the very early stage of the study. The corresponding author is partially supported by the USDA grant ( 16-TMTSD-NJ-0008 ). The second author is partially supported by GEIRI North America, San Jose, California, under SGCC Science and Technology Project Fund SGRIJSKJ[2015]1029.
Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2019/3
Y1 - 2019/3
N2 - Production-inventory systems with continuous production or continuous manufacturing have been implemented in a variety of manufacturing contexts. Most recently, the Commissioner of the FDA has called on drug and biological product manufacturers to begin switching from batch manufacturing processes to continuous production. Motivated by prevailing applications and the emerging and promising landscape in the healthcare and pharmaceutical industries, this paper studies a continuous-review production-inventory system with a constant production rate and compound Poisson demands, in which the cost of the system is assessed via inventory holding, stockout penalty and production costs. For any initial inventory, we derive a closed-form expression for the expected discounted cost function until stockout occurrence. We systemically quantify the stockout risk on four different dimensions (i.e., time, volume, frequency and percentage) and derive explicit expressions for each type of risk metric. The objective is to derive the production rate that minimizes the expected discounted system cost subject to a given risk tolerance level on stockouts. With the aid of the derived explicit forms of stockout risk and the cost function, we develop a computationally-efficient algorithm for the optimal solution. Extensive numerical studies are conducted to illustrate our results with rich insights. Numerically, we show that it is outrageously costly to reduce stockout risk, especially when this risk is relatively low; the value of risk is more sensitive to the stockout risk level if the demand distribution has a higher volatility.
AB - Production-inventory systems with continuous production or continuous manufacturing have been implemented in a variety of manufacturing contexts. Most recently, the Commissioner of the FDA has called on drug and biological product manufacturers to begin switching from batch manufacturing processes to continuous production. Motivated by prevailing applications and the emerging and promising landscape in the healthcare and pharmaceutical industries, this paper studies a continuous-review production-inventory system with a constant production rate and compound Poisson demands, in which the cost of the system is assessed via inventory holding, stockout penalty and production costs. For any initial inventory, we derive a closed-form expression for the expected discounted cost function until stockout occurrence. We systemically quantify the stockout risk on four different dimensions (i.e., time, volume, frequency and percentage) and derive explicit expressions for each type of risk metric. The objective is to derive the production rate that minimizes the expected discounted system cost subject to a given risk tolerance level on stockouts. With the aid of the derived explicit forms of stockout risk and the cost function, we develop a computationally-efficient algorithm for the optimal solution. Extensive numerical studies are conducted to illustrate our results with rich insights. Numerically, we show that it is outrageously costly to reduce stockout risk, especially when this risk is relatively low; the value of risk is more sensitive to the stockout risk level if the demand distribution has a higher volatility.
KW - Continuous manufacturing
KW - Continuous production
KW - Drug shortage
KW - Pharmaceutical manufacturing
KW - Production-inventory systems
KW - Risk metrics
KW - Stockout risk
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U2 - 10.1016/j.omega.2018.03.001
DO - 10.1016/j.omega.2018.03.001
M3 - Article
AN - SCOPUS:85044309491
SN - 0305-0483
VL - 83
SP - 181
EP - 198
JO - Omega
JF - Omega
ER -