Lot-Size Models with Uncertain Demand Considering Its Skewness/Kurtosis and Stochastic Programming Applied to Hospital Pharmacy with Sensor-Related COVID-19 Data.

Fernando Rojas,Mauricio Huerta,Carlos Martin-Barreiro,Víctor Leiva

doi:10.3390/s21155198

Abstract

Governments have been challenged to provide timely medical care to face the COVID-19 pandemic. Under this pandemic, the demand for pharmaceutical products has changed significantly. Some of these products are in high demand, while, for others, their demand falls sharply. These changes in the random demand patterns are connected with changes in the skewness (asymmetry) and kurtosis of their data distribution. Such changes are critical to determining optimal lots and inventory costs. The lot-size model helps to make decisions based on probabilistic demand when calculating the optimal costs of supply using two-stage stochastic programming. The objective of this study is to evaluate how the skewness and kurtosis of the distribution of demand data, collected through sensors, affect the modeling of inventories of hospital pharmacy products helpful to treat COVID-19. The use of stochastic programming allows us to obtain results under demand uncertainty that are closer to reality. We carry out a simulation study to evaluate the performance of our methodology under different demand scenarios with diverse degrees of skewness and kurtosis. A case study in the field of hospital pharmacy with sensor-related COVID-19 data is also provided. An algorithm that permits us to use sensors when submitting requests for supplying pharmaceutical products in the hospital treatment of COVID-19 is designed. We show that the coefficients of skewness and kurtosis impact the total costs of inventory that involve order, purchase, holding, and shortage. We conclude that the asymmetry and kurtosis of the demand statistical distribution do not seem to affect the first-stage lot-size decisions. However, demand patterns with high positive skewness are related to significant increases in expected inventories on hand and shortage, increasing the costs of second-stage decisions. Thus, demand distributions that are highly asymmetrical to the right and leptokurtic favor high total costs in probabilistic lot-size systems.

Highlights

The Coronavirus disease 2019 (COVID-19) is a severe acute respiratory syndromeCoronavirus 2 (SARS-CoV-2) detected in China in December 2019
Under the COVID-19 pandemic, the decision-making plays a vital role when setting up timely medicine availability at a low cost since an inadequate decision could affect an entire country
Hospitals do have a critical role in their ability to rapidly deploy a large number of attentions to patients, supply clinical services in emergencies, and support local clinics and laboratories, as well as decrease the risk of a communicable virus that is transmitted from person-to-person by contact

Summary

Introduction

The Coronavirus disease 2019 (COVID-19) is a severe acute respiratory syndromeCoronavirus 2 (SARS-CoV-2) detected in China in December 2019. The COVID19 pandemic has changed the usual people behavior around the world, and its impact on health and the worldwide economy and finance is notorious [2,3,4]. The healthcare industry has played a relevant role facing COVID19. The time and quality in the administration of this industry can be favored by an efficient inventory management, which gives structure and direction to the decision-making in an organization regarding the supply chain [7]. Even more in the COVID-19 pandemic, efforts have been made to increase the installed capacity of diagnostics [8], beds for the care of critical patients, and the inclusion of new hospital equipment and supplies, considering drug management. Note that the studies on efficient inventory management in the healthcare industry focus on an internal analysis, but an attempt has been made to investigate this problem from the perspective of supply chain management [9,10,11]

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