Study on the Centralization Strategy of the Blood Allocation among Different Departments within a Hospital
In this paper, we address a two-level supply chain of bloodproducts(red blood cells) consisting of one hospital and elevendepartments in hospital which contain orthopedics,gynaecology and obstetrics, emergency treatment, digestivedepartment, hematology, gastroenterology department, thoracicsurgery, cardiac surgery, urology department, hepatopancreatobliliary and neurosurgery. Fig.1 shows the configuration ofour two-level system. We need to work out the appropriateinventory setting for every department so as to minimize theshortage and wastage costs in the two-level system. https://codeshoppy.com/shop/product/hospital-management-mobile-app/ And themost important thing is to find out the optimal centralizationnetwork of blood allocation, which means finding the best wayto integrate some of the departments’ blood requirements, forthe purpose of reducing the total cost and making sure of thefreshness of blood. Fig.2 shows an example of centralizeddepartments in the second level. Therefore, we present thecentralization principle in integrating the blood inventoryrequirements of some departments in hospital and formulate aninteger programming model to solve the covering problem.
A. The Centralization PrincipleIntegrating the blood requirements of different departmentscould let some departments in urgent need of blood utilize theblood items left by other departments. In this way, the shortageand wastage in various departments could be avoidedeffectively. What’s more, the blood would be transfused to thepatients as soon as possible assuring the freshness of blood andthe treatment effect.The centralization principle in integrating the bloodinventory requirements of some departments in hospitalcontains two steps:First, group of different departments by calculating thedifference between the averages applied amount of blood andthe averages actual amount of blood transfused to patients,according to the historical blood data of 24 months recorded byvarious departments, the computational formula as follow
whereiDrepresents the difference,iArepresents the averageapplied amount of blood of 24 months,iBrepresents theaverage actual amount of blood transfused to patients, irepresents department i.IfiDis higher than 10, department i will be divided intogroup one named the wastage group, ifiDis lower than -10,department i will be divided into group two named the shortagegroup, and ifiDis between -10 and 10, department i will bedivided into group three named the normal group.Second, according to the priority of the demand degree offresh blood, match the departments chosen from group onewith departments from group two. In other words, fresh bloodproducts are required for certain types of patients. And it ishighly preferable for operations like cardiac surgery,hematology department, oncology, and orthopedics department,according to the study from the University of TexasSouthwestern . However, blood products of any age can beused for traumatology or other general departments .Therefore, group the departments which are highly preferredthe fresh blood at first, and then match the secondary issues. Inthis way, the effect of surgery could be improved and thewastage of fresh blood could be avoided.
B. Model FormulationAssuming that general blood issuing policy for the hospitaland departments is FIFO (First in First out). The blood itemsarrive at the hospital from a stationary Poisson process, anddemand occurs at different departments by a stationary Poissonprocesses as well. The hospital and departments use an (s-1, s)inventory policy. This policy means when one item is used oroutdated, an order must be placed to replenish the inventory tos level .
The first constraint computes the demand in everydepartment i after centralization. The second constraint makessure that the department held no blood inventory could onlyreceive items from one of the other departments. The thirdconstraint ensures that the department which receives blooditems from other departments could not distribute items toother departments. And the fourth constraint guarantees that thedepartment can receive blood items according to thecentralization principle mentioned at subsection 3.1, where wesetijxto determine the configuration of the centralization forthe two-level allocation system. The last constraintsetsiMsetas the maximum value to downside the searchingspace for optimal setting inventory. Click Here