Ensuring blood is available when it is needed most

Clay, N 2018, Ensuring blood is available when it is needed most, Doctor of Philosophy (PhD), Science, RMIT University.

Document type: Thesis
Collection: Theses

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Title Ensuring blood is available when it is needed most
Author(s) Clay, N
Year 2018
Abstract The provision of blood to patients in need is an imperative faced by all countries.  Red blood cells (RBCs) are perishable with a life of 42 days.  Inventory managers at hospitals need to know how many RBCs to order so that the probability of experiencing shortages or outdates is minimised.  This is complicated by demand for RBCs being doubly stochastic.  Both the number of patients that need RBCs and quantity of RBCs they will need are random.  For centralised blood banks not only are the orders they receive from hospitals apparently random, the supply of blood is also random.

This thesis shows that, in addition to the previously mentioned sources of volatility, the structure of the supply chain induces further volatility.  This occurs due to the presence of delivery delays and negative feedback loops in two locations within the supply chain.  It is shown how this volatility can be addressed with some simple structural changes.  But simply removing system induced volatility does not imply that the supply chain is optimised.  To address optimality the problem is formulated as a Markov decision process (MDP).  A solution to this process uses Stochastic Dynamic Programming (SDP), but this results in a combinatoric explosion making the computation of an exact solution within a reasonable time impossible.  Instead, Stochastic Average Approximation (SAA) is used to derive an approximate solution.  Repeated, sequential application of this is an exercise in Discrete Time Stochastic Control.  A working control solution is provided in python.  This solution can be arranged so as to mimic the two echelon supply chain found in blood inventories.  It is general enough to apply to any discrete perishable inventory system with random demand and/or supply.

The approach for blood inventories requires credible estimates of demand for RBCs.  It is shown, using hierarchical Bayesian modelling and Discrete Phase-Type (DPH) distributions, that credible estimates of demand at hospitals of any size can be derived from publicly available information.  In particular a new method for obtaining the parameters of a DPH distribution is formulated and applied to estimating transfusion quantities from publicly available sources.

An application of the proposed solution is presented for RBC inventories at both hospitals and at the blood bank.  For the blood bank in particular it is shown how this can be used to determine the quantity of donors needed to meet demand within a desired probability of adequacy.
Degree Doctor of Philosophy (PhD)
Institution RMIT University
School, Department or Centre Science
Subjects Operations Research
Keyword(s) Stochastic Control
Perishable Inventory
Discrete Phase-Type
Bayesian Estimation
System Dynamics
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Created: Wed, 06 Mar 2019, 12:43:04 EST by Adam Rivett
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