Blood Platelet Inventory Management

Abstract

This paper illustrates how MDP or Stochastic Dynamic Programming (SDP) can be used in practice for blood management at blood banks; both to set regular production quantities for perishable blood products (platelets) and how to do so in irregular periods (as holidays). The state space is too large to solve most practical problems using SDP. Nevertheless an SDP approach is still argued and shown to be most useful in combination with simulation. First the recipe for the stationary case is briefly reviewed as referred to earlier research. Here the regular production problem is periodic: demand and supply are weekday dependent but across weeks the problem is usually regarded as stationary. However, during a number of periods per year (roughly monthly) the problem is complicated by holiday periods and other events that imply non-stationary demand and production processes. This chapter particularly focuses on how to deal with the Blood Platelet (PPP) problem in non-stationary periods caused by holidays. How should production quantities anticipate holidays and how should production resume after holidays. The problem will therefore also be modelled as a finite horizon problem. To value products left in stock at the end of the horizon we propose to use the relative state values of the original periodic SDP. An optimal policy is derived by SDP. The structure of optimal policies is investigated by simulation. Next to its stationary results, as reported before, the combination of SDP and simulation so becomes of even more practical value to blood bank managers. Results show how outdating or product waste of blood platelets can be reduced from over 15% to 1% or even less, while maintaining shortage at a very low level.

Appendix: Notation

This section describes the relation of the terminology in this chapter related to the general notation in the book.

s	= (d, x) = is the state on weekday d and stock state x with elements
x r	= number of products in stock with remaining shelf life of r days
π(s)	optimal policy = number of products to order on week day d
	if stock state is x
c(s)	$\mathbb{E}C(d,\mathbf{x})$ single period (expected) cost in state s
V n (s)	value function storing (relative) expected costs of an optimal policy
	over n days