Inventory-Responsive Donor Management Policy: A Tandem Queueing Network Model

Abstract

Problem definition: In the blood donor management problem, the blood bank incentivizes donors to donate, given blood inventory levels. We propose a model to optimize such incentivization schemes under the context of random demand, blood perishability, observation period between donations, and variability in donor arrivals and drop-outs.

Methodology/results: We propose an optimization model that simultaneously accounts for the dynamics in the blood inventory and the donor’s donation process, as a coupled queueing network. We adopt the Pipeline Queue (Bandi and Loke 2018) paradigm, which leads us to a tractable convex reformulation. The coupled setting requires new methodologies to be developed upon the existing Pipeline Queue framework. Numerical results demonstrate the advantages of the optimal policy by comparing it with the commonly adopted and studied threshold policy, and a no-incentivization benchmark. Our optimal policy can effectively reduce both shortages and wastage.

Managerial Insights: Our model is the first to operationalize a dynamic and heterogeneous donor incentivization scheme, by determining the optimal number of donors of different donation responsiveness to receive each type of incentive. It can serve as a decision-support tool that incorporates practical features of blood supply chain management not addressed thus far to the best of our knowledge. Simulations on existing policies indicate the dangers of myopic approaches and justify the need for smoother and forward-looking donor incentivization schedules that can hedge against future demand variation. Our model also has potential wider applications in supply chains with perishable inventory.

Keywords: blood collection, donor management, perishable inventory management, humanitarian operations, Pipeline-Queue