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

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 altruistic incentives, blood perishability, observation period between donations, and variability in donor arrivals and drop-outs. Academic/Practical relevance: While donor incentivization schemes have been proposed in the literature, their optimality and hence effectiveness in operations have yet to be studied. Our work addresses this. Our model also has potential wider applications in supply chains with perishable inventory. Methodology: 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. Results: Numerical results indicate sensitivity of the optimal incentivization policy to donor responsiveness, rate of new donors, and level of demand for blood. Our simulations also demonstrate that even at times of ample supply in the inventory, it may still be optimal to incentivize a small proportion of donors to donate. Managerial Insights: Our model is the first in the literature to operationalize donor incentivization schemes, by determining the optimal number of donors of each sub-population to receive each type of incentive.