Production Timing for Decaying Medical Radioisotopes to Meet a Fixed Delivery Schedule

Over 85% of nuclear medicine procedures are conducted with Technetium-99m (Tc-99m), a decay product of Molybdenum-99 (Mo-99). Mo-99 has a half-life of 66 hours and is primarily produced in nuclear research reactors before it is processed and distributed worldwide via commercial passenger flights. Due to its continuous decay, the alignment of the supply chain’s just-in-time processes are critical. This paper studies the critical decision of production timing at a single research reactor. Once produced, Mo-99 naturally begins to decay. After several processing steps Mo-99 is then flown to its final destination. Thus, production should be be timed to minimize further decay while waiting at the airport. The objective is to maximize the viable amount of Mo-99 that departs on a flight with a possible penalty for earliness and tardiness. We analyze the objective function and show that it is a periodic function when flights depart according to a periodic schedule. The penalty for earliness/tardiness breaks the periodicity but the objective is still multi-modal in general. We present multiple search heuristics to determine production timing. The numerical results show that a greedy heuristic is near optimal, whereas a naïve approach has optimality gaps up to 34%. We also explore how different delivery schedules can allow more viable Mo-99 to reach patients.