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| Markov Decision Processes with Application to Budgetary Radioactive Waste Treatment |
Kizito Paul Mubiru, Christopher Senfuka, Maureen N Ssempijja
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Abstract:
Reliable methods for budgetary planning of radioactive waste treatment are crucial to cater for waste handling from its generation to its storage, from treatment to disposal and subsequent monitoring. This can ensure financial sustainability of radioactive waste treatment programs. In this study, we present a markov decision process model that can assist radioactive waste treatment plants to optimally allocate funds for radioactive waste treatment. We formulate this decision problem as a discrete-time, discrete-state markov decision process where states of a markov chain represent possible states of radioactivity under a finite period planning horizon. The waste treatment cost represents the long run measure of performance for the markov decision process problem. We consider generated waste at two waste treatment plants in Uganda; and using monthly equal intervals, the decisions of whether or not to allocate additional funds for radioactive waste treatment are made using dynamic programming over a finite period planning horizon. We test the developed model to determine the optimal decision for allocating additional funds and the corresponding radioactive waste treatment costs. The study considers stationary radioactivity transition probabilities for easier computational purposes. We follow this theoretical part of the study to demonstrate the applicability of our model; where stochastic states of radioactivity are put into consideration. A numerical example presented shows how the decision to allocate or not to allocate additional funds are impacted by the stochastic levels of radioactivity. Results indicate the existence of an optimal state-dependent decision for allocating additional funds and the corresponding costs for the radioactive waste treatment plants considered in this study.
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