Delivery time Acceleration 1 Advance payment 1 Advance payments 1 Costs 1 Dose delivery 1 Energy scale 1 Extraction 1 FLASH therapy 1 Fundamental physics 1 Inventory control 1 Optimal ordering policy 1 Partial backordering 1 Partial prepayment 1 Period length 1 Phase displacement 1 Probability distributions 1 Probability: distributions 1 Profit maximization 1 Profitability 1 Proton synchrotrons 1 RF phase displacement 1 Resonant slow extraction 1 Sales 1 Slow extraction 1 Stochastic control systems 1 Stochastic models 1 Stochastic period length 1 Stochastic systems 1 Stochastics 1