The production and inventory management of blood products at blood banks and hospitals is a problem of general human interest. As a shortage may put lives at risk, shortages are to be kept to a minimum. As the supply is voluntary and costly, any spill of unused blood (products) is also to be minimized. Blood platelets (thrombocytes), which are the most expensive and perishable blood product, have the complication of a limited "shelf life" of only 5–7 days. A general figure in the Western world (the USA and Western Europe) for the spill of blood platelets is in the order of 15–20%. A combined new approach is therefore presented which combines stochastic dynamic programming (SDP) and simulation to provide: (i) Practical simple order-up-to rules that are nearly optimal. (ii) Formal theoretical support. The approach has been applied to a Dutch regional Blood bank. Numerical results show a significant reduction of the figures from: 1% to 1‰ for shortages; 20% to 1% for spill. A practical question for blood bank managers that still remains is: "How to anticipate irregular production breaks like at Easter and Christmas?" The present paper therefore will extend the combined SDP–Simulation approach to include such breaks. The main findings are: • Also for these breaks a simple order-up-to rule remains to be nearly optimal. • Also for these breaks the outdating and shortages can be kept less than 1%. • The (stationary) periods with production and the (non-stationary) breaks without can be integrated. The approach thus seems suitable for practical implementation.