Model categories 10 — Is every monoidal model category Quillen equivalent to a simplicial monoidal model category?

Is every monoidal model category Quillen equivalent to a simplicial monoidal model category? This would remove the loose end in my book on model categories, where I am unable to show that the homotopy category of a monoidal model category is a central algebra over the homotopy category of simplicial sets. The centrality is the problem, and I can cope with this problem for simplicial monoidal model categories.