Replace Switch/Case with Pattern

I have code very similar to this example three times in a code behind. Each time the switch is toggling off of an option that is sent to it. Each time the code inside the case is exactly the same except for a parameter based off of the case. Is using a switch/case and methods the best way to do this? Should I think of using sometype of design pattern to avoid the repeative switch/case structure?

string option = dropDownList.SelectedValue.ToString();
switch (option.ToUpper())
{
    case "ALPHA":
        // do repeative code method here; only change is a parameter
        break;
    case "BRAVO":
        // do repeative code method here; only change is a parameter
        break;
    case "CHARLIE":
        // do repeative code method here; only change is a parameter
        break;
    case "DELTA":
        // do repeative code method here; only change is a parameter
        break;
    default:
        break;
}