Your code should work. But I think you can achieve the same by following way,
xhtml:
<h:selectOneMenu id="listExample">
<f:selectItems value="#{myBean.ddl_example_options}"/>
</h:selectOneMenu>
JSF Managed Bean:
public class MyBean implements Serializable{
List<SelectItem> ddl_example_options;
String ddl_example;
public List<SelectItem> getDdl_example_options() {
return ddl_example_options;
}
public void setDdl_example_options(List<SelectItem> ddl_example_options) {
this.ddl_example_options = ddl_example_options;
}
public String getDdl_example() {
return ddl_example;
}
public void setDdl_example(String ddl_example) {
this.ddl_example = ddl_example;
}
private void setDdl_example(){
ddl_example_options=new ArrayList<>();
ddl_example_options.add(new SelectItem("1","Option-1"));
ddl_example_options.add(new SelectItem("2","Option-2"));
}
@PostConstruct
public void init(){
setDdl_example();
}
public MyBean() {
}
}