I received a phone call recently from a prospective client that highlighted the ever-present choice between training and managing behavior in dogs. The caller had adopted a terrier mix from a local shelter and the dog was chewing on shoes frequently. "Can I train her to leave the shoes alone? Or should I put the shoes away?"
Well, yes and yes. You can certainly train your dog to leave the shoes alone and chew on appropriate items instead, but you may find it a lot simpler and easier to put your shoes away and make sure your dog has plenty of appropriate chew toys.
The same strategy applies to the garbage can. My kitchen garbage lives under the sink, and my bathrooms have lidded cans. An ounce of prevention is often the answer.
In solving behavior problems, management is often combined with training. What if your dogs bark and run around the living room when the doorbell rings, and then rush to the door barking as you go to answer it? To modify this behavior, the first step is to prevent the dogs from practicing this undesirable routine as much as possible. You also need to decide exactly what WANT your dogs to do when the doorbell rings. Would you like your dogs to go to their bed in a different room, or bark a few times and then sit quietly a short distance away from the door? Define a specific chain of behavior and then implement a training plan using positive reinforcement to replace the undesirable behavior with the new routine.
Management (a covered garbage can or putting shoes away) is often easy. Training the new routine will take more time and effort. Is it worth it? That is for you to decide.