You probably don't have a practical legal remedy. Why haven't you changed carriers?
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If this is a serious enough problem, you may wish to take insurance out to cover the expenses you have to pay to make the merchandise good for your own customers.
Going to another carrier may be your best option, if that is really possible.
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Your remedy most likely is contractual. If you have a contract with the company, look to the terms of your contract. If you don't have a contract with the shipping company, you should seek to obtain one. As part of the contract, you can then negotiate whatever remedies you deem appropriate subject to the shipping company's approval. Note: the greater liability you seek to place on the shipping company most likely means that your cost of shipping will go up.
The information provided herein is for informational purposes only and is not intended to create an attorney-client relationship or provide legal advice.