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For LTL, we have a contract with YRC logitistics. All of our product ships at class 77.5, so we only need to know the number of pallets, the weight, and cubes, and delivery zip. Here, we do a bit more estimating than exact cost. However, any order shipping LTL for us usually has enough built in profit that we don't mind losing undercharging on freight -- they typically have 5-10 high cost, high margin items to require LTL shipping. I figure, if the person is ordering so much that we really vastly under charge for freight in this manner, the order is either fraud or we'll make so much that no one will notice losing money on the freight charge. Granted, we have warehouses all over the country and ship regular freight to ourselves and regular containers being imported, which YRC handles...so we have a bit of weight to throw around to get good rates and to lock ALL shipments in at a single weight class.
Both connect directly with the API's offered. Each product in the database has a weight and dimensions. A fairly complicated algorithm determines the total volume, the maximum package dimensions for the service without going into "oversize" (divides into multiple boxes in this case,) adds a percentage for padding, and adds the box weight based on weight per square foot.
Once the number of packages, dimensions, and destination are compiled it passes these to the API of the shipper via an XML silent post. The API returns all the available choices to the user, costs, and delivery times (ex: Choose shipping; First Class $1.85, 7-10 days . . . Priority Mail, $5.95, 3-5 days . . . )
Over the last 4 years this has been very close to actual shipping, sometimes it runs a little over but very rarely do we lose on it.