The most efficient way to send a negotiation to all supplier contacts for a supplier is to use a negotiation style that has the supplier control option of "All supplier contacts" enabled. This option allows you to automatically include all the contacts associated with a supplier when you add the supplier to the negotiation. You do not need to manually add each contact or rely on the supplier bidder contact to forward the negotiation. You can also create a negotiation template with this option enabled and use it to create a negotiation.
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Examples of Negotiation Controls, Section 1: "Examples of Negotiation Controls", Subsection: "Supplier Controls" Create Supplier Negotiations from Template, Section 1: "Create Supplier Negotiations from Template"