This paper presents an optimal algorithm based on Branch and Bound approach for determining lot sizes for purchased component in Material Requirement Planning (MRP) environments with deterministic time-phased demand and constant ordering cost with zero lead time. Backlog is not permitted and the unit purchasing price depends on the quantity of an order and resale of the excess is possible at the ordering time. We assume an all-units discount system with single price break point. Based on proven properties of an optimal order policy, a tree search procedure is designed to construct the sequences of orders and resales amount in optimal order policy. Some useful fathom rules have been proven to make the algorithm very efficient. Copyright © (2008) by Computers & Industrial Engineering.