Decision criteria on the branch-and-bound method for optimal single-level lot sizing with backlogging

Branches are used to represent decisions that can be taken during a particular period. A simple branch-and-bound procedure is presented that can be applied to single-item, single-level lot-sizing with back ordering under the conditions of variant holding, ordering, and shortage costs on a period-by-period basis. At the beginning of the procedure there are no stocks, then, three possible decisions can occur in any period. Yet, with some simple decision criteria, the rule can be simplified and presented as a decision tree in an easy form. The simplified algorithm is also shown in this paper with PASCAL language written modules.