השוואת שיטות

	Branch and Bound	תכנון בשלמים
תחום	אופטימיזציה	אופטימיזציה
משפחה	Process / pipeline	Process / pipeline
שנת המקור	1960	1958
הוגה השיטה	Ailsa Land & Alison Doig	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)
סוג	Exact combinatorial optimization algorithm	Mathematical optimisation — exact combinatorial method
מקור מכונן	Land, A. H., & Doig, A. G. (1960). An automatic method of solving discrete programming problems. Econometrica, 28(3), 497–520.	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669
כינויים	B&B, Land-Doig Algorithm, Implicit Enumeration, Dal ve Sınır	IP, MIP, mixed-integer programming, mixed-integer linear programming
קשורות	3	4
תקציר	Branch and Bound is a systematic exact algorithm for combinatorial and integer optimization problems, introduced by Ailsa Land and Alison Doig in 1960. It organizes the search space as a tree of subproblems, uses relaxation-derived upper bounds to prune branches that cannot improve the best known solution, and guarantees finding a globally optimal integer solution. It is the backbone of modern mixed-integer programming solvers used in operations research, logistics, scheduling, and engineering design.	Integer programming (IP), also called mixed-integer programming (MIP) when only some variables are restricted to whole numbers, is a branch of mathematical optimisation in which some or all decision variables must take integer or binary values. Building on linear programming, it was formalised through Ralph Gomory's cutting-plane method (1958) and the Land-and-Doig branch-and-bound algorithm (1960), and it has since become the standard exact framework for scheduling, assignment, routing, and resource-allocation problems.