قارن الطرق

	البرمجة الصحيحة	تحليل منطقة الخدمة
المجال	التحسين	التحليل المكاني
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1958	2001
صاحب الطريقة	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Harvey Miller & Shih-Lung Shaw
النوع	Mathematical optimisation — exact combinatorial method	Network GIS pipeline
المصدر التأسيسي	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669	Miller, H. J., & Shaw, S.-L. (2001). Geographic Information Systems for Transportation: Principles and Applications. Oxford University Press. ISBN: 978-0-19-512394-4
الأسماء البديلة	IP, MIP, mixed-integer programming, mixed-integer linear programming	Isochrone Analysis, Network Catchment Area Analysis, Travel-Time Polygon Analysis, Hizmet Alanı Analizi
ذات صلة	4	3
الملخص	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.	Service Area Analysis delineates the geographic region reachable from one or more origin facilities within a specified travel cost — typically time, distance, or generalized impedance — by traversing a real road or transit network. It is widely used by urban planners, public health officials, logistics managers, and emergency response coordinators who need to understand actual accessibility rather than simple straight-line buffers.