Demand allocation with latency cost functions

We address the exact resolution of a Mixed Integer Non Linear Programming model where resources can be activated in order to satisfy a demand (a covering constraint) while minimizing total cost. For each resource, there is a fixed activation cost and a variable cost, expressed by means of latency fu...

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Bibliographic Details
Published in:Mathematical programming Vol. 132; no. 1-2; pp. 277 - 294
Main Authors: Agnetis, Alessandro, Grande, Enrico, Pacifici, Andrea
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.04.2012
Springer
Springer Nature B.V
Subjects:
Activation
Algorithms
Analysis
Applied sciences
Branch & bound algorithms
Calculus of variations and optimal control
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Cost function
Costs
Demand
Exact sciences and technology
Flows in networks. Combinatorial problems
Full Length Paper
Integer programming
Linear programming
Marketing
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Nonlinear programming
Numerical Analysis
Operational research and scientific management
Operational research. Management science
Sciences and techniques of general use
Source code
Studies
Theoretical
65K05
Resource allocation
90C27
90C30
Branch and bound
90C57
90C25
90C11
65K10
M.I.N.L.P
Convex functions
49M37
Latency functions
Tree(graph)
Constraint
Fixed cost
Variable cost
Iterative method
Non linear programming
Combinatorial optimization
Convex programming
Relaxation
Allocation
Variational calculus
Cost function
Convex function
Mathematical programming
Symmetry
Branching
Enumeration
Branch and bound method
Linear programming
Mixed integer programming
Enumeration(counting)
Latency
Non linear model
Implicit enumeration method
NP hard problem
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Description
Summary:We address the exact resolution of a Mixed Integer Non Linear Programming model where resources can be activated in order to satisfy a demand (a covering constraint) while minimizing total cost. For each resource, there is a fixed activation cost and a variable cost, expressed by means of latency functions. We prove that this problem is -hard even for linear latency functions. A branch and bound algorithm is devised, having two important features. First, a dual bound (equal to that obtained by continuous relaxation) can be computed very efficiently at each node of the enumeration tree. Second, to break symmetries resulting in improved efficiency, the branching scheme is n -ary (instead of binary). These features lead to a successful comparison against two popular commercial and open-source solvers, CPLEX and Bonmin.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-010-0398-y